68 GS13 Abstracts

IP1 IP4 Approximation of Transport Processes Using Junior Scientist Award Lecture: Interpreting Geo- Eulerian-Lagrangian Techniques logical Observations Through the Analysis of Non- linear Waves Transport processes are common in geoscience applications, and ﬁnd their way into models of, e.g., the atmo- Geological and environmental systems are rich in examples sphere, oceans, shallow water, subsurface, seismic inver- of self-organization and pattern formation. These patterns sion, and deep earth. Our objective is to simulate transport contain information about processes as diverse as seawa- processes over very long time periods, as needed in, e.g., ter intrusion into coastal aquifers, the long-term safety of the simulation of geologic carbon sequestration. A good geological CO2 storage, and the formation of the oceanic numerical method would be locally mass conservative, pro- crust. I will discuss how important observations in these duce no or minimal over/under-shoots, produce minimal three areas can be explained by non-linear waves. This numerical diﬀusion, and require no CFL time-step limit for illustrates the potential of the mathematical analysis of stability. The latter would allow better use of parallel com- non-linear waves to contribute to our understanding of fun- puters, since time-stepping is essentially a serial process. damental geological phenomena and applied environmental Moreover, it would be good for the methods to be of high problems. order accuracy. Our approach is to develop locally conservative Eulerian-Lagrangian (or semi-Lagrangian) methods Marc A. Hesse combined with ideas from Eulerian WENO schemes, since University of Texas they have the potential to attain the desired properties. Department of Geological Sciences [email protected] Todd Arbogast Dept of Math; C1200 University of Texas, Austin IP5 [email protected] An Unstructured Grid Model Suitable for Flooding Studies with Applications to Mega-tsunamis

IP2 Mega-thrust earthquakes and tsunamis cause untold de- The Spatiotemporal Dynamics of Waterborne Dis- struction. In this talk a new finite volume unstructured eases grid tsunami model is presented. The model is a finite volume analogue of the P1nc-P1 finite element, in which Dynamics of waterborne diseases in space and time is stud- mass conservation is guaranteed not only in a global sense, ied via multi-layer network models, consisting of coupled but within each cell. The model conserves momentum, and ODEs. They account for the interplay between epidemio- accurately handles flooding and drying problems. Results logical dynamics, hydrological transport and long-distance from the Indian Ocean and Japanese Tsunami compare dissemination of pathogens due to human mobility, de- well with flooding and run-up data. scribed by gravity models. Conditions for the outbreak of an epidemic are given in terms of the dominant eigen- Julie Pietrzak value of an appropriate reproduction matrix, while the ini- Faculty of Civil Engineering and Geosciences tial disease distribution is linked to the dominant eigen- Delft University of Technology vector. The theory is tested against epidemiological data [email protected] of the extensive cholera outbreaks occurred in KwaZulu- Natal (South Africa) during 2000-2001 and in Haiti during Haiyang Cui, Guus Stelling 2010-2012. Delft University of Technology [email protected], [email protected] Marino Gatto Politecnico di Milano [email protected] IP6 Data Assimilation in Global Mantle Flow Mod- els:Theory, Modelling and Uncertainties to Recon- IP3 struct Earth Structure Back in Time Career Award Lecture: Some Successes and Chal- lenges in Coastal Ocean Modeling The ability to extract the history of motion associated with large-scale geologic structures that are now imaged seismi- The coastal ocean is rich with physical and biological pro- cally in the Earth’s interior, such as plumes and subducting cesses, often occurring at vastly different scales. In this slabs, is crucial to constrain the fundamental deformation talk, we will outline some of these processes and their math- processes of mantle convection. Here we show how fluid ematical description. We will then discuss the current state dynamic inverse theory, based on a variational approach, of numerical methods for coastal ocean modeling and re- can be applied in a global circulation model of the mantle cent research into improvements to these models, focusing to project Earth structure back in time. We present the on accuracy and efficiency for high performance comput- basic theory of the forward and inverse problem, review ing. We will also highlight some of the successes of these geologic constraints, provide computational considerations models in simulating complex events, such as hurricane relevant to the global flow problem with about 1 billion storm surges. Finally, we will outline several interesting finite elements, and discuss uncertainties. The latter re- challenges which are ripe for future research. strict the problem in practice, as our knowledge of deep Earth structure and its interpretation in terms of dynam- Clint Dawson ically relevant buoyancy anomalies is necessarily limited. Institute for Computational Engineering and Sciences University of Texas at Austin [email protected] Hans-Peter Bunge Department of Earth and Environmental Sciences, LMU GS13 Abstracts 69

Munich DMMMSA [email protected] University of Padova [email protected]

IP7 Carlo Janna, Massimiliano Ferronato Data Assimilation and Inverse Modeling in Earth Dept. ICEA - University of Padova System Sciences [email protected], [email protected] Physical theories in the Earth System sciences are designed to explain and possibly predict natural phenomena. Both, CP1 the explanation and prediction necessarily include a quan- Coupled Geomechanics and Flow for Unstructured titative representation of the natural system state. Quan- Naturally Fractured Reservoir Models titative assessment of the actual, true, state is fundamen- tally achievable only by measurements. The theories and We consider unstructured reservoir models composed of models based on them are consequently designed to ex- a deformable saturated matrix and a network of natural plain and predict the measurements. A synergy of the fractures. A finite-volume method is used for the flow. models and measurements is necessary for achieving such Galerkin finite elements are used to discretize the poro- goal. Methodology of data assimilation and inverse model- elasto-plasticity equations. We account for normal and ing provides objective means for that purpose. An overview shear stresses on the fracture surfaces. The correspond- of the currently used methodology will be presented, in- ing nonlinear coupled equations are solved using either cluding examples of application in atmospheric sciences in the sequential-implicit fixed-stress approach, or the fully- domain of cloud analysis and modeling and tropical cyclone implicit method. The framework is demonstrated using modeling and prediction. several test cases with discrete fracture models. Tomislava Vukicevic Timur T. Garipov NOAA Department of Energy Resources Engineering, AOML Hurricane Research Division, Miami Stanford University [email protected] [email protected]

IP8 Hamdi Tchelepi Stanford University Efficient Numerical Numerical Computation of Energy Resources Engineering Department Multi-Phase Flow in Porous Media [email protected] Appropriate models, accurate discretization schemes and efficient solvers for the arising linear systems are the ba- CP1 sis for any numerical simulation. In this talk I will address these aspects by first considering a model for compositional Mechanics of Fluid Injection into Deformable two-phase flow with equilibrium phase exchange that is Porous Materials able to handle phase appearance/disapperance properly. Poroelasticity, where the mechanical deformation of a Then a new fully-coupled discontinuous Galerkin scheme porous solid is coupled to internal fluid flow, has been for two-phase flow with heterogeneous capillary pressure studied intensely in geophysics in the context of pressure will be presented. The third part of the talk is devoted to buildup during fluid injection, such as in carbon seques- the efficient solution of the arising linear systems by means tration or enhanced oil recovery. Here, we develop a novel of algebraic multigrid methods. All numerical schemes experimental system that allows us to visualize and quan- have been implemented in the Distributed and Unified Nu- tify the dynamic, flow-driven deformation of a quasi-two- merics Environment and have been scaled up to 300000 dimensional poroelastic material. We use it to study the cores. This is joint work with Olaf Ippisch and Rebecca coupling between fluid injection and mechanical deforma- Neumann. tion patterns. Peter Bastian Christopher W. MacMinn Interdisciplinary Center for Scientific Computing MIT University of Heidelberg Mechanical Engineering [email protected] [email protected]

CP1 Eric Dufresne A Mixed and Galerkin Finite Element Formulation Yale University for Coupled Poroelasticity New Haven, CT, USA [email protected] The numerical treatment of coupled poroelasticity is a demanding task because of the instabilities affecting the pore John S. Wettlaufer pressure solution. A combination of Mixed and Galerkin Yale University Finite Element methods is employed to obtain stable nu- [email protected] merical solutions at the interface between different materials. A comparison of the performance of monolithic and sequential schemes in solving the algebraic systems aris- CP1 ing from the balance equations is presented. Some results A Finite Volume Method for the Solution of Fluid relative to real field large scale simulations are finally dis- Flows Coupled with the Geomechanics of Compact- cussed. ing Porous Media Nicola Castelletto A numerical approach in which a coupled geomechani- 70 GS13 Abstracts

cal/fluid flow problem in porous media is solved in a single for Data Assimilation in the Mediterranean Sea grid using a Finite Volume Method is advanced. The possibility of using a unique grid and the same conservative OceanVar is a data assimilation (DA) software which is method for both problems renders to the scheme robustness being used in Italy within the Mediterranean Forecasting and generality. Details of the coupling strategy are also ad- System (MFS) to combine observational data (SLA, SST, dressed. The novel developments offer an interesting route Argo-floats profiles) with backgrounds produced by com- for solving coupled problems in a unified approach using putational models of ocean currents of the Mediterranean full conservative schemes. Sea (namely, the NEMO framework). OceanVAR implements a three-dimensional variational scheme. We discuss Clovis R. Maliska the design of a fully parallel version of OceanVar, based Mechanical Engineering Department on domain decomposition approach, which is able to face Federql University of Santa Catarina to the ever greater multi-level parallelism and scalability maliska@sinmec.,ufsc.br of the current and the next generation of leadership computing facility systems (multi processors, many core and Alessandro Dal Pizzol GPUs), while fulfilling the specific requirements of Ocean- Federal University of Santa Catarina Var within the MFS. Mechanical Engineering Department [email protected] Luisa D’ Amore University of Naples Federico II Naples, ITALY Mathematics and Applications CP1 [email protected] Solution Strategies for Coupled Geomechanical and Flow Problems Recent Experiences Rossella Arcucci Euro-Mediterranean Center on Climate Change Many geoscience problems involve coupled THM (thermal- CMCC- Lecce, Italy hydrodynamic-mechanical) processes. The strength of cou- [email protected] pling has varying degrees, ranging from problems that can be solved sequentially to those requiring full nonlinear cou- Luisa Carracciuolo pling. The selection of the method and the degree of cou- Italian National Research Council (CNR) pling are highly problem-dependent. The best strategy for ITALY THM processes depends critically on the physics of the [email protected] problem. We will give a survey of the methods (used in coupled reservoir geomechanics) and discuss examples of Livia Marcellino our experience with their stability and implementation. University of Naples, Parthenope A . (Tony) Settari ITALY [email protected] University of Calgary [email protected] Almerico Murli Euro-Mediterranean Center on Climate Change CP1 ITALY A Fully Coupled Multiphase Flow and Geomechan- [email protected] ics Solver for Highly Heterogeneous Porous Media This paper introduces a fully coupled multiphase flow and CP2 geomechanics solver that can be applied to modeling highly Scalable Reservoir Simulation on Massively Paral- heterogeneous porous media. In this work, we developed lel Computers a coupled multiphase flow and geomechanics solver that solves fully coupled governing equations, namely pressure, We investigate parallel performance for reservoir simula- velocity, saturation, and displacement equations. The tion on multiple massively parallel computing architec- solver can deal with full tensor permeability and elastic tures. A deliberate strategy of performance-based devel- moduli for modeling a highly heterogeneous reservoir sys- opment of the major types of computations encountered in tem. reservoir simulation programs is employed. Even though most operations are memory-bandwidth bound, it is pos- Daegil Yang sible with careful implementation, to get excellent parallel Texas A&M University efficiency to several 1000s of cores. We discuss numerical [email protected] issues, scalability and parallel efficiency of reservoir simulator on several very large and geologically challenging George Moridis examples. Lawrence Berkeley National Laboratory Serguei Y. Maliassov [email protected] ExxonMobil URC [email protected] Thomas Blasingame Texas A&M University Bret Beckner [email protected] ExxonMobil Upstream Research Company [email protected] CP2 A Domain Decomposition-Based Parallel Software Vadim Dyadechko ExxonMobil URC [email protected] GS13 Abstracts 71

CP2 the parameter information (material properties, topogra- Scalable Multi-Level Preconditioning Techniques phy or bathymetry data, etc.) required for adaptive refine- for Variable Viscosity Stokes Flow Problems Aris- ment and coarsening. ing from Geodynamic Applications Sebastian Rettenberger Over long million year time scales, many geological pro- Technische Universitaet Muenchen cesses can be described as incompressible, variable viscos- Department of Informatics, Chair of Scientific Computing ity Stokes flow. Such descriptions of rock deformation are [email protected] challenging to handle as the viscosity structure is inherently heterogeneous and may possess both continuous and Alexander Breuer discontinuous local variations on the order of 109.Herewe Technische Universität München explore the performance of a parallel matrix-free geomet- Department of Informatics, Scientific Computing ric multi-grid preconditioner combined with several exotic [email protected] coarse grid solvers to study high resolution 3D geodynamic processes. Oliver Meister Technische Universität München Dave May [email protected] ETH Zurich [email protected] Michael Bader Technische Universitaet Muenchen CP2 Department of Informatics Sam(oa)2, a Parallel Cache-Efficient Simulation En- [email protected] vironment

We present an integrated approach for parallel adaptive CP3 grid refinement and respective solution of PDEs. Using Some Strategies of Linear and Nonlinear Precondi- a stack-and-stream system and an element order defined tioning for Reactive Transport Model by the Sierpinski space filling-curve to store and process the grid and simulation data, we obtain an inherently We investigate block preconditioning for accelerating a memory- and cache-efficient simulation algorithm. The lo- Newton-Krylov method applied to a reactive transport cality properties introduced by the Sierpinski curve are re- model. Work by Kern and Taakili (2011) for a single tained even throughout adaptive refinement and coarsen- species with sorption is extended to the multi-species case, ing of the grid, and are exploited for efficient parallelisa- with complex chemistry. The block structure of the model tion and load balancing. We will focus on parallelisation is exploited both at the nonlinear level, by eliminating one and discuss a run-length encoding to deal with the data unknown, and at the linear level by using block Gauss- exchange on the shared inter-process edges. These data Seidel preconditioning. A link is made between physics include the numerical unknowns, refinement flags on the based preconditioning and the algebraic methods. edges, and load balancing information. We present two Laila Amir test case scenarios: A Discontinuous Galerkin solver for Faculty of Science and Techniques the Shallow Water Equations and a coupled problem for Cadi Ayyad University, porous media flow using FEM for the pressure equation [email protected] and finite volumes for the advection term.

Kaveh Rahnema Michel Kern University of Stuttgart INRIA Institute of Parallel and Distributed Systems [email protected] [email protected] Abdelaziz taakilli Oliver Meister Faculty of Science and Techniques, Technische Universit Errachidia, Morocco Department of Informatics, Scientific Computing taakili [email protected] [email protected] CP3 Michael Bader Technische Universitaet Muenchen High Performance Computing Using Local Time- Department of Informatics Stepping Methods for Elastodynamics [email protected] The simulation of seismic wave propagation in heterogeneous media requires local mesh refinements that prevent CP2 the use of finite difference schemes widely used in the oil industry. In this talk, we will present a mesh refinement A Parallel Server for Adaptive Geoinformation strategy combining local time stepping and a discontinu- In this talk we present ASAGI, a library that provides ous Galerkin discretization using quad elements enabling a simple and efficient interface to large input data sets the use of embedded Cartesian grids. We will also discuss with multiple resolutions in a high performance comput- how this regular structure can be exploited in a parallel ing context. The key feature of ASAGI is to decouple the implementation to tackle large 3D examples. data management from the actual simulation by introduc- Yohann Dudouit ing caching strategies on node level. Thus, for dynami- HiePACS Project cally adaptive simulations with parallel partitions that may joint INRIA-CERFACS lab. on High Performance change their spatial position and extent, ASAGI provides 72 GS13 Abstracts

Computing [email protected], [email protected], [email protected] [email protected]

Jean-Luc Boelle TOTAL CP3 [email protected] Unconditionally Stable Transport Solvers for Two Phases Flow with Polymer.

Luc Giraud We present a nonlinear Gauss-Seidel algorithm for solving Inria Bordeaux Sud-Ouest implicitly discretized saturation equations. NGS relies on Joint Inria-CERFACS lab on HPC the well-posedness of single-cell problems (residual equa- [email protected] tion for one cell with all other saturations known). Uncon- ditional stability of the single-cell problem guarantees that Florence Millot a global solution exists for any time step. We give nec- CERFACS essary and sufficient conditions on discretized flux for un- [email protected] conditional stability of the single-cell problem and present such flux discretizations for two-phase flow with polymer Sébastien Pernet and gravitation splitting. ONERA [email protected] Xavier Raynaud Sintef [email protected] CP3 Geosounding Inversion with Bregman Iterative Knut-Andreas Lie Methods SINTEF ICT, Dept. Applied Mathematics [email protected] In this contribution, several novel algorithms for nonlinear inversion of electrical, electromagnetic and resistivity Halvor Nilsen, Atgeirr Rasmussen soundings based on Bregman iterations are presented. Re- SINTEF ICT sults are reported of algorithm implementation for several [email protected], [email protected] geosounding methods applying Bregman distance to minimize the TV functional. Implemented algorithms consist of a Taylor linearization for the forward functional, Bregman CP3 distance applied to the regularization functional and stop Precisely, How Fast Is Your Fully Implicit Newton- criteria. The resulting algorithms are easy to implement Like Solver? and do not require any optimization package. Positivity constrained version of the algorithms are also presented This work characterizes the convergence rate of Newton- by applying projected Barzilai-Borwein method with box- like methods that are applied to solve nonlinear residual constrains. A comparison of developed models for Breg- systems arising in implicit numerical simulations. The man based algorithms with those obtained with a linear analysis exploits the Asymptotic Mesh Independence Prin- programming package is also presented for synthetic and ciplerelatingtheconvergencerateofdiscreteNewton field data. methods to their infinite-dimensional counterparts. By characterizing the precise evolution of the nonzero spa- Hugo Hidalgo tiotemporal support of the infinite-dimensional iterations, CICESE-Ciencias de la Computacion the analysis reveals the asymptotic scaling relations be- [email protected] tween nonlinear convergence rate and time-step and mesh sizes. Enrique Gomez-Treviño CICESE Rami M. Younis Geofisica Aplicada Postdoctoral Research Fellow [email protected] Stanford University [email protected]

CP3 Algebraic Multigrid Preconditioner for Numeri- CP4 cal Finite-Element Solutions of Electromagnetic In- A Computational Method for Simulating Immis- duction Problems cible Incompressible Three Phase Flow Model in Heterogeneous Porous Media We present a parallel nodal finite-element solver for the three-dimensional electromagnetic modelling in anisotropic We describe a computational method for simulating three- media. The method can be used for modelling different phase immiscible incompressible flow problem in inhomo- controlled-source and magnetotelluric problems. To im- geneous media taking the form of a nonlinear transport sys- prove efficiency of the method, we have developed an alge- tem with spatially varying flux functions under combined braic multigrid preconditioner for Krylov subspace solvers. convective, capillary and gravity effects. Our new method Tests for various problems show that, compared to other is an operator splitting procedure for decoupling the non- preconditioners, our preconditioner improves the conver- linear three-phase flow system with mixed and conserva- gence of different solvers and reduces the execution time tive discretization methods leading to purely hyperbolic, by up to an order of magnitude. parabolic and elliptic subproblems. Preliminary numerical experiments will be also presented and discussed. Jelena Koldan, Vladimir Puzyrev, Jose Maria Cela Barcelona Supercomputing Center Eduardo Abreu GS13 Abstracts 73

Instituto Nacional de Matematica Pura e Aplicada - CP4 IMPA Using Coupled Implicit and P-Adaptive Discontin- [email protected] uous Galerkin Method to Model Miscible Displace- ment with Adverse Mobility Ratio CP4 Many EOR or stimulation processes require an accurate Co2 Storage Simulations Using Low Complex estimation of the distribution of the injected fluid. Tra- Model Geometries ditional reservoir simulators based on low order finite volume method suffers grid orientation effects when modeling Complex 3D models are a potential way to precisely de- miscible displacement with adverse mobility ratio. In this scribe the heteroeneous flow paths in a reservoir, but the talk, we propose a fully coupled and implicit discontinuous uncertainties of material parameters are quite large. Due Galerkin (DG) formulation which can accurately compute to long simulation times, 3D approaches only allow a small the flux direction and effectively remove the grid orienta- number of realizations. Thus, we perform Monte-Carlo tion effects. P-adaptive DG scheme will also be proposed simulations using simplified model grids of lower complex- so that high order DG is used only at locations where high ity to describe the fate of CO2 at the Ketzin test site lo- gradients of concentration are present. Numerical results cated in Germany. showthatthetimespentforp-adaptiveschemeiscompa- rable to the low order methods. Norbert Böttcher TU Dresden Hao Huang, Huafei Sun, Aruna Mohan, Jichao Yin [email protected] ExxonMobil Upstream Research Company [email protected], [email protected], Wenqing Wang [email protected], Department of Environmental Informatics [email protected] Helmholtz Centre for Environmental Research [email protected] Guglielmo Scovazzi Duke University Björn Zehner, Uwe-Jens Görke [email protected] Helmholtz-Centre for Environmental Research - UFZ [email protected], [email protected] CP4 Olaf Kolditz Co2 Vertical Migration Through a Piecewise Ho- Helmholtz Centre for Environmental Research mogeneous Porous Medium [email protected] We consider the migration of a CO2 plume through a vertical column filled with a piecewise homogeneous porous CP4 medium. The impact of capillary pressure and flux con- A Conservative Numerical Methodology for Multi- tinuities at the interface on the CO2 migration is studied phase Flow in Heterogenous Porous Media Allow- numerically and mathematically. We analyze how satura- ing Changes in Porosity tions and saturation gradients on either side of the interface evolve with time and if a local steady state is reached. In this work we present a conservative numerical methodol- Different cases are considered : capillary dominant, grav- ogy for simulating multiphase-flow in highly heterogenous ity dominant and intermediate case. The influence of this porous media, which allows changes of the porosity field micro-scale dynamics on upscaled migration is discussed. in time and space. This methodology combines stabilized mixed-hybrid finite elements for the flow subsystem (ve- Emmanuel Mouche locity and pressure) with a semi-discrete central scheme CEA, DRN for the transport problem, based on a generalization of the France Kurganov and Tadmor (KT) scheme. This methodology [email protected] is proposed to be used as a block for coupling multiphase flows with geomechanics. Tri Dat Ngo CEA, DSM-LSCE Maicon R. Correa [email protected] National Laboratory of Scientific Computing LNCC, Brazil Pascal audigane [email protected] BRGM, D3E-SVP [email protected] Marcio Borges National Laboratory of Scientific Computation LNCC/MCT CP4 Petropolis Reservoir Modelling Based on Transmissibility Up- [email protected] scaling

Jesus Obregon Prediction of reservoir performances requires coarse models National Laboratory of Scientific Computing coherent with fine scale geology. In Eni methodology effec- LNCC/MCT tive coarse transmissibility (T*) is used in place of perme- [email protected] ability. This is motivated by the results achieved whenever T* has been implemented on field models where geological and simulation grids are aligned. The issue is to deal with geometries where coarse and fine grids are misaligned. In this work real field applications will show T* benefit on 74 GS13 Abstracts

aligned 3D grids, while the effectiveness on misaligned is closure relations. We use a stiff temporal integrator to proved on 2D synthetic cases. create 1D simulations of the model. We will discuss both results and numerical difficulties. Paola Panfili Eni E&P Deena Hannoun paola.panfi[email protected] North Carolina State University [email protected] Alberto Cominelli ENI E&P [email protected] CP5 Structure of Reaction Fronts in Porous Media Luca Turconi, Anna Scotti Multicomponent reactive flow and transport in permeable Politecnico di Milano media gives rise to reaction fronts with complex morphol- [email protected], [email protected] ogy. The first-order structure of these patterns can be analyzed in the hyperbolic limit of the governing equa- CP5 tions. Comparisons between analytic solutions, numerical simulations and field as well as experimental data for ion- On the Impact of Anisotropic Mesh Adaptation on exchange reactions shows good agreement. New theoretical Solute Transport Modeling in Porous Media results for reactive transport with pH-dependent surface We propose an anisotropic mesh adaptation technique for complexation reactions show a more complex morphology modeling solute transport in porous media. The method of the reaction front and provide the first semi-analytic relies on a recovery-based error estimator and is coupled benchmarks for numerical simulations of this phenomenon. with a finite element code solving the Advection Disper- Marc A. Hesse sion Equation. The proposed methodology is assessed University of Texas against experimental breakthrough curves collected in ho- Department of Geological Sciences mogeneous and heterogeneous media. We compare results [email protected] obtained by adapting the mesh according to various indicators. We analyze the impact of mesh adaptation on optimal parameter estimation for the experiments considered. CP5 Bahman Esfandiar Jahromi A Comparison of Closures for Stochastic Transport PhD student at D.I.I.A.R. Perturbation-based moment equations for randomly ad- Hydraulic section, Politecnico di Milano vected solute produce unrealistic multimodality, contrary [email protected] to macrodispersion theory despite strong similarities between the two. A study of basic macrodispersion ap- Alberto Guadagnini proximations reveals higher-order terms that are effectively Los Almos National Laboratory added to conventional moment-equation approximations at [email protected] second and fourth order. We propose a closed-form approximation to two-point (auto)covariance in a manner con- Giovanni Porta sistent with macrodispersion theory and illustrate its im- D.I.I.A.R., Sezione Idraulica provement upon moment-equation approximations for an Politecnico di Milano example of transport in stratified random media. [email protected] Kenneth D. Jarman, Alexandre M. Tartakovsky Simona Perotto Pacific Northwest National Laboratory MOX - Modeling and Scientific Computing [email protected], [email protected] Dipartimento di Matematica [email protected] CP5 Large - Time Behavior of the Solution for Nonlin- CP5 ear Random Boussinesq - Glover Equation Driven Simulating Non-Dilute Transport in Porous Media by Colored Noise Using a Tcat-Based Model We study the nonlinear random Boussinesq Glover equa- Predicting the transport of non-dilute species in fluids of tion in Banach spaces, driven by a colored noise and with variable density in porous media is a challenging problem random initial condition. The noise process is defined as for which existing models are unable to represent accu- stationary solution of a stochastic differential equation in rately the experimental data collected to date. We consider finite dimensional (or Hilbert) spaces. Under suitable as- the displacement of an aqueous phase with dense brine so- sumptions, we prove the existence of stationary solution lutions. Displacement experiments were conducted in ver- and the path wise global attractor. The attractor is P a. tically oriented 1D columns. Simulation of a non-dilute s. independent of probabilitary variable. Similar results system based upon the thermodynamically constrained av- arise in nonlinear random reaction diffusion equations. eraging theory (TCAT) using an entity-based momentum Fejzi Kolaneci equation was compared to data. The model accounts for University of New York, Tirana the effects of non-dilute, non-ideal systems and consists [email protected] of a nonlinear set of equations including a flow equation, a species transport equation, and closure relations. We rewrite the entity-based model as a system of two cou- CP5 pled partial differential-algebraic equations with relevant Multilevel Monte Carlo (MLMC) for Two Phase GS13 Abstracts 75

Flow and Transport in Random Heterogeneous CP6 Porous Media A Multi-Scale Method to Include Analytical Solu- tions for Multi-Phase Leakage Through Faults in a Monte Carlo (MC) is an established method for quantifying Numerical Model uncertainty arising in subsurface flow problems. Extend- ing MC by means of multigrid techniques yields the MLMC A computationally efficient approach to multi-phase flow method. In this study, MLMC is applied to assess uncer- modeling of geologic basins containing faults is developed tain two phase flow and transport in random heterogeneous based on embedding analytical solutions within coarse- porous media. It was found that the computational costs scale numerical models. The analytical solutions are used of MLMC are substantially lower compared to MC. to determine the fluxes in and around the fault and the pressure corrections that relate pressure at a given fault to Florian Müller the coarse-scale pressure in the numerical grid blocks. This Institute of Fluid Dynamics method accounts for both vertical and lateral flow within ETH Zürich the fault. fl[email protected] Mary Kang Patrick Jenny Princeton University Institute of Fluid Dynamics [email protected] ETH Zurich [email protected] Jan M. Nordbotten Department of Mathematics Daniel W. Meyer University of Bergen Institute of Fluid Dynamics [email protected] [email protected] Florian Doster Dep. of CEE, Princeton University CP6 Dep. of Mathmatics, University of Bergen From Nonlinear Adsorption at Microscale to Non- [email protected] linear Diffusion at Macroscale. We have considered the coupled convection-diffusion equa- Karl Bandilla tions for the bulk and surface concentrations at the mi- Princeton University croscale of a periodic porous medium. The coupling is [email protected] through a reaction term expressing nonlinear adsorption phenomena at the solid-fluid interface. Two-scale asymp- Michael A. Celia totic expansion with drift helps to pass from microscale to Princeton University macroscale description. Upscaled equation is a nonlinear Dept of Civil Engineering diffusion equation. Numerical simulations are done to ap- [email protected] proximate the solution for the microscale problem using correctors. CP6 Harsha Hutridurga Ramaiah, Gregoire Allaire A Multiscale Finite Element Method for Transport Ecole Polytechnique Modeling [email protected], [email protected] Simulating flows in porous media often requires the resolution of convection-diffusion problems where diffusion coefficient and velocity exhibit strong variations at a much CP6 smaller scale than the domain of resolution. This work pro- A Multi-Scale Numerical Simulation of Carbonate poses a new multiscale finite element method to first solve Rocks Properties Using 3D Micro-Tomography Im- this kind of problems on coarse grids and then reconstruct ages the variations of the solution on a finer grid. An a priori error estimate is established and numerical results are We have estimated the porosity, the permeability and the presented. elastic moduli of fifteen samples from a carbonate reservoir using numerical simulations on 3D micro-tomography im- Franck Ouaki, Guillaume Enchéry ages. Core plugs were scanned at a coarse scale and a few IFP Energies nouvelles millimeters subsets were extracted and digitalized at a finer [email protected], [email protected] scale to take into account rock heterogeneity. The comparison between simulated and experimental laboratory prop- Sylvain Desroziers erties showed a relative good agreement. Advantages and IFP Energies Nouvelles limitations of the proposed methodology will be discussed. [email protected]

Gr´egoire Allaire Mohamed S. Jouini CMAP, Ecole Polytechnique The Petroleum Institute of Abu [email protected] [email protected]

Sandra Vega CP6 The Petroleum Institute of Abu Dhabi A Multi-Scale Approach to Assessing the Hydro- [email protected] 76 GS13 Abstracts

logical Connectivity of Road and Stream Networks Modelling of Flow and Transport Problems

We study a forested, upland landscape in northeastern An introductory overview of level set methods and their USA to understand the downstream effects of roads on applicability to solve flow and transport problems with in- streams. Previously, only simple metrics have character- terfaces will be given. Finite volume discretization of all ized road-stream connectivity; few studies have examined involved partial differential equations will be described that scale or quantified effects on channel morphology. Using is very natural for modelling the flow and transport pro- newly-derived proximity and orientation metrics, statisti- cesses in porous media. Some particular examples will be cal analyses show proximity to be successful at distinguish- presented that shall illustrate a potential of level set meth- ing among categories of stream geomorphic condition at ods in general. P. F.: Application of level set method for the reach scale. These proximity metrics are even more groundwater flow with moving boundary. Adv. Wat. Res., revealing when reanalyzed at the tributary scale. 47:56–66, 2012. Alison Pechenick Peter Frolkovic College of Engineering & Mathematical Sciences Department of Mathematics University of Vermont Slovak University of Technology [email protected] [email protected]

Donna Rizzo School of Engineering CP7 University of Vermont A Locally Conservative Eulerian-Lagrangian Finite [email protected] Volume Weno Scheme for Hyperbolic Conservation The object of this talk is to define a locally conserva- Leslie Morrisey tive Eulerian-Lagrangian finite volume scheme with the Rubenstein School of Environment & Natural Resources weighted essentially non-oscillatory property (EL-WENO) University of Vermont for hyperbolic conservation law. This locally conservative [email protected] method has the advantages of both WENO and Eulerian- Lagrangian schemes. It is formally high-order accurate in Kerrie Garvey space (we present the fifth order version) and essentially The Rubenstein School of Environment & Natural non-oscillatory. Moreover, it is free of a CFL time step re- Resources striction for linear advection equations, with a relaxed CFL University of Vermont time step restriction for nonlinear hyperbolic equations and [email protected] has small time truncation error. A subcell WENO reconstruction procedure is defined, and this procedure makes Kristen Underwood it possible for this Eulerian-Lagrangian schemes. Flux cor- School of Engineering rections are carried out over the approximated characteris- University of Vermont tic lines using the Runge-Kutta method with natural con- [email protected] tinuous extension scheme. Numerical results are provided to illustrate the performance of the scheme. Beverley Wemple Department of Geography Chieh-Sen Huang University of Vermont ational Sun Yat-sen University [email protected] Kaohsiung, Taiwan [email protected]

CP6 Todd Arbogast Adaptative Multi-Scale Parameterization in Frac- Dept of Math; C1200 tured Porous Media University of Texas, Austin [email protected] Flow in fractured porous media is very complex. An inverse model using a double porosity approach is developed solving the direct problem with a Quasi-Newton algorithm CP7 coupled with the adjoint-state method to calculate the ob- A Locking-Free Lowest-Order Discretization of jective function gradient (OFG). The inverse problem is Biot’s Consolidation Model on General Meshes solved on a reduced number of parameters using an Adap- tative Multi-scale Parameterization with successive mesh We present an original Euler-Gradient Scheme discretiza- refinement depending on the OFG value. The model is vali- tion (i.e. implicit Euler in time and Gradient Scheme in dated on the Hydrogeological Experimental Site of Poitiers. space) of Biot’s consolidation model on general meshes. Gradient Schemes are a generic framework which encom- passes a large class of nonconforming methods such as the Nicolas Trottier Hybrid Finite Volumes. Under sufficient conditions on the Commissariat à l’Energie Atomique space discretization, and under minimal regularity assump- Laboratoire d’Hydrologie et de Géochimie de Strasbourg tions on the solution, we prove the convergence of this [email protected] generic scheme on general meshes. The discretization is also proved to be locking-free, in the sense that a discrete inf-sup condition guarantees the absence of spurious spa- CP7 tial oscillations on the pore pressure in the first time steps Applications of Level Set Methods in Numerical in poorly permeable regions.

Simon Lemaire GS13 Abstracts 77

IFP Energies nouvelles taken to be anisotropic, at times heterogenerous, and/or [email protected] discontinuous.

Daniele Di Pietro Qiang Zhao University Montpellier 2 Institute of Applied Physics and Computational I3M - ACSIOM Mathematics [email protected] Beijing,P.R.China [email protected] Robert Eymard University Paris East Xia Cui [email protected] Institute of Applied Physics and Computational Mathematics Laboratory of Computatinal Physics,Beijing,P.R.China CP7 [email protected] Space-Time Hybridizable Discontinuous Galerkin Methods for Incompressible Flows Guangwei Yuan Institute of Applied Physics and Computational I will discuss a new Discontinuous Galerkin (DG) method, Mathematics namely the Hybridizable DG (HDG) method. We recently Laboratory of Computational Physics extended the HDG method to a space-time formulation [email protected] allowing efficient and accurate computations on deforming grids/domains. I will introduce the method for the Incompressible Navier-Stokes (INS) equations. A compari- CP8 son of results and efficiency will then be made between the In Search for a Robust Representation of Cloud Mi- space-time HDG and DG method for the INS equations on crophysics for Aerosol-Cloud-Aerosol Interactions deforming domains. Representation of such processes as cloud drops formation Sander Rhebergen on aerosol particles and further processing of the aerosol University of Minnesota physicochemical properties by precipitation-forming clouds School of Mathematics represents a challenge for classical bulk, multi-moment and [email protected] bin models of cloud microphysics. Several alternative approaches have been recently proposed such as Lagrangian Bernardo Cockburn particle-tracking simulations or multi-dimensional bin ap- School of Mathematics proaches. In this study we intercompare these novel University of Minnesota schemes using a 2-dimensional prescribed-flow simulations [email protected] of drizzling marine stratocumulus to systematically analyze the mechanisms by which the physiochemical properties of Jaap van Der Vegt aerosols change in warm clouds. University of Twente Sylwester J. Arabas [email protected] Institute of Geophysics, Faculty of Physics University of Warsaw, Poland CP7 [email protected] A Cell-Centered Scheme for the Heterogeneous and Anisotropic Diffusion Equations on Distorted Miroslaw Andrejczuk Meshes Department of Physics, University of Oxford, UK [email protected] In this paper, we derive a finite volume scheme for the heterogeneous and anisotropic diffusion equations on gen- Wojciech Grabowski eral, possibly nonconforming meshes. This scheme has National Center for Atmospheric Research, Boulder, both cell-centered unknowns and vertex unknowns. The Colorado vertex unknowns are treated as intermediate ones and are [email protected] expressed as a linear combination of the neighboring cell- centered unknowns, which reduces the scheme to a com- Anna Jaruga pletely cell-centered one. The coefficients in the linear Institute of Geophysics, Faculty of Physics combination are known as the weights and two types of University of Warsaw, Poland new explicit weights are proposed, which allow arbitrary [email protected] diffusion tensors, and are neither discontinuity dependent nor mesh topology dependent. These new weights can re- Zachary Lebo duce to the one-dimensional harmonic-average weights on National Center for Atmospheric Research, Boulder, the nonuniform rectangular meshes, and moreover, are eas- Colorado ily extended to the unstructured polygonal meshes and [email protected] non-matching meshes. Both the derivation of the nine- point scheme and that of new weights satisfy the linear- ity preserving criterion which requires that a discretization Hanna Pawlowska scheme should be exact on linear solutions. Numerical ex- Institute of Geophysics, Faculty of Physics periments show that, with these new weights, the resulting University of Warsaw, Poland new scheme and its simple extension maintain optimal con- [email protected] vergence rates for the solution and flux on general polygonal distorted meshes in case that the diffusion tensor is 78 GS13 Abstracts

CP8 Luigi Burlini Asymptotic Modeling of Insittue of Geoscience, ETH Zürich Non-Hydrostatic/Hydrostatic Dynamical Coupling [email protected] in the Ocean Surface Boundary Layer Taras Gerya A primary challenge in physical oceanography is the sys- Geophysical Institute tematic representation of non-hydrostatic boundary-layer ETH-Zurich (BL) turbulence in numerical models and stability analyses [email protected] of hydrostatic flows. Here, we use asymptotic analysis to derive a multiscale PDE model that captures the coupling Neil Mancktelow between wind-driven Langmuir turbulence and O(10)-km Insittue of Geoscience, ETH Zürich submesoscale flows in the ocean surface BL. Numerical sim- [email protected] ulations and nonlinear WKBJ analysis confirm that non- hydrostatic/hydrostatic coupling gives rise to a variety of novel upper ocean phenomena. CP8 Greg Chini A Non-Hydrostatic Spectral-Element Model of the Program in Integrated Applied Mathematics Atmosphere University of New Hampshire To perform climate simulations at resolutions greater than [email protected] 1/8th of a degree, the hydrostatic primitive-equations must be replaced with non-hydrostatic Euler equations valid in Ziemowit Malecha this regime. To this end, we are working to develop a University of New Hampshire non-hydrostatic version of CAM-SE, the spectral-element Program in Integrated Applied Mathematics Community Atmosphere Model used at NCAR. We will [email protected] discuss the design choices made in the new non-hydrostatic dynamical core and present some preliminary results. Zhexuan Zhang University of New Hampshire David M. Hall Department of Mechanical Engineering University of Colorado at Boulder [email protected] Department of Computer Science [email protected] Keith Julien Applied Mathematics CP9 University of Colorado, Boulder [email protected] Perfectly Matched Layers for the Wave Equation in Discontinuous Media

CP8 Applications arising in geophysics and electromagnetic problems can be composed of layers of rock, water and pos- Weather Models of Anomalous Diffusion sibly oil. The ultimate goal of this project is to investigate The numerical simulation of fractional diffusion equations the efficiency of the PML in a layered media. We consider in three dimensions is considered, to describe fluid flow a computational set-up consisting of smaller structured do- through porous media. A fractional version of the Alter- mains that are patched together to a global domain, using nating Direction Implicit (ADI) scheme is proposed. A high order difference operators for approximating spatial strategy improving the speed of convergence by an extrap- derivatives and weak enforcements of interface conditions. olation method is also presented. Numerical results are Numerical simulations will be presented demonstrating the given to support our theoretical analysis. stability and high order accuracy of our schemes. Keywords: anomalous diffusion; fractional diffusion, frac- Kenneth Duru tional partial derivatives; Alternating Direction Implicit Division of Scientific Computing (ADI) scheme; extrapolation techniques. Uppsala University Moreno Concezzi [email protected] University of Roma Tre [email protected] CP9 Numerical Approximation for a Model of Methane CP8 Hydrates Water in the Subducting Oceanic Plate: a Trilogy We consider a simplied model for evolution of methane In this presentation we summarize the results of a project hydrates in the hydrate zone, which includes a parameter- focused on geological processes related to water in the slab dependent maximum solubility constraint represented as a at different stages of subduction. We discuss numerical nonlinear complementarity constraint (for solubility). Our modeling results of fluid flow during slab hydration and model consists of a single PDE and two unknowns (sol- dehydration, potential geophysical implications of an hy- ubility and saturation) which are bound by a parameter drated slab at intermediate-depths and deep subduction of dependent family of graphs. We analyze solvability and fluids. other properties of the fully discrete scheme for the model, and discuss current extensions. Manuele Faccenda Dipartimento di Geoscienze F. Patricia Medina UniversitàdiPadova Department of Mathematics [email protected] Oregon State University GS13 Abstracts 79

[email protected] mogeneity of linear type associated with the rigidity and density of the medium. Dispersion equation has been ob- Nathan L. Gibson tained in the terms of HypergeometricU and LaugurreL Oregon State University function. The dispersion equation reduces to a classical [email protected] form as a particular case. The influence of various parameters has been depicted by means of graphs for both Malgorzata Peszynska reinforced and reinforcement free medium. Department of Mathematics Sumit K. Vishwakarma, Shishir Gupta Oregon State University Indian School of Mines, Dhanbad, Jharkhand, [email protected] India-826004 [email protected], shishir [email protected] Ralph E. Showalter Oregon State University [email protected] CP10 A Fourier Finite Element Method for the Simula- tion of 3D Csem Measurements CP9 Fast Uncertainty Quantification of Subsurface Flow We present a novel numerical method to simulate 3D geo- and Transport with Markovian Velocity Processes physical controlled source electromagnetic (CSEM) measurements. The method combines a 2D finite element Contaminant transport predictions in large subsurface sys- method (FEM) in two spatial dimensions with a hybrid tems involve high uncertainties due to sparse conductivity discretization based on a Fourier-FEM along the third spa- measurements. To quantify these uncertainties, we propose tial dimension. The method delivers high accuracy simu- a simulation method that is about three orders of magni- lations of marine CSEM problems with arbitrary 3D ge- tude faster than conventional Monte Carlo simulation. The ometries while it considerably reduces the computational new method is based on parameterized Markov processes complexity of traditional 3D simulators, since Fourier basis for the velocity of fluid particles, which allow for the pres- functions are mutually orthogonal within the background ence of an arbitrary number of conductivity measurements. layers. Daniel W. Meyer Shaaban A. Bakr Institute of Fluid Dynamics Senior Researcher, Uni CIPR, P.O. Box 7810, N-5020 [email protected] Bergen, Norway Hamdi Tchelepi [email protected] Stanford University Energy Resources Engineering Department David Pardo [email protected] Department of Applied Mathematics, Statistics, and Operational Research, University of the Basque Country Patrick Jenny [email protected] Institute of Fluid Dynamics ETH Zurich Trond Mannseth [email protected] Centre for Integrated Petroleum Research University of Bergen, Norway [email protected] CP9 A Bioventing Mathematical Model Based on Pure Oxygen Injection CP10 Expected Value Estimators in Nuclear Well- A mathematical model and the simulation of subsoil decon- Logging Simulations tamination by bioventing will be presented. The bases for the model construction are the following: (1) the pollutant Simulation of nuclear well-logging tools and their responses is considered as immobile and confined in the unsaturated is a long-standing problem, usually solved in the framework zone; (2) only oxygen is injected in the subsoil by wells; of transport theory by Monte-Carlo methods. Widely used (3) the bacteria acting the pollutant removal are immobile conventional Monte Carlo algorithms are often unaccept- and their growth depends on oxygen and pollutant concen- able, and variance reduction techniques are required. In tration. this talk, the algorithms with expected value estimators are considered. These algorithms showed their efficiency when Filippo Notarnicola applied to different types of nuclear well-logging problems. Istituto Applicazioni Calcolo, I.A.C. - CNR, Bari The description and analysis of the results are the subjects [email protected] of the presentation.

Bair Banzarov CP9 Baker Hughes Inc. Torsional Wave Dispersion Relation in a Self- [email protected] Reinforced Layer over a Gravitating Viscoelastic Half Space CP10 The present paper constitute the study of torsional surface Seismic Stratigraphic Modelling Through Comput- wave propagation in a self-reinforced layer resting over a gravitating viscoelastic half space. The layer has an inho- 80 GS13 Abstracts

ing in Bengal Basin at Higher Depths [email protected], [email protected], [email protected] Stratigraphic seismic modelling through software package STICHA between two wells of Bengal Basin at different depths between 2000ft to 4400 ft,the zone of interest for CP11 crude oil bearing, has been made and analysis has been Gradient-Based Techniques for Data Assimilation made geologically for potential oil-bearing.The Depth mod- in Reservoir Simulation els and respective synthetic seismic setion models at different interesting layers have been developed. The results A computational framework that combines a full-featured match comfortably .The drilling data agrees with seismic compositional reservoir simulator with adjoint-based in- models made.This is economic in oil exploration. verse modeling is presented. Automatic differentiation is applied to facilitate construction of the required deriva- Dr Sisir Kumar Bhowmick tives. The spatial correlation structure of the geological GMIT,Balarampur,Baruipur model is captured using a PCA-based regularization, with Kolkata-700144 the PCA basis determined from geostatistical modeling. A sisirkr@rediffmail.com new zonation procedure based on sensitivity magnitude is introduced. History matching results using the new framework are presented for challenging problems. CP10 Inexact Interior Point Algorithms for Seismic Vladislav Bukshtynov, Oleg Volkov, Lou J. Durlofsky Imaging Stanford University [email protected], [email protected], An inexact interior-point algorithm is devised and its per- [email protected] formance is compared against the exact one on several linear and nonlinear PDE-constrained optimization prob- Khalid Aziz lems. Schur-complement preconditioners for the resulting Stanford University KKT systems are constructed and their robustness is in- Department of Energy Resources Engineering vestigated for every benchmark problem considered. Ap- [email protected] plication areas include parameter estimation in diffusion problems, super-conductivity and seismic imaging both in the frequency and time domains. CP11 Drosos Kourounis Polymer Injection Optimization Using the Ensem- USI - Università della Svizzera italiana ble Kalman Filter [email protected] Eni is currently studying the applicability of polymer-based EOR to brown fields. A workflow hinged on the Ensemble Johannes Huber Kalman filter (EnKF) has been developed to assimilate Universität Basel production data, evaluate the efficiency of the polymer, Department of Mathematics quantify process-relevant uncertainties and maximize the [email protected] economical revenue. In this work, EnKF is used to generate an ensemble of history matched models for a field sector, Marcus J. Grote with careful estimation of the boundary condition. Then, Universität Basel the ensemble logic is used for a robust optimisation of the [email protected] economic return of the EOR project.

Olaf Schenk Laura Dovera, Stefano Raniolo, Alberto Cominelli, USI - Università della Svizzera italiana Chiara Callegaro, Franco Masserano [email protected] ENI E&P [email protected], [email protected], [email protected], [email protected], CP10 [email protected] Mathematical Techniques for Very Large Scale To- mographic Inversion CP11 We present an approach to find regularized solutions to Dual States Estimation Using Ensemble Kalman very large linear systems arising from a tomographic in- Filtering for Subsurface Flow-Transport Coupled verse problem that are difficult to handle directly even with Models large computational resources. We present a system using matrices that reach terabytes in size. We use a multi-step Modeling contaminant evolution in geologic aquifers re- approach to work with such systems, consisting of wavelet quires coupling a groundwater flow model with a contam- compression and randomized low rank SVD approxima- inant transport model. Assuming perfect flow, an ensem- tions. We obtain significant reductions in size and speed-up ble Kalman filter can be directly applied on the transport in computation time. model but this is very crude assumption as flow models can be subject to many sources of uncertainties. If the Sergey Voronin flow is not accurately simulated, contaminant predictions Princeton University will likely be inaccurate even after successive Kalman up- [email protected] dates of the contaminant with the data. In this study, we propose a dual strategy for this one way coupled system by Guust Nolet, Dylan Mikesell, Jean Charléty treating the flow and the contaminant models separately Universite de Nice Sophia-Antipolis while intertwining a pair of distinct Kalman filters; one CNRS, Obs. de la Cote d’Azur, Geoazur on each model. Preliminary results suggest that on top GS13 Abstracts 81

of simplifying the implementation of the filtering system, efficient as adjoints, has recently received significant at- the dual approach provide time consistent updating scheme tention for solution of optimization problems where ad- and more stable and accurate solutions than the standard joints are not available or difficult to implement. These joint approach. methods are generally much easier to implement as they are non-intrusive and treat the simulator as a black box. Mohamad El Gharamti In this work, we propose the application of quasi-Monte King Abdullah University of Science and Technology Carlo methods for improving the efficiency and accuracy [email protected] of the stochastic gradient compared to current methods. While the existing approaches rely on Monte Carlo sam- Ibrahim Hoteit pling, quasi-Monte Carlo sampling has a better conver- King Abdullah University of Science and Technology gence rate leading to more accurate and efficient gradi- (KAUST) ent approximation. In particular, we apply the Sobol se- [email protected] quence for sampling, which demonstrates better convergence compared to other quasi-Monte Carlo sampling tech- Johan Valstar niques. More than 30% improvement was obtained in the Deltares - Utrecht, Netherlands accuracy of the stochastic gradient calculated with Sobol [email protected] sampling over standard Monte Carlo sampling. Pallav Sarma CP11 Chevron Energy Technology Company Geodetical Data Assimilation with Ensemble San Ramon CA Kalman Filter [email protected]

Geomechanical phenomena are fundamental in explaining Wen Chen the dynamic behaviour of the reservoir: surface displace- Chevron ETC ments measurements can provide additional insight into [email protected] the nature of the reservoir rock and help constrain the reservoir model. In this study, an integrated workflow for the assimilation of dynamic flow measure data and surface CP12 displacements observations has been developed through the Subglacial Water Flow Beneath Ice Streams Ensemble Kalman Filter approach, in order to estimate reservoir flow and material properties and to identify com- Ice streams, characterised by high basal sliding velocities, partments not yet drained. play a dominant role in ice sheet drainage. Subglacial hydrology is believed to be one of the main controlling fac- Silvia Monaco, Francesca Bottazzi, Marco Sciortino, tors in their spatial and temporal evolution: how the water Laura Dovera drains beneath an ice sheet has important implications for ENI E&P the ice-bed boundary condition. We pose a model to de- [email protected], [email protected], scribe subglacial stream flow through the underlying sed- [email protected], [email protected] iment, and consider the coupled behaviour of the ice and meltwater systems. CP11 Teresa M. Kyrke-Smith Impact of Model Order Reduction to Hydrological University of Oxford Data Assimilation. [email protected] Sophisticated data assimilation (DA) techniques, e.g. particle filters with MCMC, have been recently developed to CP12 address inverse problems. These methods are difficult to Towards a New Marine Ice-Sheet Model apply to high-dimensional models, since they require many system solutions. Reduced order models (RM) reduce the We present a unified model in order to model an ice flow. computational burden required to solve transient PDEs. The grounded part (ice sheet and ice shelf) leads to a Here we investigate the application of DA schemes with a unique lubrication-type model. A new model for the float- large number of realizations computed with the RM. Our ing ice mass is developed. We consider the ice shelf as a preliminary results show that DA techniques correct the two free surface problem with a lateral sea pressure force at RM errors. calving front. We obtain an integro-differential evolution equation of the ice shelf thickness. Damiano Pasetto, Mario Putti UniversitàdiPadova Marc Boutounet, Jérôme Monnier [email protected], [email protected] Institut de Mathématiques de Toulouse INSA dpt GMM William W-G. Yeh [email protected], University of California, [email protected] Los Angeles williamy@seas.ucla.edu CP12 Control Method Inversions for Ice Stream Bed CP11 Conditions Using a Higher-Order Glacier Model Improved Estimation of the Stochastic Gradient Ice streams undergo drag from sliding over their beds, but with Quasi-Monte Carlo Methods this stress is not measurable remotely. However, one can Stochastic approximation of the gradient, although not as use observed ice velocities to invert a glacier model for the 82 GS13 Abstracts

spatially-varying bed friction. In this talk, I will compare mate deconvolution to mitigate these errors. Results from the results of inverting two different models from observa- a flat boundary layer with one grid refinement interface are tions at Pine Island Glacier: the shelfy stream equations presented. and the more complex L1L2 equations. These models are depth-averaged perturbations of the 3D Stokes equations. Lauren Goodfriend UC Berkeley Daniel Shapero [email protected] University of Washington [email protected] Fotini K. Chow University of California, Berkeley [email protected] CP12 A Conceptual Model for Permafrost-Climate Feed- Marcos Vanella, Elias Balaras back. George Washington University The permafrost methane emission problem is the focus [email protected], [email protected] of attention in different climate models. As a result of tundra permafrost thawing, a number of small lakes have CP13 formed and extended, and methane has entered the atmosphere. In turn, atmosphere methane can reinforce warm- Hypothesizing and Testing Causal Relationships in ing, and there appears to be a positive feedback loop that Correlated Time-Series Observations can lead to a climate catastrophe. Mathematically, per- Biogeochemical archives record time progression of envi- mafrost thawing can be described by the classical Stefan ronmental conditions. Co-varying measurements entice approach. From this assumption we obtain a determinis- cause-effect explanations, but establishing causal relation- tic equation that serves as an extremely simplified model ships requires rigorous epistemology. Correlation is neces- for lake growth. This equation are improved and trans- sary for hypothesizing causation, but insufficient for form- formed to a more realistic model for estimation of positive ing conclusions. Amplitude and phase response over fre- permafrost-climate feedback. quency tests cause-effect scenarios: measured cause must Ivan A. Sudakov precede proportionate effect consistent with direct forcing University of Utah theory. Signal coherence offers methods for quantifying Mathematics Department probabilistic confidence in cause-effect hypotheses. Meth- [email protected] ods are applied to ice core proxies of temperature and carbon dioxide concentration.

Sergey Vakulenko Gary B. Hughes Institute for Mechanical Engineering Problems California Polytechnic State University San Luis Obispo Russian Academy of Sciences [email protected] [email protected]

CP13 CP13 Asymptotic Approaches for Rotationally Con- Scale-Aware Parametrization of Eddy Transport strained Flows Mesoscale eddies are most energetic in the ocean, and are Geostrophy, the dominant force balance between the Cori- responsible for a significant portion of the tracer transport. olis and pressure gradient forces, is often the prevailing fea- Multi-resolution ocean models require eddy parametriza- ture observed in the convective dynamics of atmospheres tion schemes that can scale across a wide range of length and oceans and planetary interiors. The presence of fast in- scales existing on the grids. This talk present results from ertial waves and thin momentum boundary layers pose sig- a recent project in designing scale-aware eddy parametriza- nificant challenges for direct numerical simulations. In this tion schemes, which includes a scale-aware generalization talk, I will demonstrate how multiscale asymptotic meth- of the anticipated potential vorticity method, the Gent- ods can be utilized to derive reduced PDEs that overcome McWilliams closure with spatially-varying coefficients, and these restrictions. Simulations reveal new flow regimes that some ideas for moving forward. remain inaccessible DNS of the Navier-Stokes equations.

Qingshan Chen Keith A. Julien Florida State University Department of Applied Mathematics [email protected] University of Colorado at Boulder [email protected] CP13 Approximate Deconvolution for Large-Eddy Simu- CP13 lation (LES) of the Atmospheric Boundary Layer A Stochastic Hydrodynamic Model for Biogenic (ABL) on Adaptive Grids Mixing Simulating the ABL in complex terrain (such as cities) As fish or other bodies move through a fluid, they stir their could be faster and more accurate using LES and adap- surroundings. This can be beneficial to some fish, since the tive grids. However, combining these techniques generates plankton they eat depends on a well-stirred medium to feed errors. Inaccuracies in subfilter models limit LES solution on nutrients. Bacterial colonies also stir their environment, reliability at the grid scale, contaminating the interpolated and this is even more crucial for them since at small scales solution at grid interfaces. The grid interface also reflects there is no turbulence to help mixing. It has even been high wavenumber solution components. We test approxi- suggested that the total biomass in the ocean makes a sig- GS13 Abstracts 83

nificant contribution to large-scale vertical transport, but low Water Equations with Horizontal Temperature this is still a contentious issue. We propose a simple model Gradients of the stirring action of moving bodies through both inviscid and viscous fluids. In the dilute limit, this model can We consider a modification of the Saint-Venant system of be solved using Einstein and Taylor’s formula for diffusion shallow water equations. The studied model, proposed by (Brownian motion). We compare to direct numerical simu- Ripa, takes into account temperature variations, which ef- lations of objects moving through a fluid. This is joint work fect the pressure term while the temperature is transported with Jean-Luc Thiffeault (Wisconsin) and Steve Childress by the fluid, which makes the model substantially more (NYU). complicated than the classical Saint-Venant system. We introduce a central-upwind scheme for the Ripa system. The Zhi George Lin scheme is well-balanced, positivity preserving and does not Zhejiang University develop spurious pressure oscillations across temperature [email protected] jumps. Such oscillations would typically appear when conventional Godunov-type methods are applied to the Ripa system, and the nature of the oscillation is similar to the CP13 ones appearing at material interfaces in compressible mul- A Thermostat Approach to Correction of Kinetic tifluid computations. The resulting scheme is highly ac- Energy Spectra curate, preserves two types of lake at rest steady states, and is oscillation free across the temperature jumps, as it Numerical simulations of atmospheric flows typically use is illustrated in a number of numerical experiments. artificial viscosity to avoid spectral blocking. This disrupts the vorticity cascade and suppresses the growth of distur- Alina Chertock bances. We introduce a thermostat to correct the spectrum North Carolina State University by adding a small stochastic perturbation to each mode in Department of Mathematics a spectral truncation. In Burgers’ equation this approach [email protected] yields the correct energy spectrum with mild perturbation of dynamics. We also discuss prospects for application to Alexander Kurganov two-dimensional flow. Tulane University Department of Mathematics Keith Myerscough [email protected] Delft University of Technology [email protected] Yu Liu Tulane University Jason Frank Mathematics Department Centrum Wiskunde & Informatica [email protected] [email protected]

Benedict Leimkuhler CP14 University of Edinburgh Robust Code-to-Code Validation by Means of Pa- [email protected] rameter Uncertainty Propagation and Anova

We consider the issue of robust code-to-code validation for CP14 long wave run-up on complex bathymetries. The objective Goal-Oriented Adaptive Meshing for the Shallow is the assessment of the output sensitivity w.r.t. model Water Equations parameters affecting the properties of the schemes. We will compare the behavior of two shallow water codes using the The dual-weighted residual method provides an error esti- second order scheme of Nikolos and Delis (CMAME 198 matorwhichcanbeusedasamesh refinement criterion for 2009) and of Ricchiuto (AIP Proc. 1389 2011). Robust adaptive methods. By utilization of the adjoint, the DWR validation is achieved by using uncertainty propagation and method takes the discretization error of the scheme and analysis of variance to compare the codes single parameter also user specified quantities of interest into account. We sensitivities. tested the DWR method with a discontinuous Galerkin discretization of the shallow water equations. Our test prob- Pietro M. Congedo lem is a 2D storm track simulation which is sensitive to the INRIA Bordeaux Sud-Ouest (FRANCE) grid refinement. [email protected] Susanne Beckers Anargyros Delis KlimaCampus, Universität Hamburg Technical University of Crete [email protected] [email protected] Jörn Behrens KlimaCampus, University of Hamburg Mario Ricchiuto INRIA [email protected] [email protected] Winnifried Wollner University of Hamburg, Department of Mathematics CP14 [email protected] Shallow Water Simulations with the Source Term by the Depth Gradient and Weighted Average Flux CP14 Central-Upwind Schemes for the System of Shal- 84 GS13 Abstracts

Methods transformation.’

A finite volume scheme based on depth gradient method Burkhard Schaffrin, Kyle Snow (DGM) and weighted average flux (WAF) method with School of Earth Sciences source term has been formulated to solve the two- The Ohio State University dimensional shallow water equations. Approximated so- aschaff[email protected], [email protected] lutions are updated in time using predictor-corrector types of methods. The predictor step is calculated by the DGM Frank Neitzel with piecewise-linear reconstructions in each cell volume. Dept. of Geodesy and Geoinformation Science Computations at the corrector step are performed using Berlin University of Technology a total variation diminishing (TVD) variant of the WAF [email protected] method. The accuracy of numerical solutions is demonstrated by applying it to variety of benchmark problems. It is shown that the method is accurate and robust. Also, CP15 it can be used to solve problems involving shock-capturing. A Numerical Approach to Fluid Induced Sediment Processes Lanchakorn Kittiratanawasin Fluvial bedforms like dunes, ripples or scour marks are Department of mathematics, Faculty of Science formed by current driven sediment transport processes. Kasetsart University This includes the interaction of entrainment and deposition [email protected] of sediment particles. In this study we use a numerical simulation of the three dimensional fluid flow and the simul- Anand Pardhanani taneous transport to reproduce these processes. To solve Department of Mathematics, Natural Sciences Division the incompressible two-phase Navier-Stokes equations we Earlham College, U.S.A. use NaSt3D as three dimensional fluid solver for incom- [email protected] pressible flow problems. High order schemes are applied for spatial as well as for temporal discretization. The main Montri Maleewong variants of sediment transport are modelled by applying na Department of mathematics, Faculty of Science advection-diffusion equation for suspension load and Exner Kasetsart University, Bangkok, Thailand equation to bed load transport. The rearrangement of sed- [email protected] iment leads to a new sediment surface height which results in new bedforms. To test our model we simulate the evolution of a scour mark around an obstacle and the erosion CP14 of sediment from a dune crest. Central-Upwind Schemes for Shallow Water Mod- els Markus Burkow Institute for Numerical Simulation, University Bonn The talk will be focused on recent applications of the finite- [email protected] volume central-upwind schemes to several shallow water models including the two-layer shallow water equations, Michael Griebel the Savage-Hutter type model of submarine landslides and Institute for Numerical Simulation generated tsunami waves, and the non-hydrostatic Saint- University of Bonn Venant system. The main advantages of the central- [email protected] upwind schemes are their simplicity and robustness, their ability to preserve a delicate balance between the fluxes, (possibly singular) geometric source term and friction CP15 terms as well as to preserve positivity of the computed Numerical Modeling of Flow Over Flexible Vegeta- water depth. tion Alexander Kurganov The existence of vegetation in a region can greatly increase Tulane University the resistance to flow. The vegetation is often highly flexi- Department of Mathematics ble and moves as the flow field changes which complicates [email protected] quantifying the resistance and incorporating it into a flow model. We present a method to model resistance due to bending vegetation using the immersed boundary method CP14 for fluid-structure interaction. Comparisons to several ex- Total Least-Squares Adjustment for Various Forms perimental benchmark problems are shown. of Coordinate Transformations: A Comparison Steven A. Mattis In recent years, the Total Least-Squares adjustment within The Institute for Computational Engineering and Sciences Errors-In-Variables models has been used frequently when University of Texas at Austin estimating parameters of certain coordinate transforma- [email protected] tions from empirical data. While the affine-transformation parameters could be solved efficiently in a multivariate Clint Dawson setting, the similarity transformation required algorithms Institute for Computational Engineering and Sciences for general weight matrices to reflect its special struc- University of Texas at Austin ture. Here, an attempt will be made to develop a unifying [email protected] framework that also will allow the treatment of intermediate forms, such as the prototypical “orthogonal coordinate Christopher Kees, Matthew Farthing US Army Engineer Research and Development Center [email protected], GS13 Abstracts 85

[email protected] Delft University of Technology [email protected]

CP15 Alla Kolechkina A Residual Based Approach for the Madsen and Aronwis Sorensen Boussinesq Model [email protected] We consider the discretization of the Boussinesq model of Madsen and Sorensen using a residual based ap- CP16 proach. Following previous work of Ricchiuto and Boller- Incorporating Tidal Uncertainty Into Probabilistic man (J.Comput.Phys 228, 2009), we write discrete nodal Tsunami Hazard Assessment (ptha) equations as weighted averages cell residuals obtained by integrating the time-discretized Madsen and Sorensen We describe two new methods for incorporating tidal un- equations over a cell. We will discuss the influence of certainty into the probabilistic analysis of tsunami hazard various discretization choices (weights, time discretization assessment. These methods couple inundation informa- etc.) on dispersion and accuracy properties of the result- tion from multiple GeoClaw simulations with tidal patterns ing scheme, and show results on relevant nonlinear wave from the site of interest. Performance of the methods for propagation and transformation tests. a recent Crescent City, California study will be illustrated, and advantages over existing methods will be given. Mario Ricchiuto INRIA Loyce Adams [email protected] University of Washington Department of Applied Mathematics Andrea Filippini [email protected] Inria andrea.fi[email protected] Randall J. LeVeque University of Washington [email protected] CP15 Pebble Shape Evolution Along the Williams River, FRANK I. González Australia: a Numerical Abrasion Model Dept. of Earth and Space Sciences Modeling sediment transport and abrasion in various en- University of Washington vironments is a long-standing problem in sedimentology. fi[email protected] We present a new numerical abrasion model describing the collective evolution of size and shape in large pebble col- CP16 lections as a Markov process, due to mutual abrasion and friction. We apply the model to the Williams River in or- Strongly Nonlinear Internal Wave Models for Two der to reconstruct the downstream variation in grain size Layer Fluids and shape. We present a generalized class of strongly nonlinear inter- T´ımea Szabó nal long wave models in a two-fluid layer system. Key Department of Mechanics, Materials and Structures steps in the derivation of models tailored for different sta- Budapest University of Technology and Economics bility properties and accuracy goals will be discussed. Non- [email protected] stationary time evolution for their performance tests will be presented as well.

Stephen Fityus Tae-Chang Jo Centre for Geotechnical and Materials Modelling Inha University The University of Newcastle, Australia [email protected] stephen.ﬁ[email protected] Roberto Camassa G´abor Domokos University of North Carolina Department of Mechanics, Materials and Structures [email protected] Budapest University of Technology and Economics [email protected] CP16 Generation of Provably Correct Curvilinear CP15 Meshes Interval Output of a SISO Linear System with Known Impulse Response for Incompletely De- The development of high-order numerical technologies for scribed Input CFD is underway for many years now. In many contributions, it is shown that the accuracy of the method strongly In hydrology convolutions are used in the context of hydro- depends of the accuracy of the geometrical discretization. graphs and tracer hydrology. They represent the action of a In other words, the following question is raised:we have linear system on an input. Usually the impulse response is the high order methods, but how do we get the meshes? a parametrized function and only a time series of averages This talk focus on the generation of highly curved ocean of the input is available. For input that is non-negative meshes. We propose a robust procedure that allows to and has an essential supremum we apply interval analysis build a curvilinear mesh for which every element is guar- to construct upper and lower bounds for the convolution. anteed to be valid. The technique builds on standard optimization method (BICG) combined with a log-barrier ob- Ronald R. Van Nooijen jective function to guarantee the positivity of the elements 86 GS13 Abstracts

Jacobian. To be valid is not the only requirement for a CP16 good-quality mesh. If the temporal discretization is ex- An Unstructured Approach to Ocean Wave- plicit, even a valid element can lead to a very stringent Generation Modeling. constraint on the stable time step. The optimization of the curvilinear ocean meshes to obtain large stable time Ocean surface gravity waves are an important component stepsisalsoanalyzed. of the atmospheric and oceanic boundary layer and the inclusion of such in a global climate model has the potential Jonathan Lambrechts to correct model biases and improve air-sea interactions. Université catholique de Louvain However, existing wave-generation models used for weather [email protected] forecasting are computational expensive and ill-suited for studying polar-ice-free scenarios. Here, a comparison of Jean-Fran¸cois Remacle, Thomas Toulorge an unstructured node approach (using RBF-generated fi- Univ. catholique de Louvain nite differences) will be presented as well as an update on jean-franois remacle ¡jean-francois.remacle@uclou, the the coupled wave-generation component to the NCAR [email protected] Community Earth System Model.

Vincent Legat Adrean Webb Universit´e catholique de Louvain University of Colorado at Boulder Belgium Cooperative Institute for Research in Environmental [email protected] Sciences [email protected]

CP16 CP17 Unsteady Nonlinear Gravity Waves in Water of Fi- nite Depth Synthetic Wavelet Using a Hydrographic Data: Comparing Methods to Solve It In this work, we consider two-dimensional gravity waves generated by a moving pressure distribution in water of Recently the seismic method is applied in water column finite depth. The fully nonlinear model in Euler equa- in the ocean, looking for mesoescales features. For this tion form is solved numerically by the mixed Eulerian and process is necessary to use hydrographic data to fit seis- Lagrangian approach. The stability of gravity waves for mic image data. Was compared the traditional method subcritical and supercritical flows is presented. Subcriti- and the method that Ruddick et al. (2009) suggested, to cal flow solution approaches limiting Stoke’s wave for high calculate the acoustic impedance, reflectivity and wavelet. amplitude applied pressure while a solitary wave trapped Though there are lightly differences, results show that the by a localized pressure is detected for supercritical flows. traditional method is more accuracy for calculation to the synthetic wavelets than other suggestion. Montri Maleewong Department of Mathematics, Faculty of Science Ana M. Gonzalez-Orduno Kasetsart University Posgrado de Ciencias del Mar y Limnologia, UNAM [email protected] [email protected] Jaime Urrutia Fucugauchi CP16 Instituto de Geofisica, UNAM An Efficient Parallel Implementation of Multirate juf@geofisica.unam.mx Schemes for Ocean Modeling Maria Adela Monreal-Gomez Although explicit time integration schemes require small Instituto de Ciencias del Mar y Limnologia computational efforts per time step, their efficiency is UNAM severely restricted by stability limits. In particular, un- [email protected] structured meshes can lead to a very restrictive global stable time step. Multirate methods offer a way to increase Guillermo Perez-Cruz the efficiency by gathering grid cells in appropriate groups. Facultad de Ingenieria, UNAM The parallelization of these schemes is challenging because [email protected] grid cells have different workloads. We propose a strategy that shares the workload almost equitably between all processors at every multirate stage. Performance analyses are David Alberto Salas-De-Leon provided for ocean modeling applications. Instituto de Ciencias del Mar y Limnologia UNAM Bruno Seny, Jonathan Lambrechts [email protected] Université catholique de Louvain [email protected], jonathan lambrechts ¡jonathan.lambrechts@uclouvain CP17 Using Chaos in Groundwater Remediation

Vincent Legat Ineffective mixing constrains groundwater remediation, Université catholique de Louvain limiting reactions between contaminants and treatment so- Belgium lutions. We address this constraint with chaos, using engi- [email protected] neered injection and extraction to stretch and fold a plume of treatment solution. The periodic points of this flow can Jean-Fran¸cois Remacle be elliptic (poor mixing) or hyperbolic (good mixing); the Université catholique de Louvain manifolds of hyperbolic periodic points reveal the asymp- [email protected] GS13 Abstracts 87

totic plume geometry; adjusting the magnitude of water in- CP17 jected generates a bifurcation structure that provides guid- Homogenization in Case of Transient Motion of a ance for remediation system optimization. Fluid Through a Porous Medium. David C. Mays We consider transient motion of a fluid through a medium University of Colorado Denver with periodic structure of pores. We use a homogeniza- [email protected] tion procedure to carry out a multiple-scale asymptotic analysis. The determination of the components of effective Roseanna Neupauer permeability tensor is reduced to the numerical solution of University of Colorado Boulder periodic problems in cells. We find that the dependence of [email protected] the viscosity and drag coefficient on the pressure can have a significant effect on the nature of the solution. James D. Meiss University of Colorado Viktoria Savatorova Dept of Applied Mathematics Physics Department, [email protected] National Research Nuclear University [email protected], [email protected]

CP17 Alexander Vlasov Uncertainty Quantification for Transport Problems Institute of Applied Mechanics Russian Academy of in the Shallow Subsurface Science [email protected] We model heat transport in the shallow subsurface using a parabolic differential equation together with initial con- Alexey Talonov ditions and boundary conditions. The parameters in the NRNU MEPhI model may be related by a mixture model, making the [email protected] problem more complex. In this work we use Markov Chain Monte Carlo methods to solve the parameter calibration problem. CP17 Uncertainty Quantification in Subsurface Flows Anna Meade, Tim Kelley with Stochastic Hydrological Laws North Carolina State University [email protected], tim [email protected] The effects of uncertainty in hydrological laws are studied on subsurface flows modeled by Richards’ equation. One- Owen Eslinger dimensional infiltration problems are treated and the influ- US Army Research and Development Center ence of the variability of the input parameters on the po- [email protected] sition and the spreading of the wetting front is evaluated. A Polynomial Chaos expansion (with a non-intrusive spectral projection) is used. Test cases with different laws are CP17 presented and demonstrate that second order expansions Optimizing In Situ Groundwater Remediation with are well-adapted to represent our quantities of interest. Engineered Injection and Extraction Pierre Sochala Groundwater remediation requires mixing in aquifers, BRGM which can be enhanced using engineered injection and ex- [email protected] traction (EIE), in which transient flow fields are induced using a sequence of injections and extractions of clean wa- Olivier P. Le Maitre ter at wells surrounding the contaminant plume. This pre- LIMSI-CNRS sentation uses a multiobjective evolutionary algorithm to [email protected] determine a set of EIE sequences that balance multiple objectives, such as maximizing the amount of reaction while minimizing the treatment solution required and the con- CP18 taminant mass extracted. Shear Banding in a Partially Molten Mantle Amy N. Piscopo We investigate the nonlinear behaviour of partially molten University of Colorado Boulder mantle material under shear. Numerical models of com- [email protected] paction and advection-diffusion of a porous matrix with a spherical inclusion are built using the automated code gen- Joseph R. Kasprzyk eration package FEniCS. The time evolution of melt distri- Department of Civil and Environmental Engineering bution with increasing shear in these models is compared The Pennsylvania State University to laboratory experiments that show high-porosity shear [email protected] banding in the medium and pressure shadows around the inclusion. Roseanna Neupauer University of Colorado Boulder Laura Alisic, John Rudge [email protected] Bullard Laboratories University of Cambridge [email protected], [email protected] David C. Mays University of Colorado Denver [email protected] Garth Wells Department of Engineering 88 GS13 Abstracts

University of Cambridge [email protected] [email protected]

Richard F. Katz, Sander Rhebergen CP18 University of Oxford Variational Methods for a Problem of Rate- and [email protected], [email protected] State-Dependent Friction Rate- and state-dependent (RS) friction is a standard CP18 model in geophysics. We consider a problem of RS fric- Fracture Indicators for the Localization of Frac- tion between an elastic body and a rigid foundation, the tures in Porous Medium weak form of which can be written as a coupling of variational equations (VEs). This problem is discretised in time, We are concerned with the determination of the location yielding elliptic VEs. We give some answers to the ques- and the permeability of fractures in a porous medium. We tion of existence and uniqueness of solutions and present a use a reduced, discrete fracture, flow model for the forward numerical algorithm based on Finite Elements and a fixed problem, and to solve the inverse problem we minimize a point iteration. least squares function evaluating the misfit between given pressure measurements and the calculated pressure. The Elias Pipping sought fractures are obtained iteratively using fracture in- Free University of Berlin dicators inspired by the idea of refinement indicators. The Mathematical Institute first numerical results are promising. [email protected] Fatma Cheikh Inria Paris-Rocquencourt CP18 [email protected] Bayesian Selection of Models for the Near Real- Time Earthquake Source Inversion Hend Ben Ameur We present results of quantitative Bayesianranking, under ENIT LAMSIN uncertainty, of kinematic earthquakerupture modelswith [email protected] respect to their ability to replicate recorded seismic data. This work on rigorously quantifying uncertainties in earth- Guy Chavent quake models is part ofour research on Bayesian near real- INRIA time earthquake source inversion, withthe long term ob- Universite Paris-Dauphine jective of helping to mitigate human and economical loss- [email protected] esin case of large earthquakes that possibly may generate tsunamis. Fran¸cois Clément Inria Paris-Rocquencourt Martin Mai [email protected] KAUST [email protected] Vincent Martin UTC Ernesto E. Prudencio [email protected] Institute for Computational Engineering and Sciences University of Texas at Austin Jean E. Roberts [email protected] INRIA Paris-Rocquencourt France Olaf Zielke [email protected] Division of Earth Science and Engineering King Abdullah University of Science and Technology [email protected] CP18 Heterogeneous Material Properties and Off-Fault Plastic Response in Earthquake Cycle Simulations CP18 An Immersed Interface Method for a 1D Poroelas- We have developed a numerical method for studying how ticity Problem with Discontinuous Coefficients heterogeneous material properties and off-fault plasticity affect the earthquake cycle. The fault is governed by a We introduce an immersed interface method (IIM) based nonlinear friction law and we discretize the medium using on a staggered grid for the 1D poroelasticity equations summation-by-parts finite difference operators and weak (Biot model) when the coefficients have discontinuities enforcement of boundary conditions. Our time stepping along material interfaces. The IIM uses standard finite dif- method is capable of handling multiple time scales, effi- ference method away from the interface and modifies the ciently integrating the system through both an interseismic numerical schemes near or on the interface to treat the ir- period and into earthquake rupture. regularities. We will derive and analyze the new method, and show some numerical results to confirm the theoretical Brittany A. Erickson error estimates. Stanford University [email protected] Son-Young Yi, Maranda Bean The University of Texas at El Paso Eric M. Dunham [email protected], [email protected] Department of Geophysics Stanford University GS13 Abstracts 89

MS1 MS1 High-Order and Low-Cost Stabilized Finite Ele- High Performance Adaptive Finite Element ment Solvers of Primitive Equations Method for Ocean Models We present in this talk an anlisis technique for some We present a computational framework based on parallel penalty stabilized solvers for the Navier-Stokes equations. adaptive FEM for ocean simulations. In order to achieve We consider low-order and high-order methods. The low- efficient representation of spatial scales we use adaptive order method is a pure penalty method, while the high- mesh refinement based on goal oriented a posteriori error order one is a projection-stabilized method. For this control. The framework can utilize massively parallel ar- method the projection operator is generalized to a locally chitecture to achieve the required model resolution. In our stable interpolation operator. We perform their numerical framework we treat the ocean as a turbulent incompress- analysis (stability and convergence) for unsteady flows. In ible fluid with variable density. We conclude this talk with this analysis, the stability is based upon specific inf-sup results on the ongoing work. conditions. No local orthogonality properties are needed for the projection-interpolation operator. The convergence Kaspar Müller is based upon the representation of the stabilizing terms School of Computer Science and Comunication by means of bubble finite element spaces. We include some Royal Institute of Technology KTH numerical tests for realistic flows. [email protected]

Tomas L. Chacon Rebollo Johan Hoffman University of Sevilla Royal Institute of Technology KTH Departamento de Ecuaciones Diferenciales y Análisis jhoff[email protected] Numérico [email protected] MS1 Boundary Conditions for the Inviscid Linear and MS1 Nonlinear Shallow Water Equations in Space Di- Large Eddy Simulation of the Quasi-Geostrophic mension One and Two Equations Motivated by problems of geophysical fluid mechanics, we This talk surveys some recent developments in the mod- derive a set of boundary conditions which are suitable for eling, analysis and numerical simulation of the quasi- the inviscid Shallow Water equations in space dimension geostrophic equations, which describe the wind-driven one and two. For the linearized two-dimensional equa- large scale ocean circulation. A new large eddy simulation tions, five different cases occur depending on the back- model, which is based on approximate deconvolution, is ground flow. proposed for the numerical simulation of the one-layer and two-layer quasi-geostrophic equations. A finite element dis- Roger M. Temam cretization of the streamfunction formulation of the quasi- Inst. f. Scientific Comput. and Appl. Math. geostrophic equations is also proposed. This conforming Indiana University discretization employs the Argyris element. Optimal error [email protected] estimates are derived. To the best of our knowledge, these are the first optimal error estimates for the finite element Arthur Bousquet, Aimin Huang discretization of the quasi-geostrophic equations. Numeri- Indiana University Bloomington cal experiments that support the theoretical estimates are Department of Mathematics also presented. [email protected], [email protected] Traian Iliescu Department of Mathematics Madalina Petcu Virginia Tech Universite de Poitiers [email protected] Laboratoire de mathematiques et applications [email protected]

MS1 MS2 Assessments of Discretizations of Convection- Dominated Scalar Problems Investigation of Pore-Scale Processes with the Vol- ume of Fluid Method Oceanic flow models include often convection-dominated scalar equations that model the transport of species (salin- Recent advances in computational facilities enable to simu- ity) or temperature. It is well known that stabilized dis- late two-phase flow with sub-pore resolution. These simu- cretizations are necessary for this kind of equations. This lations can be used to investigate the limits of the clas- talk presents a review about our recent experience with sical continuum approach and devise alternative Darcy stabilized finite element and finite difference methods. scale models. We present Navier-Stokes simulations of two- phase flow in complex geometry, using the Volume of Fluid Volker John method. Particular attention is paid to investigate finger- Weierstrass Institute for Applied Analysis and Stochastics ing, trapping, corner and film flow and their impact on the Research Group Numerical Mathematics and Sci. capillary pressure-saturation relationship. Computing [email protected] Andrea Ferrari Institute of Geophysics University of Lausanne [email protected] 90 GS13 Abstracts

Ivan Lunati S. Majid Hassanizadeh, Chris Spiers University of Lausanne Utrecht University [email protected] [email protected], [email protected]

MS2 MS2 Computation of Three-Phase Fluid Configurations Pore Scale Modeling of Two and Three Phase Flow at the Pore Scale by a Variational Level Set Method and Transport Through Porous Media: Where Are We and What Is to Be Done? We present a variational level set method to simulate capillary-controlled displacement of three fluids in 3D pore In this talk, I will review one pore scale modeling approach structures. The evolutionary level set equations for each from rock reconstruction to network extraction and subse- fluid is derived based on constrained energy minimization quent flow modeling using network modelling. Examples in the pore space, whereas contact angle formation are en- applying this approach in both two and three phase flow forced at the zero level sets in the solid. The method is ap- are discussed. In particular, the role of wettability of the plied to simulate equilibrium fluid configurations and the porous medium on multiphase flow physics will be studied. corresponding mean and principal interface curvatures in Future research directions in this area will be considered small subsets of 3D rock images. and the prospect for true prediction of macroscopic flow parameters is assessed. Johan Helland Senior Research Engineer Ken Sorbie International Research Institute of Stavanger Department of Petroleum Engineering [email protected] Heriot-Watt University [email protected] Espen Jettestuen Research Scientist International Research Institute of Stavanger MS3 [email protected] An Efficient Finite Volume Discretization to Sim- ulate Flows on 3D Discrete Fracture Network for Transient Flow Analysis and Equivalent Permeabil- MS2 ity Upscaling Kinetic Methods for Pore-Scale Simulations of Coupled Transport Problems The organization of natural fracture networks induces flow paths that control fluid flows in reservoirs. Taking into In our presentation we will present three-dimensional tran- account all heterogeneities is computationally very costly, sient pore-scale simulations based on Lattice-Boltzmann therefore, equivalent multi-porosity and multi-permeability models for coupled transport problems in porous media in- models have to be used. We present an innovating dis- cluding multiple phases and components, thermal effects cretization procedure allowing to simulate flow on 3D Dis- and interaction with electric and magnetic fields. After crete Fracture Networks involving over 100.000 fractures. an introduction of the basic kinetic models we will discuss We then demonstrate how to improve the computation of the suitability of our approach both in terms of modeling an equivalent permeability tensor by combining analytical accuracy as well as numerical efficiency. and clever-meshed numerical solutions. Manfred Krafczyk Matthieu Delorme, Nina Khvoenkova, Benoit Noetinger Tech. Univ. of Braunschweig IFP Energies nouvelles Germany [email protected], [email protected], [email protected] [email protected]

Maik Stiebler, Ying Wang Michel Quintard Inst. for Computational Modeling in Civil Engineering Institut de Mécanique des Fluides de Toulouse TU Braunschweig [email protected] [email protected], [email protected] MS3 MS2 An Interface Fault Model for Sedimentary Basin Pore-Network Modeling of Reactive Transport un- Simulation der (Variably-)Saturated Conditions We present an interface fault model which is compatible A modular pore scale model is developed to study reactive with basin modeling. It considers that the fault zone is and adsorptive transport under (variably-) saturated con- represented by two interfaces, one for each side of the fault ditions, looking at various applications. The continuum that is meshed conformal with its neighboring block and porous structure is discretize into a network of pore bod- that can move relatively to the other side. Combined with ies and pore throats, both with finite volumes. For each a Finite Volume discretisation, this approach leads to fault- pore element, transport of solute is calculated by solving fault fluxes across fault faces that do not match. Results the governing mass balance equations, while chemical reac- for one-phase and two phase flow are shown. tion of the fluid phase with reactive solid components may change the pore geometries. Isabelle Faille IFP Energies Nouvelles Amir Raoof France University of Utrecht, Netherlands [email protected] [email protected] GS13 Abstracts 91

Marie Christine Cacas, Sylvain Desroziers, Pascal Havé, metric. In the discretization of time, stepping needs to fran¸coise Willien, Sylvie Wolf adapt to the wide range of flow velocities. Here we present IFP Energies Nouvelles models of fractured rock where discretization is adapted to [email protected], [email protected], fracture geometry, fluid-pressure-error and flow speed. [email protected], [email protected], [email protected] Stephan K. Matthai Montan University of Leoben Leoben, Austria MS3 [email protected] Flow Modeling Techniques for Fractured Reser- voirs - Gridding, Discretization, and Upscaling MS4 Detailed procedures for constructing upscaled fracture Multiphase Flow, Deformation and Wave Propaga- models are presented. Fine-scale models are formed by tion in Porous Media combining sets of triangulated surfaces, and discretization is accomplished using discrete fracture modeling tech- Single and multiphase flows are determined by Lattice niques. Coarse cells are formed by agglomerating fine- Boltzmann Models and elastic deformations of the solid grid cells, and new flow-based upscaling techniques pro- matrix by Lattice Spring Models. These two codes are vide coarse-grid transmissibilities. The local pressure fields coupled by using a momentum exchange. Then, wave needed for upscaling are constructed using linear combi- propagation is addressed either by direct simulations or nations of (pre-computed) large-scale pressure solutions. homogeneization. A few comparisons with analytical so- Simulations of flow through 3D fractured reservoirs demon- lutions or results obtained by different numerical methods strate the accuracy of the proposed techniques. are given. Some applications to real porous media, possibilities and extensions of these codes are discussed. Mohammad Karimi-Fard Stanford Pierre Adler [email protected] Université Pierre et Marie Curie France Lou J. Durlofsky [email protected] Stanford University Dept of Petroleum Engineering Aliaksei Pazdniakou [email protected] Sisyphe Université Pierre et Marie Curie [email protected] MS3 Is Discrete-Fracture Modeling Helpful for Reser- voir Engineer? MS4 Mixed Mortar Methods for Flow in Heterogeneous Discrete fracture and matrix modelling and flow simulation Porous Media of detailed small-scale representation of heterogeneities are not routinely used for fractured reservoirs studies, even With the equation in mixed form, we use a nonoverlap- for upscaling purposes, to field-scale simulation with dual ping mortar domain decomposition method, which is effi- porosity approach. However new techniques and tools are cient in parallel if the mortar space is small. We define now available. Could such DFM models be of any use for formally first and second order multiscale mortar spaces the reservoir engineer? If so, in which situation, and how using homogenization. For locally periodic permeability, it impacts our workflow today and in the future? Practical the method achieves optimal order error estimates in the examples will illustrate our works in this domain. mesh spacing and heterogeneity period. Otherwise, numerical results show the method works well. It can be adapted Alexandre Lapene as a two-level solver for the fine-scale system. Energy Resources Engineering, Stanford. [email protected] Todd Arbogast Dept of Math; C1200 Olivier Gosselin University of Texas, Austin TOTAL E&P France [email protected] Imperial College [email protected] Zhen Tao Institute for Computational Engineering and Sciences Luc Pauget The University of Texas at Austin TOTAL E&P France [email protected] [email protected] Hailong Xiao ICES MS3 The University of Texas at Austin Discretizing Fractured Porous Media for Multi- [email protected] phase Flow Simulation

Adaptive discretization is key for physically realistic and MS4 efficient simulation of multiphase fluid flow through porous Theoretical and Computational Perspectives on rock with discrete fractures. For goal-based simulation, Chemical Enhanced Oil Recovery Processes where space-time accuracy is predefined by the user, spatial discretization errors need to be dealt with using an error In this talk, I will give a brief overview of some of the fun- 92 GS13 Abstracts

damental theoretical and computational problems in EOR [email protected], technology that are of interest to the speaker. Then I will [email protected] give some recent results on some of these problems obtained by the speaker and his collaborators. The research Gabriel Wittum to be presented has been made possible by a grant (NPRP Goethe Center for Scientiﬁc Computing 08-777-1-141) from the Qatar National Research Fund (a Goethe University Frankfurt member of The Qatar Foundation). [email protected] Prabir Daripa Texas A&M University MS5 Department of Mathematics A Uniﬁed Fe Approach for Wave Propagation in [email protected] Elastic Media - from Near Incompressibility to Acoustics

MS4 The CMU Quake group has been working on large-scale The Riemann Problem for Three-Phase Flow earthquake simulations using Hercules –an octree-based finite-element wave propagation simulator. This code is We focus on a particular system of two conservation laws based on trilinear displacement elements. One limitation which models immiscible flow in porous media relevant for is its inability to provide reliable results for low S- to P- petroleum engineering. The Riemann solutions are found wave velocity ratios. Here, we assess the performance of a for a range of initial conditions important in applications, quadratic displacement-based formulation versus that of a representing the injection of two fluids (water, gas) into a mixed displacement-pressure formulation for nearly incom- horizontal reservoir containing a third fluid (oil) to be dis- pressible and acoustic wave-propagation applications, and placed. Despite loss of strict hyperbolicity, the solutions explore their applicability to gravity waves. for each data exists and is unique. Also, it depends L1 continuously on the Riemann data. Such solutions always Jacobo Bielak display a lead shock involving one of the injected fluids and Carnegie Mellon University the fluid already present. There is a threshold solution sep- Department of Civil & Env. Eng arating solutions according to which of the injected fluids [email protected] is present in the lead shock. Frederico C. Furtado Haydar Karaoglu University of Wyoming Carnegie Mellon University Dept of Mathematics [email protected] [email protected] MS5 Arthur Azevedo High Order One-Step Pnpm Schemes on Unstruc- University of Brasilia tured Meshes for Hyperbolic Balance Laws [email protected] In this talk we present a new unified approach of general Aparecido de Souza PN PM schemes on unstructured meshes in two and three Federal University of Campina Grande space dimensions for the solution of time–dependent partial [email protected] differential equations, in particular hyperbolic conservation laws. The new PN PM approach uses piecewise polynomi- Dan Marchesin als uh of degree N to represent the data in each cell. For Instituto Nacional de Matematica Pura e Aplicada the computation of fluxes and source terms, another set of [email protected] piecewise polynomials wh of degree M ≥ N is used, which is computed from the underlying polynomials uh using a reconstruction or recovery operator. The PN PM method MS4 contains classical high order finite volume schemes (N =0) Modelling and Computation of Thermohaline and high order discontinuous Galerkin (DG) finite element Groundwater Flows methods (N = M) just as two particular special cases of a more general class of numerical schemes. Our method also We study salinity- and thermohaline-flow in fractured uses a novel high order accurate one–step time discretiza- porous media. We adopt two approaches: (i) the fraction, based on a local space–time discontinuous Galerkin tures are treated as thin flow subregions having the same predictor, which is also able to solve PDE with stiff source dimension as medium in which they are embedded; (ii) the terms. fractures are regarded as manifolds of reduced dimension. We discuss the validity of both approaches and, in the case Michael Dumbser of salinity-driven flow, investigate the deviations of the re- Universität Stuttgart sults determined by employing the Forchheimer correction Germany with those predicted by Darcy’s law. [email protected]

Alfio Grillo Dept. of Mathematical Sciences MS5 Polythecnic of Turin, Italy Large-Scale Bayesian Seismic Inversion alfi[email protected] We present a computational framework for solution of Dmitry Logashenko, Sabine Stichel discretized infinite-dimensional Bayesian inverse problems. Goethe Center for Scientific Computing We address several computational issues related to the Goethe University Frankfurt a.M. appropriate choice of prior, consistent discretizations, GS13 Abstracts 93

tractable treatment of the Hessian of log posterior, and Universität Basel scalable parallel MCMC algorithms for sampling the pos- [email protected] terior. We apply the framework to the problem of global seismic inversion, for which we demonstrate scalability to Michaela Mehlin 1M earth parameters, 630M wave propagation unknowns, University of Basel and 100K cores on the Jaguar supercomputer. [email protected] Omar Ghattas The University of Texas at Austin Teodora Mitkova [email protected] University of Fribourg [email protected] Carsten Burstedde Institut fuer Numerische Simulation MS5 Universitaet Bonn High-Performance 3D Numerical Simulations for [email protected] Seismic Scenarios: An Engineering Perspective Tan Bui-Thanh In spite of the progress in computational tools for seismic The University of Texas at Austin wave propagation, the vast majority of engineering studies [email protected] are still routinely performed using 1D approaches, relying on the assumption of vertical plane wave propagation in a James R. Martin horizontally layered soil. Although this is a rational ap- University of Texas at Austin proach for many engineering applications, it may provide Institute for Computational Engineering and Sciences unrealistic results when applied to earthquake ground mo- [email protected] tion prediction and to the generation of ground shaking maps in the vicinity of a seismic fault. Relying on a non- Georg Stadler conforming strategy, the SPEED high performance com- University of Texas at Austin puting code (SPectral elements in elastodynamics with Dis- [email protected] continous Galerkin) has been developed to study complex 3D models and provide the capability to simulate seismic wave propagation from the source to the structure. This Lucas Wilcox may open new perspectives to solve earthquake engineering Department of Applied Mathematics problems. Naval Postgraduate School [email protected] Roberto Paolucci Department of Structural Engineering Politecnico di Milano MS5 [email protected] High-Order Explicit Local Time-Stepping Methods for Wave Propagation Paola F. Antonietti, Ilario Mazzieri We propose high-order explicit local time-stepping (LTS) Politecnico di Milano schemes based either on classical or low-storage Runge- [email protected], [email protected] Kutta schemes for the simulation of wave phenomena. By using smaller time steps precisely where smaller elements Roberto Guidotti, Chiara Smerzini in the mesh are located, these methods overcome the bot- Dipartimento di Ingegneria Strutturale tleneck caused by local mesh refinement in explicit time Politecnico di Milano integrators. In (J. Diaz and M.J. Grote, Energy conserv- [email protected], [email protected] ing explicit local time-stepping for second-order wave equations, SIAM J. Sci. Comput., 31 (2009), pp. 1985–2014.), Marco Stupazzini explicit second-order LTS integrators for transient wave Munich RE motion were developed, which are based on the standard [email protected] leap-frog scheme. In the absence of damping, these time- stepping schemes, when combined with the modified equation approach, yield methods of arbitrarily high (even) or- MS6 der. To achieve arbitrarily high accuracy in the presence Hybrid Multiscale Finite-Volume Galerkin Method of damping, while remaining fully explicit, explicit LTS for Elliptic and Parabolic Problems methods for the scalar damped wave equation based on Adams-Bashforth multi-step schemes were derived in (M. The iterative multiscale finite-volume method can be re- J. Grote and T. Mitkova, High-order explicit local time- garded as a domain decomposition method with the partic- stepping methods for damped wave equations, J. Comput. ular advantage that conservative fluxes are obtained at any Appl. Math., 239 (2013), pp. 270–289). Here we propose iteration level. This is of great advantage e.g. for transport explicit LTS methods of high accuracy based either on ex- in heterogeneous porous media. Recently, enriched multi- plicit classical or low-storage Runge-Kutta (RK) schemes. scale methods have been proposed to improve robustness In contrast to Adams-Bashforth methods, RK methods are and along this line, here a hybrid multiscale finite-volume one-step methods; hence, they do not require a starting Galerkin (MSFVG) method is introduced. procedure and easily accommodate adaptive time-step selection. Although RK methods do require several further Patrick Jenny evaluations per time-step, that additional work is compen- Institute of Fluid Dynamics sated by a less stringent CFL stability condition. ETH Zurich [email protected] Marcus J. Grote 94 GS13 Abstracts

Davide Cortinovis MS6 ETH Convergent Non-Linear Upscaling for Multiphase [email protected] Flow and Transport in Porous Media Upscaling of nonlinear multiphase flow and transport prob- MS6 lems in porous media is challenging, but often necessary to Generalized Multiscale Finite Element Methods. lower computational cost. We propose a method that automatically upscales in the appropriate limiting flow regimes In this talk, we present a general approach called Gener- and acts as a preconditioner to the fine scale nonlinear alized Multiscale Finite Element Method (GMsFEM) for system otherwise. Communication between the numerical performing multiscale simulations for problems without scales is handled by physically based compression and re- scale separation over a complex input space. In the pro- construction operators. Further, fine scale computations posed approach, we present a general procedure to con- are automatically localized to the more demanding regions struct the offline space that is used for a systematic en- of the domain. richment of the coarse solution space in the online stage. In the online stage, for any input parameter, a multiscale Jan Skogestad, Eirik Keilegavlen space is constructed to solve the global problem on a coarse University of Bergen grid. We present various examples in the paper and some [email protected], [email protected] numerical results to demonstrate the effectiveness of our method. Jan M. Nordbotten Department of Mathematics Yalchin Efendiev University of Bergen Dept of Mathematics [email protected] Texas A&M University [email protected] MS6 Juan Galvis Multiscale Mortar Methods for Multiphysics Ap- Universidad Nacional de Colombia plications [email protected] We discuss a multiscale framework for multiphysics prob- Tom Hou lems based on mortar domain decomposition methods. The Clatech domain is decomposed into a series of subdomains (coarse [email protected] grid) with different physical processes, mathematical models, and numerical methods. The equations are discretized locally on a fine scale, while interface conditions are im- MS6 posed weakly on a coarse scale using mortar finite elements. Dynamic Upscaling/downscaling for Multi-Phase By eliminating the subdomain unknowns, the global prob- Flow in a Multiscale Finite Volume Framework lem is reduced to a coarse scale interface problem that is solved efficiently using a multiscale flux basis. Applications We propose an upscaling/downscaling method that is to Stokes - Darcy and porous media flow - geomechanics based on dynamic simulation of a model in which the accu- couplings are presented. racy of the upscaled model is continuously monitored via indirect error-measures. If the error measure is bigger than Ivan Yotov a specified tolerance, the upscaled model is updated with Univeristy of Pittsburgh approximate fine scale information that is reconstructed Department of Mathematics from a multiscale finite volume method. We apply adaptive [email protected] prolongation and restriction operators for flow and transport equations in constructing an approximate fine scale solution. MS7 Applications of Shaping Regularization in Geo- Seong H. Lee physical Inverse Problems Chevron ETC [email protected] Shaping regularization is a general framework for solving inverse problems. Instead of specifying an objective func- Hamdi Tchelepi tion for optimization, shaping requires a forward operator, Stanford University a backward (approximate inverse) operator, and a model Energy Resources Engineering Department shaping operator, which can be a projection of the esti- [email protected] mated model into the space of acceptable models. I will show several examples of using shaping regularization in geophysical inverse problems: data regularization, simulta- Ivan Lunati neous source separation, and seismic velocity estimation. University of Lausanne [email protected] Sergey Fomel University of Texas at Austin XWang [email protected] Stanford University [email protected]

Rouven Kunze UNIL [email protected] GS13 Abstracts 95

MS7 Media Flow and Transport Inversion of Large Scale Electromagnetic Data We present two non-overlapping domain decomposi- Abstract not available at time of publication. tion methods for solving heterogeneous time-dependent advection-diffusion problems in a mixed formulation: Eldad Haber a time-dependent Steklov-Poincaréoperatorwitha Department of Mathematics Neumann-Neumann preconditioner and a Schwarz wave- The University of British Columbia form relaxation method with optimized transmission con- [email protected] ditions. Thus, different time steps can be used in different subdomains adapted to their physical properties. We derive the formulations using a splitting approach. We show MS7 numerical results in 2D on a simplified test case suggested Full Waveform Inversion of Blended Data: Analysis by the nuclear waste disposal problems. of Multi-frequency Inversion Strategies Thi-Thao-Phuong Hoang One way to reduce the overall cost of waveform inversion INRIA Paris-Rocquencourt is via the adoption of blended or simultaneous sources, phuong.hoang thi [email protected] where multiple sources are simultaneously fired with random time delays. This can be achieved by assembling Jerome Jaffre multiple sources into super-shots. In the present study, INRIA-Roquencourt we examine the effect of different multi-frequency selection 78153 Le Chesnay cedex France strategies on the inversion of complex velocity models with Jerome.Jaff[email protected] data that simulate a simultaneous source acquisition. Mauricio D. Sacchi, Amsalu Y. Anagaw Caroline Japhet University of Alberta Paris 13 university, France [email protected], [email protected] [email protected]

Michel Kern MS8 INRIA Coupling Two-Phase Compositional [email protected] Porous-Medium and Free Flow Jean E. Roberts The numerical simulation of flow and transport phenom- INRIA Paris-Rocquencourt ena in porous media is quite often based on Darcy’s law, France whereas in free flow regions the Navier-Stokes model has [email protected] to be used. Of special interest are structures composed of a porous part and an adjacent free flowing fluid. So far, the coupling of free flow with porous medium flow has been MS8 considered only for a single-phase system. We extend this ”Heterogeneous Domain Decomposition Methods classical concept to two-component non-isothermal flow for Surface and Saturated/unsaturated Ground with two phases inside the porous medium and a single Water Flow” phase inside the free flow region. Our coupling concept also takes into account evaporation and condensation processes Our approach to the mathematical modelling of coupled at the interface. We discuss our new model and introduce surface and ground water flow is based on Richards equa- different coupling conditions. Moreover, some numerical tion and a clogging-type coupling to the shallow water examples illustrate the coupling between the two model equations or simple compartement models for surface wa- domains. ter. The seepage along river beds and lakes is described by Signorini-type boundary conditions. We will present Rainer Helmig Poincare-Steklov formulations of this heterogeneous prob- IWS, University of Stuttgart, Germany lem and an iterative solver of Robin-Neumann-type tak- Institut fur Wasserbau ing the multiple time scales of ground and surface water [email protected] flow into account. We present numerical experiments with model problems illustrating the basic properties of our ap- Klaus Mosthaf proach, such as mass conservation, as well as the perfor- Universitaet Stuttgart, IWS mance of our iterative scheme. [email protected] Ralf Kornhuber Katherina Baber FU Berlin Dept. of Hydromechanics Fachbereich Mathematik und Informatik University of Stuttgart [email protected] [email protected] MS8 Bernd Flemisch Multidimensional Coupling for Shallow Water University of Stuttgart, Germany Flows bernd.fl[email protected] The motion of water in a complex hydrodynamic config- uration is characterized by a wide spectrum of space and MS8 time scales. Consequently, the numerical simulation of a Space-Time Domain Decomposition for Porous hydrodynamic system of this type is characterized by a large computational cost. In the last years a lot of work 96 GS13 Abstracts

has been done concerning 1D-2D coupling. In this talk Los Alamos National Laboratory 3D-1D and 3D-2D coupling strategies will be introduced. [email protected]

Edie Miglio Politecnico di Milano (Italy) MS9 MOX, Dept. of Mathematics Coupling of Stokes and Darcy Flows using Dis- [email protected] continuous Galerkin and Mimetic Finite Difference Method MS9 We present a numerical method for coupling Stokes and A Multiscale Formulation Based on CVD-MPFA Darcy flows based on discontinuous Galerkin (DG) el- Schemes on Structured and Unstructured Grids ements for Stokes and mimetic finite difference (MFD) methods for Darcy. Both methods are locally mass conser- Families of Darcy-flux approximations have been developed vative and can handle irregular grids. The MFD methods for consistent approximation of the general tensor pres- are especially suited for flow in heterogeneous porous me- sure equation arising from Darcy’s law together with mass dia, as they provide accurate approximation for both pres- conservation. The schemes are control-volume distributed sure and velocity and can handle discontinuous coefficients (CVD) with flow variables and rock properties sharing the as well as degenerate and non-convex polygonal elements. same location in a given control-volume and are comprised We develop DG polygonal elements for Stokes, allowing for of a multipoint flux family formulation (CVD-MPFA). The coupled discretizations on polygonal grids. Optimal con- schemes are used to develop a CVD-MPFA based multi- vergence is obtained for the coupled numerical method and scale formulation applicable to both structured and un- confirmed computationally. structured grids in two-dimensions. Konstantin Lipnikov Michael G. Edwards Los Alamos National Laboratory Swansea University [email protected] School of Engineering [email protected] Danail Vassilev University of Exeter Elliot Parramore [email protected] Swansea University [email protected] Ivan Yotov Univeristy of Pittsburgh Department of Mathematics MS9 [email protected] Mimetic Finite Difference Methods and Virtual El- ement Discretizations for Porous Media Applica- tions MS9 Nonlinear Discretizations for Multi-Phase Flows in We present the family of mimetic finite difference meth- Porous Media ods and of virtual element discretizations and discuss how these approaches can be used to design efficient schemes We consider approaches to the design of a monotone to approximate flow and transport models in porous me- cell-centered finite volume discretization of convection- dia. The permeability tensor in the diffusive terms may be diffusion equations describing multiphase flows. The per- heterogeneous, full and anisotropic. These numerical tech- meability tensor may be heterogeneous, full and essen- niques can be applied to computational meshes of polygo- tially anisotropic. The conformal computational mesh is nal or polyhedral cells with very general shape, also non- assumed to consist of convex polygonal or polyhedral cells. conforming as the ones of the Adaptive Mesh Refinement The schemes possess the minimal stencil containing the (AMR) method and non-convex, and used to approximate closest neighboring cells only. The cornerstone of the ap- linear and non-linear models like the Richards equation. proaches is the nonlinear discretization of fluxes derived on faces of mesh cells, see Rus. J. Numer. Anal. Math. Gianmarco Manzini Modelling 27(4) 2012 and references therein. Los Alamos National Laboratory [email protected] Yuri Vassilevski, Kirill Nikitin Institute of Numerical Mathematics Russian Academy of Sciences MS9 [email protected], [email protected] Nonlinear Monotone Finite Volume Method for Richards Equation Kirill Terekhov The Richards equation is often used to model subsurface INM RAS flow in unsaturated media. We present a new nonlinear [email protected] finite volume method which guarantees the discrete maximum principle in every subdomain with homogeneous per- MS10 meability. In state-of-the-art methods the monotonicity is achieved by using the first order upwind of the relative Equal-order Finite Elements for Hydrostatic Flow permeability which decreases the accuracy of a method. Equations of the Ocean Our approach provides the second order of accuracy for Simulation of flow phenomena in the ocean and in other the pressure which is confirmed by numerical tests. large but relatively flat basins are typically based on Daniil Svyatskiy the primitive equations, which result from application of the hydrostatic approximation. We analyze such ”2.5- GS13 Abstracts 97

dimensional” systems and formulate stabilized ﬁnite ele- [email protected] ment schemes with equal-order interpolation. We show stability and give an a priori error estimate for several estab- Irina Rypina, Lawrence Pratt lished stabilized equal-order schemes, as pressure-stabilized Woods Hole Oceanographic Institution Petrov-Galerkin (PSPG), Galerkin least squares (GLS) and [email protected], [email protected] local projection schemes (LPS) which are extended here to the hydrostatic approximation. Mike Brown Malte Braack RSMAS Christian-Albrechts-Universit¨at zu Kiel Miami University [email protected] [email protected]

Madlen Kimmritz MS11 CAU Kiel Energy Stable Scheme for Shallow Water Equations [email protected] The subject of the talk is the numerical solution of shallow water equations with bathymetry. It is known that in some MS10 cases spurious oscillations in the numerical solution may Recent Results on Inviscid Limits for the Stochas- arise. This is due to the conservation properties of the tic Navier-Stokes Equations and Related Systems adopted numerical scheme. In this talks we are going to revise energy stable and energy preserving finite volume One of the original motivations for the development of scheme in order to end up with an oscillation free method. stochastic partial differential equations traces it’s origins Some preliminary numerical results are also presented. to the study of turbulence. In particular, invariant measures provide a canonical mathematical object connecting Mustafa Altinakar the basic equations of fluid dynamics to the statistical prop- NCCHE - University of Mississippi erties of turbulent flows. In this talk we discuss some recent [email protected] results concerning inviscid limits in this class of measures for the stochastic Navier-Stokes equations and other re- Edie Miglio lated systems arising in geophysical and numerical settings. Politecnico di Milano (Italy) MOX, Dept. of Mathematics Nathan Glatt-Holtz [email protected] Indiana University [email protected] Jaswant Singh NCCHE - University of Mississippi [email protected] MS10 Velocity-Pressure Proper Orthogonal Decomposi- tion Methods For Flow Problems MS11 Modelling Solute Transport in Meandering Chan- Proper Orthogonal Decomposition is one of the most suc- nels using a High-order DG Method cessful tools in the context of reduced-order modeling for flow problems modeled by incompressible Navier-Stokes A third-order accurate numerical method for the 2D shal- equations. The standard approach in combination with low water equations, inclusive of the convection-diffusion very common assumptions leads to a reduced-order model terms due to the streamlines curvature, is discussed. The (ROM) only for velocity. However, the need for compu- hydrodynamics and the behaviour of a passive contaminant tation of pressure is a given. In this talk, the numerical are analyzed, using recent advances in river mechanics and studies of some already existing pressure ROMs and of a novel findings in RKDG methods. The comparison with new one will be presented. selected laboratory data shows that good results can be obtained using relatively coarse grids, supporting the use Swetlana Schyschlowa of high-order methods in engineering practice. Weierstrass Institute for Applied Analysis and Stochastics [email protected] Valerio Caleffi, Alessandro Valiani University of Ferrara valerio.caleffi@unife.it, [email protected] MS10 An Ergodic Theory and Harmonic Analysis Based Method for Analyzing Ocean Flows MS11 Comparison Between Sph and Level Set Methods We consider an approach, called the ergodicity defect, for for Free Boundary Problems for Incompressible analyzing ocean flows. The ergodicity defect distinguishes Euler and Navier-Stokes Equations individual trajectories via their complexity, which in turn allows for the identification of Lagrangian coherent struc- A new finite difference ghost cell level set multigrid method tures. The approach combines the mathematical areas for the numerical solution of free boundary problems for of ergodic theory and harmonic analysis/wavelet theory. incompressible Euler and Navier-Stokes equations is pre- The advantages, practical uses, and disadvantages of the sented. The equations are discretized in primitive variable method are discussed and several examples are presented. on a fixed Cartesian grid. The free surface is taken into account by a level set function, which is evolved by the normal velocity of the fluid at the surface. The Poisson Sherry Scott equation on the pressure, obtained by the incompressibility Marquette University condition, is efficiently solved by multigrid. Applications 98 GS13 Abstracts

to some test problems will be presented. The numerical so- Olaf Ippisch lutions will be compared to those obtained by a smoothed Interdisziplinary Center for Scientific Computing particle hydrodynamic code, in which the incompressibility University of Heidelberg is replaced by a weakly compressible equation of state, with [email protected] a sound speed one order of magnitude larger than a typical flow velocity. The comparison shows a good agreement, and emphasizes the relative merits of the two approaches. MS12 A Discontinuous Galerkin Based Quasi-Linear Geo- statistical Approach Giovanni Russo University of Catania The quasi-linear geostatistical approach can be used to es- Department of Mathematics timate the spatial distribution of heterogeneous hydraulic [email protected] conductivity fields based on point-wise measurements of observable quantities. The accurate and efficient solution Armando Coco of steady-state solute transport problems is crucial for the Dipartimento di Geologia e Geofisica, UNIBA inversion. The discontinuous Galerkin method incorpo- [email protected] rates upwinding in a natural way, yielding a robust solver even in the convection dominated case. The benefits and Giuseppe Bilotta drawbacks as compared to the streamline diffusion method DMI, UNICT are discussed. [email protected] Adrian Ngo University of Heidelberg MS11 [email protected] Second-Order Finite Volume Schemes for Geophys- ical Shallow Water Flows with Dynamic Wet-Dry Ronnie L. Schwede Front Center for Applied Geoscience University of Tübingen We propose a revisiting of second-order finite volume [email protected] schemes for 2d shallow water equations. Schemes are based on a HLLC-type solver according to [Vila86], MUSCL re- Peter Bastian constructions and IMEX time schemes, [PaRu05]. The Interdisciplinary Center for Scientific Computing well-balanced property is obtained applying the method University of Heidelberg of [AuBr05]. We show the efficiency of the direct solver on [email protected] real type river flows. Numerical experiments enhance differences between first and second-order schemes both for Olaf A. Cirpka low-water flows and wet-fry front dynamics. Center for Applied Geoscience University of Tuebingen Frederic Couderc [email protected] CNRS & IMT [email protected] Olaf Ippisch Interdisziplinary Center for Scientific Computing Jerome Monnier, Jean-Paul Vila University of Heidelberg Mathematics Institute of Toulouse [email protected] [email protected], [email protected]

MS12 MS12 Parameter Estimation by Ensemble Kalman Filters Geostatistical Inversion under Transient Flow Con- with Transformed Data: Approach and Application ditions to Hydraulic Tomography Geostatistical inversion is a valuable tool for the assess- EnKFs have been converted to tools for parameter estima- ment of aquifer permeability. In previous implementations tion in groundwater applications. EnKFs provide optimal the assumption of a stationary flow field and the solution of parameter estimates only if all involved variables are multi- one adjoint problem per measurement were necessary. We variate Gaussian. To improve EnKFs, we apply nonlinear, present an extension of geostatistical inversion methods to monotonic transformations to the observed states, render- instationary flow regimes. This facilitates the treatment ing them univariate Gaussian. The transform resembles of variable boundary conditions (e.g. nearby rivers) and an implicit quasi-linearization. For illustration of the im- large data sets. Implementation in the software framework proved convergence, we present a first-time application of DUNE makes high-performance-computing and full paral- an EnKF to parameter estimation from 3-D hydraulic to- lelization available. mography in multi-Gaussian log conductivity fields.

Ole Klein Wolfgang Nowak Interdisciplinary Center for Scientiﬁc Computing titute for Modelling Hydraulic and Environmental Heidelberg University Systems [email protected] University of Stuttgart [email protected] Olaf A. Cirpka Center for Applied Geoscience Anneli Sch¨oniger University of Tuebingen Applied Geosciences [email protected] GS13 Abstracts 99

University of Tübingen MS13 [email protected] Heterogeneous Multiscale Methods for Two-Phase Flow with Rate-Dependent Extension Harrie Jan Hendricks Franssen Agrosphere (IBG-3) Abstract not available at time of publication. Forschungszentrum Jülich [email protected] Christian Rohde University of Stuttgart Department of Mathematics MS12 [email protected] Active and Passive Hydrogeophyscial Tomographic Surveys MS13 This talk discusses uniqueness, scale, resolution, and un- Instability Effects in Hysteresis Models for Porous certainty issues associated with modeling of flow through Media Flow geologic media. We advocate that stochastic interpretation of non-redundant hydrological data from active and We present various flow models for unsaturated porous me- passive tomographic surveys is the key to the future hy- dia. Our main interest is the gravity driven penetration of drological characterization. In conjunction with geophysi- a dry material, a situation in which fingering effects can cal monitoring of responses of the subsurface, hydrological be observed experimentally and numerically. The flow is tomographic surveys/stochastic joint interpretation could described by either a Richards or a two-phase model. The be the ultimate subsurface characterization methodology. important modelling aspect regards the capillary pressure relation which can include static hysteresis and dynamic Tian-ChyiJ.Yeh corrections. We report on analytical existence and insta- The University of Arizona bility results for the corresponding models and present nu- [email protected] merical calculations. We show that fingering effects can be observed in various models and discuss the importance of the static hysteresis term. MS13 Non-Equilibrium Capillarity Effect at Different Ben Schweizer Scales TU Dortmund Fakultät für Mathematik Various studies have shown that capillary pressure is not [email protected] only a function of saturation but also depends on its time rate of change. This is known as the dynamic capillarity effect. We present an overview of computational and ex- MS14 perimental studies on dynamic coefficient and show that Convection Driven by Internal Heating its value increases with the size of domain of interest. We provide an explanation for this correlation and discuss con- Two-dimensional direct numerical simulations are consequences of scale-dependence of dynamic coefficient for ducted for convection sustained by uniform internal heat- large-scale field situations. ing in a horizontal fluid layer. Top and bottom boundary temperatures are fixed and equal. Prandtl numbers range from 0.01 to 100, and Rayleigh numbers (R)areup Majid Hassanizadeh 5 University of Utrecht to 5 · 10 times the critical R at the onset of convection. [email protected] The asymmetry between upward and downward heat fluxes is a quantity without analog in classical Rayleigh-Bénard R Simona Bottero convection and is found to be non-monotonic in .Scal- Delft University of Technology ing arguments previously applied to the Rayleigh-Bénard Faculty of Civil Engineering and Geosciences Nusselt number are applied to the mean temperature. [email protected] David Goluskin Mathematics Department MS13 Columbia University [email protected] Phase Transitions Across Scales: Discrete and Con- tinuum Models Edward Spiegel It is known that phase transitions occur differently in bulk Department of Astronomy fluid than in confined porespace, and constitutive relation- Columbia University ships at porescale differ from those at macroscale. At [email protected] porescale there are discrete and continuum models, and at macroscale there are continuum models. However, there are no methods of formal upscaling for nonsmooth non- MS14 linear processes representing phase transitions across these Effects of Velocity and Temperature Boundary scales. We discuss computational models that bridge the Conditions in Turbulent Thermal Convection scales for phase transitions in methane hydrate, coalbed methane, and ground freezing modeling. We report on results of high resolution direct numerical simulations of two-dimensional Rayleigh-Bénard con- 10 Malgorzata Peszynska vection for Rayleigh numbers up to Ra =10 in order Department of Mathematics to study the influence of both temperature and velocity Oregon State University boundary conditions on turbulent heat transport. In the [email protected] first scenario, while imposing the no-slip velocity bound- 100 GS13 Abstracts

ary condition, we consider the extreme cases of fixed heat MS14 flux and fixed temperature Both cases display identical High Rayleigh Number 2D Rayleigh-Benard Con- heat transport at high Rayleigh numbers fitting a power vection law Nu ≈ 0.138 × Ra.285 above Ra =107. The findings are compared and contrasted with results of recent Although there is a significant understanding of the ulti- three-dimensional simulations and experiments. In the mate regime of Rayleigh-Benard convection, there are still second scenario we consider the setup originally consid- some open questions regarding the transition towards it ered by Rayleigh for calculating conditions for the onset of and the logarithmic boundary layers associated with it. We thermal convection, fixed temperature boundary condition report the results of our 2D DNS that have contributed to with free-slip velocity boundary conditions. Surprisingly, understanding the transition to the ultimate regime as well at high Rayleigh numbers a strong shear flow develops with as the encountered difficulties pushing our code towards periodic ’bursting’ of the thermal boundary layers. We’ll high Ra. discuss this phenomena and its impact on the heat transport. Erwin van der Poel, Rodolfo Ostilla Monico University of Twente Hans Johnston [email protected], [email protected] Department of Mathematics & Statistics University of Massachusetts Amherst Roberto Verzicco [email protected] University of Roma [email protected] David Goluskin Mathematics Department Detlef Lohse Columbia University University of Twente [email protected] [email protected]

Da Zhu Department of Earth, Atmospheric and Planetary Science MS15 MIT Scalable Coupling of Surface-Subsurface Water [email protected] Flows

Glenn Flierl Recent advances in computing architectures push towards Department of Earth, Atmospheric and Planetary Science the development of computational codes with an optimal Massachusetts Institute of Technology scaling. We have developed a coupled surface-subsurface [email protected] water ﬂow model that solves the governing equations with discontinuous Galerkin and control volume ﬁnite element methods. Our model uses an explicit time discretisation Charles R. Doering for the 3D Richards equation and hence achieves optimal University of Michigan scaling both weakly and strongly. A wide range of test Mathematics, Physics and Complex Systems problems have been solved to highlight the model proper- [email protected] ties.

Thomas De Maet MS14 Université catholique de Louvain Large Scale Patterns in Convection: from [email protected] Rayleigh-Benard, through Prandtl problem, to moist atmospheric convection Emmanuel Hanert Large scale patterns formation in dry and moist convection UCLouvain scenarios are addressed in this paper. The first part of the Earth and Life Institute - Environmental Sciences talk will be devoted to the case of clustering of plumes [email protected] in Rayleigh-Benard convection: through a two-scale process, kinetic energy is transferred mainly to low horizontal MS15 wave numbers while the sizes of individual plumes remain on the scale of the boundary layer thickness. Again in a Evaporation from Porous Media Influenced by At- direct numerical simulation framework, the study of the mospheric Processes Prandtl problem is addressed as a simplified model of dry Evaporation from porous media into the ambient air in- atmospheric convection, kept in statistically stationary ra- volves varios interacting processes and depends on a mul- diativeconvective equilibrium. Finally the emergence and titude of properties of the fluids, of the porous medium temporal evolution of large-scale spatial-temporal oscillat- and of the flow regime. The evaporation rate can be lim- ing modes in deep moist convection, for an atmosphere ited from the porous-medium side, e.g. due to limited in radiative-convective equilibrium. To this end, we use water supply by capillary forces or by diffusion through cloud-resolving numerical simulations of the convective at- the tortuous porous medium, or from the free-flow side mosphere at very high resolution and on a very large do- involving the transfer through a boundary layer. Model- main, using WRF model in LES mode. ing such complex system on the scale of representative el- Antonio Parodi ementary volumes (REVs) is a challenging task. We have Istituto di Scienze dell’Atmosfera e del Clima developed a model for the coupled simulation of a two- [email protected] phase porous medium flow (Darcy) and a laminar free flow (Stokes) under non-isothermal conditions. Possible extensions and simplifications to the developed laminar coupled GS13 Abstracts 101

model are discussed. form of the compressed data (based on the Stieltjes-Krein- Marchenko-Gelfant-Levitan method) speeds up Gauss- Rainer Helmig Newton iterations and improves quality of inversion. We IWS, University of Stuttgart, Germany illustrate our approach using synthetic 2.5D CSEM exam- Institut fur Wasserbau ples of hydrocarbon reservoirs in the marine environment. [email protected]

Thomas Fetzer Aria Abubakar Department of Hydromechanics Schlumberger Doll Research Univerity of Stuttgart [email protected] [email protected] Liliana Borcea Klaus Mosthaf Rice University Universitaet Stuttgart, IWS [email protected] [email protected] Vladimir L. Druskin,TarekHabashy Schlumberger-Doll Research MS15 [email protected], [email protected] Transition Region Model for Coupling Free Flow and Porous Medium Systems Alexander Mamonov UT Austin A transition region model for coupling single-phase two- : [email protected] component free ﬂow and two-phase two-component porous medium systems is developed by means of the thermodynamically constrained averaging theory (TCAT) approach. Valeria Simoncini The model is averaged in the direction normal to the Universita’ di Bologna boundaries of the free ﬂow and porous medium domains [email protected] being joined. Unlike sharp interface approximations, the TCAT transition region model resolves the storage and Mikhail Zaslavsky transport of mass, momentum and energy. Schlumberger-Doll Research [email protected] Iryna Rybak Universitaet Stuttgart, IANS [email protected] MS16 Regularization for Nonlinear Inverse Problems William G. Gray Department of Environmental Sciences and Engineering, Ill-posed nonlinear inverse problems require regularized so- University of North Carolina, Chapel Hill lutions, and typically this is done iteratively with Gauss- [email protected] Newton or Levenburg-Marguart methods. The discrepancy principle determines regularization parameters by applying a χ2 test, and here we will extend that idea to show that Cass T. Miller a χ2 test can be applied at each iterate of these nonlinear University of North Carolina methods. This test is used to estimate regularization pa- Chapel Hill rameters for nonlinear problems, and results will be shown casey [email protected] on benchmark problems in Geophysics.

Jodi Mead MS15 Boise State University Numerical Assessment of Different Discretizations Department of Mathematics for Stokes-Darcy Coupling [email protected] There are a number of options in the numerical simulation of the Stokes-Darcy problem. This talk presents studies of Chad Hammerquist different approaches for applying interface conditions and Sensty Group, Inc. the use of inf-sup stable and stabilized finite elements for [email protected] the mixed (dual) Darcy problem. Ulrich Wilbrandt MS16 Free University of Berlin 3D Forward and Inverse Modeling of Geo- Department of Mathematics and Computer Science Electromagnetic Fields [email protected] The inversion of geo-electromagnetic data is a nonlinear and ill-posed problem. In large-scale settings it is gen- MS16 erally solved iteratively using regularized Newton, Quasi- Solution of transient CSEM problems in model re- Newton, Gauss-Newton or all-at-once approaches. The for- duction framework ward problem is demanding because of complex geometries imposed by natural environments, the different physical be- We suggest general model reduction framework for the haviors of the fields, a multitude of source configurations solution of large scale multidimensional transient inverse and many right-hand sides. We formulate the problem in problems. Rational Krylov subspace model reduction ac- the time and frequency domains using Nédélec finite ele- celerates the solution of the forward problem and efficiently ments on unstructured grids and apply Krylov subspace compresses the data in time and space. A nonlinear trans- 102 GS13 Abstracts

techniques to reduce the numerical costs. Universitat Polit`ecnica de Catalunya, Barcelona, Spain [email protected] Klaus Spitzer, Ralph-Uwe Boerner Institute of Geophysics and Geoinformatics TU Bergakademie Freiberg MS17 [email protected], Mathematical and Numerical Delicacies in Coupled [email protected] Ocean-atmosphere Simulations

Michael Eiermann Atmospheric and oceanic simulation models are widely TU Bergakademie Freiberg used for weather, general circulation, and climate. In Institut für Numerische Mathematik und Optimierung this context, the simulated flows are spectrally broad band [email protected] across global to micro scales. A full representation in different scales is uncomputable and numerical models contain Oliver G. Ernst parameterizations to account for unresolved processes. The TU Bergakademie Freiberg mathematical formulation of parameterization schemes is Fakultaet Mathematik und Informatik devised empirically, and often impairs the regularity of the [email protected] solutions. This problem is even more acute when considering coupled ocean-atmosphere models. In this talk, it is showed that this complexity has to be taken into account MS16 to devise mathematically consistent and efficient coupling Joint Inversion in Poroelasticty algorithms. This problem is here addressed from the point of view of Schwarz-like domain decomposition methods. Remote sensing and geodetic measurements are providing Using a hierarchy of examples, from highly simplified to a wealth of new, spatially-distributed, time-series data that fully-realistic cases, the delicacies associated with ocean- promise to improve the characterization of the subsurface atmosphere coupling are illustrated both theoretically and and the monitoring of pressure transients due to fluid in- numerically. jection and production. We formulate a Bayesian inverse problem to infer the permeability distribution in a quasi- Florian Lemarié static poroelastic model from the joint inversion of time- Institute of Geophysics and Planetary Physics series surface deformation and well pressure measurements, UCLA Dept ofAtmospheric and Oceanic Sciences and compare different methods to characterize the poste- fl[email protected] rior probability density of the permeability. Georg Stadler MS17 University of Texas at Austin An Overview of Coupling Strategies between [email protected] Ocean and Atmosphere in Earth System Models Earth system models are used to study climate variabil- Marc A. Hesse ity from decades to millennium. Historically, they have University of Texas been built from several components : ocean, atmosphere, Department of Geological Sciences sea-ice, etc. Each component comes from a scientific com- [email protected] munity. It is validated with fixed boundary conditions. Coupling consists in exchanging boundary conditions. To- Noemi Petra benefit from the communities expertise, initial methods Institute for Computational Engineering and Sciences minimize scientific and technical modifications in the com- (ICES) ponents. This review considers existing coupling strategies The University of Texas at Austin under the constraints brought by the physics, numerics and [email protected] informatics.

Omar Ghattas Olivier Marti The University of Texas at Austin Institut Pierre Simon Laplace [email protected] [email protected]

Sophie Valcke MS17 CentreEuropéen deRecherche et deFormationAvancée Coupling Navier-Stokes and Darcy Equations: enCalc Modeling and Numerical Methods [email protected] We present two possible methods to compute the finite- elements approximation of a Navier-Stokes/Darcy prob- MS17 lem to model filtration processes through porous media. Domain Decomposition for Poroelasticity and Elas- First, using suitable continuity conditions, we transform ticity with DG Jumps and Mortars the coupled problem into an equivalent one on the interface separating the fluid from the porous medium. Then, We couple a time-dependent poroelastic model in a region adopting an optimal-control approach, we couple the two with an elastic model in adjacent regions. We discretize sub-problems avoiding relying on any interface conditions. each model independently on non-matching grids and we We compare these approaches theoretically and on some realize a domain decomposition on the interface between test cases of physical relevance. the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each Marco Discacciati time step, the computation in each subdomain can be per- Laboratori de Càlcul Numèric formed in parallel. In addition, by extrapolating the dis- GS13 Abstracts 103

placement, we present an algorithm where the computa- Laboratory LJLL tions of the pressure and displacement are decoupled. We [email protected] show that the matrix of the interface problem is positive definite and establish error estimates for this scheme. MS18 Vivette Girault Soil Moisture Dynamics and Rain Interarrival University of Paris VI Times [email protected] Soil moisture data taken down to two meters has been Gergina Pencheva used for assessing the relations between the vertical dis- University of Texas at Austin cretization and rain interarrival times. A one dimensional [email protected] Richards equation solution provided the tool for also evaluating the effects of hysteresis in the soil water retention Mary F. Wheeler curve. A statistics of soil moisture time variations can be Center for Subsurface Modeling, ICES related to the pdf of interarrival times. University of Texas at Austin Stefano Ferraris [email protected] University of Turin [email protected] Tim Wildey Optimization and Uncertainty Quantification Dept. Sandia National Laboratories MS18 [email protected] A Non Linear Correction and Maximum Principle for Diffusion Operators with Hybrid Schemes and Discrete Dual Finite Volume Schemes MS18 Comparison of DDFV and DG Methods for Flow In the framework of nuclear waste disposal simulation, in Anisotropic Heterogeneous Porous Media we are interested in a transport model in porous media which can be described by a convection-diffusion equation. We consider unsteady single-phase flows modeled by the Recently, nonlinear finite volume schemes have been pro- Richards’ equation. We compare Discrete Duality Finite posed to discretize diffusion operators. For these meth- Volume and Discontinuous Galerkin schemes applied to ods, discrete maximum principle has been obtained for dis- discretize the diffusive term. Backward Differentiation For- torted meshes or highly anisotropic diffusion tensors. In mula of second order is used for the time stepping method. the present work, we extend this technique to the class Accuracy and robustness of these two types of schemes are of hybrid schemes and to the discrete dual finite volume tested and compared on various test cases, especially in methods. We show that this correction is equivalent to the anisotropic heterogeneous media. original scheme with a modified flux which is consistent. We give a few words about the coercivity of the modi- Vincent Baron fied algorithm. Finally, we show that the new method is UniversitédeNantes nonoscillating. Using an analytical solution, we show the Laboratoire de Mathématiques Jean Leray robustness and the accuracy of this algorithm in compari- [email protected] son with results obtained by linear schemes which do not satisfy the minimum principles on this test. Yves Coudiere INRIA Christophe Le Potier [email protected] CEA Gif sur yvette Pierre Sochala [email protected] BRGM [email protected] Konstantin Lipnikov Los Alamos National Laboratory [email protected] MS18 Non Linear Finite Volume Schemes For the Heat Equation in 1D MS19 Numerical Analysis of a Smagorinsky LES Model Many solutions exist for the numerical approximation of for Primitive Equations diffusive equations on general unstrutured grids. But if one needs high order and the preservation of the maxi- This work deals with the development of efficient numer- mum it becomes quite challenging. In particular the non ical solvers for the Primitive Equations of the ocean in linear techniques used for hyperbolic equations cannot be turbulent regime. We derive the numerical approximation used without strong modifications. I will review recent ad- of a reduced model by the Smagorinsky turbulence model vances in the understanding of the mathematical and nu- that includes stabilization of the pressure discretization by merical structure of this problem: in particular I will detail a penalty technique. We perform the numerical analysis of a 1D example (based on multiD Le Potier’s Finite Volume this discretization (stability, convergence, error estimates), schemes) where high order (third order in practice in 1D) obtaining error estimates of at most first order in natural and preservation of the maximum principle are obtained norms, due to the penalty structure of the Smagorinsky together. eddy viscosity. We finally perform some numerical tests for the Primitive and Navier-Stokes equations, that con- Bruno Despres University Paris VI 104 GS13 Abstracts

firm the theoretical convergence expectations. University of Miami/RSMAS [email protected] Macarena Gomez Marmol Universidad de Sevilla Andrew Poje [email protected] CUNY / College of Staten Island [email protected] MS19 Lagrangian Tools and the Assessment of the Pre- Bruce Lipphardt dictive Capacity of Geophysical Data Sets SMSP, University of Delaware, Newark DE 19716 [email protected] We examine, with recently developed Lagrangian tools, al- timeter data and numerical simulations obtained from the Brian Haus HYCOM model in the Gulf of Mexico. Our data corre- University of Miami spond to the months just after the Deepwater Horizon [email protected] oil spill in the year 2010. Our Lagrangian analysis provides a skeleton that allows the interpretation of transport Gregg Jacobs routes over the ocean surface. The transport routes are NRL further verified by the simultaneous study of the evolu- [email protected] tion of several drifters launched during those months in the Gulf of Mexico. We find that there exist Lagrangian struc- M. Josefina Olascoaga, Edward Ryan, Guillaume Novelli tures that justify the dynamics of the drifters, although the University of Miami agreement depends on the quality of the data. We discuss [email protected], [email protected], the impact of the Lagrangian tools on the assessment of [email protected] the predictive capacity of these data sets. Carolina Mendoza Angelique C. Haza Universidad Politécnica de Madrid RSMAS, University of Miami Spain [email protected] [email protected] Denny Kirwan, Jr. Ana M. Mancho University of Delaware Instituto de Ciencias Matematicas [email protected] Consejo Superior Investigaciones Cientificas [email protected] MS19 Denny Kirwan Multi-Phase Air-Sea Interface Model University of Delaware We have implemented a model of the air-sea and air-oil [email protected] interface with surface tension using a VOF multi-phase CFD model. Under hurricane conditions, the interface was Stephen Wiggins disrupted by Kelvin-Helmholtz instability, forming two- University of Bristol phase transition layer. Experiments with imposed short [email protected] wavelets revealed streamwise coherent structures and tear- ing of wave crests, formation of water sheets and spume. The numerical simulation provided an estimate for the gas MS19 phase hydrocarbons flux from the ocean to the atmosphere Grand LAgrangian Deployment (GLAD): Optimal under hurricane conditions. Launch Strategies for Dispersion Near the Deep- water Horizon Oil Spill Site Alex Soloviev Oceanographic Center Initial dispersion, residence time, and advective pathway Nova Southeastern University results obtained from the nearly simultaneous deployment [email protected] of some 300 surface drifters in the vicinity of the DwH oil spill in the DeSoto Canyon are reported. The goal of the GLAD experiment was to characterize, with unprece- MS19 dented statistical significance, multi-point and multi-scale The Search for Lagrangian Coherent Structures in dispersion properties of the flow in the region of the DwH Coastal Areas: Results from the Gelato 2012 Ex- spill site including demarcation of the advective pathways periment in the Gulf of Naples between the Canyon and larger-scale flow features in the Gulf. GLAD was designed and executed to consist of op- Abstract not available at time of publication. timal launch templates needed for dispersion calculations. For the initial time period considered, drifter motion was Enrico Zambianchi characterized by large amplitude inertial motions, over- Department of Science and Technology all strong topographic control, and significant indications Parthenope University, Napoli, Ital of interior control by frontal dynamics on 1-5 km scales. [email protected] Very limited exchange, either across-shelf or with nearby mesoscale features, was observed and residence times in the Canyon typically exceeded one week with many drifters re- MS20 maining there for more than 21 days. Absolute and Relative Permeability for Water-wet Systems Calculated in the Presence of Micro- (un- Tamay Ozgokmen GS13 Abstracts 105

resolved) Porosity discussed.

Abstract not available at time of publication. Pavel Tomin Premier Assistant (Postdoc) Christoph Arns University of Lausanne School of Petroleum Engineering [email protected] The University of New South Wales [email protected] Pavel Tomin PhD Student MS20 MIPT [email protected] Pore Geometry: Film Menisci Motion and Throats

We discuss two related problems in the motion of fluids Ivan Lunati through porous media. The first is the motion of the University of Lausanne arc-menisci governing wetting films in channel cross sec- [email protected] tions. In the second we address the question ”what is a throat” and demonstrate the importance of this question once porosity rises above 20%. MS20 Volume of Fluid Direct Numerical Simulations of W. Brent Lindquist Invasion of 3D porous media Applied Mathematics and Statistics, Stony Brook University We shall present the Volume of Fluid method with the [email protected] height function method for surface tension, and discuss contact angle implementations in the Gerris Flow Solver Daesang Kim code. Then we show some example direct numerical sim- Applied Mathematics and Statistics ulations solving the Navier-Stokes equations in 3D porous Stony Brook University media on a parallel architecture. We discuss accuracy and [email protected] scalability issues. Stephane Zaleski Joo-Won Kim Universite Pierre et Marie Curie Stony Brook University [email protected] [email protected] Igor Bondino MS20 Geoccience Research Centre, Total E&P UK [email protected] Pore Scale Coupling of Fluid and Solid Mechan- ics for Simulation of Infiltration of Fines in Porous Media Bertrand Lagrée Université Pierre et Marie Curie Due to heterogeneity, standard constitutive relationships Total and models yield poor predictions for flow and rock prop- [email protected] erties of the porous media infiltrated by fines. We couple computational fluid dynamics and discrete element modeling to simulate the particulate flow through porous me- MS21 dia. Pore scale simulations allow for visualization and A Finite Element Optimization Method for Simu- understanding of clogging processes while varying parti- lating Discrete Fracture Network Flows cle/grain size ratio, fluid viscosity, flow rate and porosity. Further, velocity fields are integrated into a distinctly We investigate a new numerical approach for the computa- non-monotonic permeability-porosity/(depth of penetration of 3D flows in a discrete fracture network that does not tion) relationship. require conforming discretization of PDEs on complex 3D systems of planar fractures. The discretization within each Masa Prodanovic, Maryam Mirabolg fracture is performed independently of the discretization of University of Texas at Austin the other fractures and of their intersections. Independent Department of Petroleum and Geosystems Engineering meshing process within each fracture is a very important [email protected], [email protected] issue for large scale simulations, making easier mesh generation. Simulations will be shown to prove the viability of the method. The resulting approach can be naturally MS20 parallelized for dealing with systems with a huge number Hybrid Multiscale Finite Volume Method for Two- of fractures. Phase Flow trough Porous Media Stefano Berrone We present a hybrid multiscale algorithm that couples Politecnico di Torino Darcy- and pore-scale descriptions of two-phase flow [email protected] trough porous media. The Darcy-scale problem is formulated using the Multiscale Finite Volume method, which Sandra Pieraccini allows adaptive reconstruction of fine-scale details. At pore Dipartimento di Matematica scale we solve the Navier-Stokes equations in combination Politecnico di Torino, Italy with Volume Of Fluid method. The results of the hybrid [email protected] simulations are compared with direct pore-scale solutions for several flow regimes and the limits of Darcy’s law are Stefano Scialo‘ 106 GS13 Abstracts

Politecnico di Torino MS21 Dipartimento di Scienze Matematiche DFM Modelling for Non-Matching Fracture and [email protected] Matrix Grids: Pressure Continuity and Boundary Conditions MS21 Fractured porous-media systems are simulated, where the Coupled Flow Model and Simulation in 3D Porous- characteristic flow behavior depends on both the fractures fractured Media and the matrix. A structured rock-matrix grid is coupled with an independent, arbitrarily orientated fracture- Taking into account water and solute exchanges between network grid of codimension one that leads to discontin- porous and fractured media is of great interest in geological uous solutions across the fractures which are handled by applications. The coupled porous-fractured flow equations an XFEM approach. Discontinuities also occur at fracture and their discretization by a Mixed Hybrid Finite Element crossings. A consistency condition which can handle arbi- Method are presented as well as the derived linear system. trary crossings is presented as well as consistent boundary An appropriate mesh generation is proposed to deal with conditions for fractured boundaries. the complexity involved by randomly generated fracture networks. Numerical experiments are shown, that provide Nicolas Schwenck flow fields for forthcoming transport simulations. University of Stuttgart [email protected] Thomas Dufaud INRIA-Rennes, France Bernd Flemisch [email protected] University of Stuttgart, Germany bernd.fl[email protected] Jocelyne Erhel INRIA-Rennes, France Barbara Wohlmuth Campus de Beaulieu Technical University of Munich [email protected] [email protected]

G´eraldine Pichot Helmig Rainer INRIA-Rennes, France University of Stuttgart Campus de Beaulieu [email protected] [email protected]

MS21 MS21 A Multiscale Model for Network Flow Embedded Reduced Models for Flow in Networks of Fractures in Porous Media

Subsurface flow is influenced by the presence of faults and In this talk, we consider the coupling between two diffusion- large fractures which act as preferential paths or barriers. reaction problems and two transport equations, one defined Several models have been proposed to handle fractures in a in a three-dimensional domain Ω ⊂ R3, the other in a one- porous medium as objects of co-dimension 1. In this work dimensional subdomain Λ ⊂ Ω, respectively. The math- we consider the case of a network of intersecting fractures, ematical analysis of such problems must be handled with with the aim of deriving physically consistent and effective care, because the coupling between Λ and Ω is established coupling conditions at the intersection between fractures. by measure terms. Finally we describe, how this model This new model accounts for the angle between fractures can provide the basis for a multiscale analysis of processes at the intersections and allows for jumps of pressure across occuring in the context with natural gas production by hy- the intersection. This permits to describe the flow more ac- draulic fracturing. curately than models that impose pressure continuity when fractures have different properties. The main mathematical Barbara Wohlmuth properties of the model are analysed. We consider a numer- M2, Centre for Mathematical Sciences, ical discretisation where fractures may be non-matching at Technische Universität München, Germany the intersection to increase the flexibility of the method [email protected] in the case of complex geometries characterized by a high number of fractures. Tobias Köppl Luca Formaggia Technische Universität München, Germany Department of Mathematics [email protected] Politecnico di Milano, Italy [email protected] MS22 An Efficient Numerical Method for ASP Flooding Alessio Fumagalli in Tertiary Oil Recovery MOX, Department of Mathematics Politecnico di Milano, Italy In this talk, we present a new efficient, high order accurate [email protected] high performance numerical method for solving a coupled highly nonlinear system of partial differential equations Anna Scotti arising in the context of the fractional flow model of Alkali- Politecnico di Milano Surfactant-Polymer flooding of oil reservoirs. The method [email protected] is based on the use of an extended FEM elliptic solver, an implicit-time linearized FDM, and level set formulation. We will present numerical results using this method. The GS13 Abstracts 107

research reported here has been made possible by a grant MS22 (NPRP 08-777-1-141) from the Qatar National Research Optimal Flux Allocation and Control of Volume Fund (a member of The Qatar Foundation). The state- Errors in Streamline-Based Flow Simulation ments made herein are solely responsibility of the authors. Advection dominated porous media flow can be solved efficiently by transporting components along a time-varying Sourav Dutta streamline grid and accounting for non-advective transport Texas A&M University on the underlying Eulerian grid using operator splitting. In [email protected] this work, we investigate the flux allocation to individual streamlines and the resulting volume errors between the Prabir Daripa streamline and Eulerian grids. We present a framework Texas A&M University for balancing these errors using optimization strategies in- Department of Mathematics volving the number of streamlines and distribution of well [email protected] fluxes to streamlines. Anna Nissen MS22 Energy Resources Engineering A Mixed Approach ”Pore-Network Model/Direct Stanford University Numerical Simulation” to Simulate Multiphase [email protected] Flow Processes Marco Thiele Many petroleum or chemical engineering processes involve Streamsim Technologies/Stanford University multiphase flows in porous media with interface dynamics [email protected] preventing the use of classical quasi-static network models. We develop mixed models involving two distinct modeliza- Margot Gerritsen tions : a classical pore-network approach, coupled locally, Dept of Petroleum Engineering whenever this is required by the flow dynamics, to a mul- Stanford University tiphase solver (VOF). The continuous dialog between both [email protected] modelizations required the introduction of an innovative penalization method for solving two-phase flows over complex geometries on simple Cartesian meshes. Gunilla Kreiss Division of Scientific Computing Pierre Horgue Uppsala University Institut de Mécanique de Fluides de Toulouse [email protected] [email protected] MS22 Michel Quintard, Marc Prat Institut de Mécanique des Fluides de Toulouse Finite Elements for Reactive Flow in a Fracture [email protected], [email protected] and Reaction-induced Boundary Movement We study the reactive flow in a thin strip where the geom- MS22 etry changes take place due to reactions. Specifically, we consider precipitation dissolution processes taking place at Scale Analysis of Miscible Density-Driven Convec- the lateral boundaries of the strip. The geometry changes tion in Porous Media depend on the concentration of the solute in the bulk (trace Scale analysis of unstable density-driven miscible convec- of the concentration) which makes the problem a free- tion in porous media reveals that both concentration vari- moving boundary problem. The numerical computations ance production and dissipation rates are independent of are challenging in view of the nonlinearities in the descrip- the Rayleigh number (beyond a critical limit). As a con- tion of the reaction rates. In addition to this, the movement clusion, ensemble averaged Darcy modeling and the large- of the boundary depends on the unknown concentration mode simulation approach are proposed to compute the (and hence part of the solution) and the computation of behavior after a short onset time. The former method tar- the coupled model remains a delicate issue. Our aim is to gets ensemble averaged solutions and the latter coarse scale develop appropriate numerical techniques for the compu- finger dynamics; in both cases a dramatic reduction of com- tation of the solutions of the coupled convection-diffusion putational cost is achieved. equation and equation describing the geometry changes. The performance is demonstrated with the help of numer- Patrick Jenny ical tests. Institute of Fluid Dynamics ETH Zurich Thomas Wick [email protected] Institute for Computational Engineering and Sciences The University of Texas at Austin [email protected] Joohwa Lee AUDI AG [email protected] Mary F. Wheeler Center for Subsurface Modeling University of Texas at Austin Hamdi Tchelepi [email protected] Stanford University Energy Resources Engineering Department [email protected] Kundan Kumar Center for Subsurface Modeling, ICES University of Texas at 108 GS13 Abstracts

[email protected] portance of 3D Physical Modeling in Insurance and Reinsurace Market

MS23 The recent earthquake sequences that hit New Zealand Dispersion Analysis by Rayleigh Quotients: An Ef- (Sep. 2010-Dec. 2011, Canterbury plain) and Northern ficient Tool for High Order Finite Element Analysis Italy (May 2012, Emilia-Romagna), proved once more that in Wave Modeling a detailed description of the seismic scenario is required. We will present a challenging case study, aiming at simu- Dispersion analysis is a very important tool for assessing lating the seismic response of the central business district the accuracy range of numerical methods for wave prop- (CBD) of Christchurch, located in the alluvial plain of Can- agation simulations. For high order schemes, as in the terbury in New Zealand. The Canterbury sequence caused case of spectral elements, the standard dispersion analysis 181 casualties and devastated the entire region. We de- can be difficult and computationally very intensive, hence a cided to focus on the Lyttleton event event, modeling the more efficient approach would be desirable. In this work we kinematic rupture along the fault and studying the wave review the Rayleigh quotient approximation of the eigen- propagation through the complex deep soft-soil sediments value problem that characterizes the numerical dispersion up to the high and middle rise buildings located inside the of spectral element methods for wave propagation prob- CBD of Christchurch. lems in homogeneous media and extend this analysis to one-dimensional, periodic layered media in the particular Marco Stupazzini case where the ratio between the wavelength and the layer Munich RE thickness is high. This regime is relevant for interpreting [email protected] stratigraphic data. In addition to spectral element methods, we study the numerical dispersion of a poly-grid spec- Roberto Guidotti tral element method in which the velocity field is written Dipartimento di Ingegneria Strutturale in terms of Haar wavelet functions within each element. Politecnico di Milano [email protected] Saulo P. Oliveira Universidade da Bahia Ilario Mazzieri [email protected] Politecnico di Milano [email protected] Saulo P. Oliveira Universidade Federal do Parana Chiara Smerzini [email protected] Dipartimento di Ingegneria Strutturale Politecnico di Milano Geza Seriani [email protected] Istituto Nazionale di Oceanografia e di Geofisica Sperimentale [email protected] MS23 Modeling Biot Systems in Porous Media MS23 In this paper we consider modeling complex processes in Seismic Wave Propagation and Earthquake Sim- porous media taking into account fluid motion and ac- ulations Based on a 3D Fourier Pseudo-spectral companying solid deformations. Important applications Method in environmental engineering and petroleum engineering include carbon sequestration, surface subsidence, pore col- We have recently implemented the Fourier pseudo-spectral lapse, cavity generation, hydraulic fracturing, thermal frac- method (FPSM) into a numerical code for effective large turing, wellbore collapse, sand production, fault activa- scale 3D modelling of seismic wave propagation and earth- tion, and waste disposal. Here we employ a multipoint quake simulation on highly parallel computers. In particu- flux mixed finite element method for modeling Darcy flow lar, the new code uses vertically stretched staggered grids, and a continuous Galerkin method for elasticity. This Biot and it includes features such as general intrinsic attenu- system is decoupled using a fixed stress iterative coupling ation of the medium, anisotropy, irregular surface topog- scheme. We present both theoretical and computational raphy and extended earthquake sources, with kinematic results demonstrating convergence of this approach as well rupture description. We present the main code features as efficiency in parallel implementation. Specific treatment and some recent application results. of discrete fractures, effects of stress dependent permeability, and multiphase flow are discussed. Enrico Priolo National Institute of Oceanography and Experimental Mary F. Wheeler Geophysi Center for Subsurface Modeling OGS-Trieste University of Texas at Austin [email protected] [email protected]

Peter Klin Andro Mikelic National Institute of Oceanography and Experimental Institut Camille Jordan, Departement de Math´ematiques Geophys. Universit´eLyon1 OGS - Trieste [email protected] [email protected] Bin Wang MS23 Center for Subsurface Modeling, ICES The University of Texas at Austin Lessons Learnt from Recent Earthquakes: the Im- GS13 Abstracts 109

[email protected] MS24 TOF-based two-phase Upscaling of Flow and Transport in Subsurface Formations MS23 A Comparison of Explicit Continuous and Discon- Flow and transport in subsurface formations are affected tinuous Galerkin Methods and Finite Differences by geological variability over multiple length scales. In for Wave Propagation in 3D Heterogeneous Media this talk, we present a TOF-based two-phase upscaling approach to generate upscaled two-phase flow functions. Traditionally, the wave equation is solved in the time do- This approach uses more accurate local saturation bound- main with the finite-difference method because of the rel- ary conditions, which are found to have a dominant impact ative ease of coding and parallelization, the use of high- (in comparison to the pressure boundary conditions) on the order spatial discretization schemes and its computational upscaled two-phase flow models. It incorporates single- speed. However, finite elements on tetrahedral meshes are phase flow and transport information into local upscaling more flexible and accurate, if the mesh follows the geome- calculations, effectively account for the global flow effects, try of the impedance contrasts and of the surface topogra- as well as the local variations due to subgrid heterogeneity. phy. We compare the DG symmetric interior penalty and The method was applied to permeability fields with differ- continuous mass-lumped finite elements with finite different correlation lengths and various fluid-mobility ratios. It ences. The results show that for simple models the finite was shown that the new method consistently outperforms differences outperform finite element method by at least an existing local two-phase upscaling techniques and provides order of magnitude. For a model with interior complexity accurate coarse-scale models for both flow and transport. and topography, the finite elements are about two orders of magnitude faster than finite differences. As applications Yan Li we consider seismic modeling and migration. Chevron [email protected] Elena Zhebel, Sara Minisini Shell Global Solutions International Yuguang Chen [email protected], [email protected] Chevron Energy Technology Company [email protected] Alexey Kononov Source Contracting BV Yalchin Efendiev [email protected] Dept of Mathematics Texas A&M University Wim A. Mulder [email protected] Shell Global Solutions International Delft University of Technology [email protected] MS24 Multiscale Finite Volume Method As a Framework for Physically Motivated Model Reduction. MS24 An Adaptive Multiscale Finite Element Method In subsurface flow simulations, multiscale methods have been developed as tools to improve computational effi- We discuss and introduce an adaptive multiscale finite ele- ciency. Some of them, however, offer an excellent frame- ment method (MsFEM) for solving elliptic problems with work to combine several physical descriptions at different rapidly oscillating coefficients. Starting from a general ver- scales and in different regions. By using the Multiscale Fi- sion of the MsFEM with oversampling, we present an a 1 nite Volume method, we discuss the possibility of choosing posteriori estimate for the H -error between the exact so- adaptive coarsening criteria based on physical considera- lution of the problem and a corresponding MsFEM approx- tions. We show application to flow through porous media, imation. Our estimate holds without any assumptions on with special attention to applications involving interface scale separation or on the type of the heterogeneity. The dynamics at the pore scale. estimator splits into different contributions which account for the coarse grid error, the fine grid error and even the Ivan Lunati oversampling error. Based on the error estimate we con- University of Lausanne struct an adaptive algorithm that is validated in numerical [email protected] experiments. Pavel Tomin Patrick Henning Premier Assistant (Postdoc) University of Münster, University of Lausanne Institut für Numerische und Angewandte Mathematik [email protected] [email protected] Pavel Tomin Mario Ohlberger PhD Student Universität Münster MIPT Institut für Numerische und Angewandte Mathematik [email protected] [email protected]

Ben Schweizer MS24 TU Dortmund Reduced Modeling by Global Transmissibility Up- Fakult¨at f¨ur Mathematik scaling for Optimzation [email protected] Reservoir models are often too detailed for optimization 110 GS13 Abstracts

purposes. We present a framework for automatic model MS25 reduction using global information that consists of three Dynamic Simulation of Tsunamigenic Earthquake components: algorithms to coarsen the grid, transmissibil- Rupture ity upscaling methods, and a robust fully implicit solver. Through a combination of these methods, one can incor- Earthquakes might generate disproportionately large porate the most important reservoir responses for use in tsunamis due to particular characteristics that include slow optimization. In particular, we discuss diﬀerent ways of rupture speed, rupture up to the trench and slip on splay using global information to partition the grid and upscale faults. I will summarize current results from models of sub- transmissibilities. duction earthquake cycle and dynamic rupture aimed at understanding which physical properties of the subduction Halvor M. Nilsen megathrust can lead to such tsunamigenic earthquakes. In SINTEF particular, I will examine the conditions that control the Oslo occurrence of large slip and slow rupture at shallow depth. [email protected]

Stein Krogstad Jean Paul Ampuero SINTEF ICT California Institute of Technology [email protected] Seismological Laboratory [email protected] Knut-Andreas Lie SINTEF ICT, Dept. Applied Mathematics MS25 [email protected] A 3D Dynamic Rupture and See Floor Displace- ment Simulations of the 2011 Mw9 Tohoku Earth- MS24 quake An Approximate Method for Multiphase Scale-Up We perform earthquakes dynamic rupture simulations of Coarsening and upscaling are common practices in reser- 2011 Mw9 Tohoku event governed by the slip weakening voir simulation for reducing model size to improve com- friction. Based on these simulations, we investigate the putational efficiency. As part of the standard simulation spatio-temporal evolution of the ground motion displace- workflow, engineers upscale geological models to simulation ment of the see floor. Moreover, we investigate the role models to speed up the run and at the same time reduce of the non-planar fault of the subduction interface and its the requirement on resources, e.g., memory. Coarsening effect on the ground motion displacement of the see floor, is also an attractive approach for reduced order modeling. that in turn provide important insights on tsunamis gen- In that case, aggressive coarsening is carried out to dras- erations. tically reduce the size of the simulation model, and hence Percy Galvez simulation time. Reduced order modeling plays a crucial role in uncertainty quantification, history match, and other Swiss Seismological Service (SED) applications where a large number of simulation runs are ETH Zurich required. This presentation describes a new method for up- [email protected] scaling relative permeability for the purpose of multiphase flow simulation. This method is simple, efficient, and treats Luis Dalguer physics factors important to recovery processes. With this Swiss Seismological Service, ETH Zurich approach, approximations are introduced to eliminate the Sonneggstrasse 5, CH-8092 Zurich, Switzerland need for local or global multiphase flow simulations for the [email protected] purpose of building coarse-scale displacement tables (pseu- dos). Instead, the technique is based on global pressure solutions and velocity fields for incompressible single phase MS25 flow. Using the velocity fields, time-of-flight (TOF) and Broadband Ground-Motion Simulations from Rup- saturation distributions are obtained by solving finite dif- ture Dynamics ference equations using a sequential procedure. For testing, coarse-scale relative permeability tables are used to simu- Broadband ground-motion calculations for earthquake engineering applications are a key challenge in seismology. late flow on fields with challenging horizontal and vertical In this talk, I present physics-based earthquake shak- permeability properties. Test results show that the use of ing simulations based on dynamic rupture computations the proposed multiphase upscaling method preserves accu- combined with seismic scattering in heterogeneous Earth. racy of simulation on the coarse scale, while speeding up I discuss our rupture-dynamics modeling strategy, using the run by more than 100 times. correlated-random initial stress that generates realistic Yahan Yang,XiaochenWang space-time rupture evolutions. We combine the resulting ExxonMobil band-limited synthetic seismograms with multiply S-to-S [email protected]., scattered high-frequency seismic waves. I also introduce [email protected] simplified rupture-modeling strategies for tsunami prediction.

Xiao-Hui Wu, Linfeng Bi Martin Mai ExxonMobil Upstream Research Company KAUST [email protected], [email protected] [email protected]

Luis Dalguer Swiss Seismological Service, ETH Zurich Sonneggstrasse 5, CH-8092 Zurich, Switzerland GS13 Abstracts 111

[email protected] MS26 On the Development and Generalizations of Cahn–Hilliard Equations within a Thermodynamic MS25 Framework Recent Advances in Numerical Simulation of Earthquake Rupture Dynamics: Application to the We provide a thermodynamic basis for the development of 2011 Tohoku-Ori Earthquake models that are usually referred to as phase-field models for compressible, incompressible, and quasi-incompressible Recent advances in numerical simulation of earthquake fluids. Using the theory of mixtures as a starting point, rupture dynamics using non-smooth Spectral Element we develop a framework within which we can derive phase- Method are discussed here in the light of canonical prob- field models both for mixtures of two constituents and for lems and of the recent 2011 Tohoku-ori earthquake. High- mixtures of arbitrarily many fluids. In order to obtain the order Spectral Element approximation, combined with ex- constitutive equations, we appeal to the requirement that plicit second-order time stepping, allows to simulate very among all admissible constitutive relations that which is accurately the rupture radiation in complex geological me- appropriate maximizes the rate of entropy production (see dia. Dynamic earthquake rupture along preexisting faults Rajagopal and Srinivasa in Proc R Soc Lond A 460:631– of complex geometry is modeled as a frictional instability 651, 2004). The procedure has the advantage that the using extension of a Barenblat-type surface energy formu- theory is based on prescribing the constitutive equations lated in terms of a slip-weakening friction law. The fric- for only two scalars: the entropy and the entropy pro- tional contact is implemented using an implicit non-smooth duction. Unlike the assumption made in the case of the contact formalism and solved locally using Moreau’s sweep- Navier-Stokes-Fourier fluids, we suppose that the entropy ing process. The frictional contact is regularized to take is not only a function of the internal energy and the density into account bi-material interfaces. Simulations of the in- but also of gradients of the partial densities or the concen- teraction between rupture propagation and free surface will tration gradients. The form for the rate of entropy pro- be in particular discussed in the light of the implications duction is the same as that for the Navier-Stokes-Fourier for tsunami source generation. fluid. As observed earlier in Heida and Malek (Int J Eng Sci 48(11):1313–1324, 2010), it turns out that the dependence Jean-Pierre Vilotte of the rate of entropy production on the thermodynamical Institut de Physique du Globe de Paris fluxes is crucial. The resulting equations are of the Cahn- CNRS - UMR 7154 Hilliard-Navier-Stokes type and can be expressed both in [email protected] terms of density gradients or concentration gradients. As particular cases, we will obtain the Cahn-Hilliard-Navier- Gaetano Festa Stokes system as well as the Korteweg equation. Compared Università di Napoli, Frederico II to earlier approaches, our methodology has the advantage [email protected] that it directly takes into account the rate of entropy production and can take into consideration any constitutive assumption for the internal energy (or entropy). MS26 On the Regularity of Non-Negative Solutions to a Josef Malek Logarithmically Singular Equation Charles University, Prague Mathematical Institute The local behaviour of solutions to a logarithmically singu- [email protected]ff.cuni.cz lar diffusion equation is investigated in some open space- time domain E × (0,T]. It is shown that if at some time level to ∈ (0,T]andsomepointxo ∈ E the solution MS26 u(·,to) is not identically zero in a neighborhood of xo,in Combined Finite Volume-Finite Element Scheme a measure-theoretical sense, then it is strictly positive in for Compressible Two Phase Flow in Porous Media a proper cylindrical neighborhood of (xo,to). As a conse- quence, solutions are analytic in the space variables and at We present an industrial scheme, to simulate the two com- least Lipschitz continuous in the time variable. pressible phase flow in porous media. For homogeneous and isotropic diffusion tensor, this scheme consists in an im- Ugo Gianazza plicit finite volume method together with a phase-by-phase Department of Mathematics upstream scheme which satisfies industrial constraints of University of Pavia robustness. We show that the proposed scheme satisfy the [email protected]fi.it maximum principle for the saturation and a discrete energy estimate on the velocity of each phase. For inhomogeneous and anisotropic diffusion tensor, we discretize the diffusion MS26 term over an unstructured mesh of the space domain by Structural Stability Problems for Nonlinear PDEs means of the piecewise linear nonconforming finite element of Porous Media method combined with an upwind scheme for the mobility of each phase. We prove the convergence of the scheme, The problems of structural stability and continuous depen- only supposing the shape regularity condition for the orig- dence on initial data for Brinkman Forchheimer Equations inal mesh.We use a priori estimates and the Kolmogorov and related systems of equations of porous media will be compactness theorem for this purpose. In addition, we discussed present some numerical tests in 2D on an unstructured Varga Kalantarov mesh for water-gas flows in porous media. Koc University, Istanbul Mazen Saad Turkey Ecole Centrale de Nantes [email protected] [email protected] 112 GS13 Abstracts

MS27 erogeneities will be demonstrated. Important issues for Towards Large-Scale Compositional Simulation of up-scaling will be addressed. CO2 Enhanced Oil Recovery (EOR) Odd Steve Hustad This talk will focus on the simulation of CO2 EOR, and dis- Statoil cuss simulation performance (accuracy and efficiency) for [email protected] various techniques. The impact of model complexity (e.g., reservoir heterogeneity, relative permeability, and miscible vs. near-miscible displacements) is illustrated, and we dis- MS27 cuss the use of upscaling to speed up the simulation. It is Accurate and Efficient Modeling of Near-Miscible shown that the combined use of parallel simulation, Adap- Gas Injection at Reservoir Scale tive Implicit (AIM) models, and upscaling makes it possible for large-scale simulation of CO2 EOR. In this presentation I will focus on important aspects of a near-miscible gas injection simulation. That will include Yuguang Chen,DengenZhou efficiency of thermodynamic computations, accurate phase Chevron Energy Technology Company state identification, important details of nonlinear formu- [email protected], [email protected] lations and nonlinear solvers. Development of miscibility and its accurate treatment in a compositional simulation as Huanquan Pan well as possible scaling strategies for gas injection processes Department of Energy Resources Engineering will be also discussed. Stanford University Denis Voskov [email protected] Energy Resources Engineering Department Stanford Univeristy MS27 [email protected] A Multi-Physics Approach to Model Composi- tional Flow on Adaptive Grids. MS28 A multi-physics approach is presented that reduces the nu- Combing Models of Ice Dynamics and Subglacial merical model complexity locally in an adaptive manner to Hydrology lower the computational efforts per cell. This approach is I will present recent attempts to model hydrologically con- combined with adaptive refinement of the grid that uses trolled acceleration and deceleration of ice-sheets. In par- a multi-point flux approximation in combination with the ticular, I will described a coupled model in which ice defor- standard two- point flux stencil. The combination of both mation is described with a vertically integrated model in- approaches allows for an efficient simulation of composi- corporating large amounts of basal slip, and the subglacial tional multi-phase flow, such as a large-scale scenario of drainage system is described by a water sheet of variable CO2 storage. thickness. The model will be forced by a prescribed rate Benjamin Faigle of melting of the ice surface, the meltwater being routed University of Stuttgart through the drainage system and causing variation in basal [email protected] slip as a result. I will explore and discuss different ways of describing the evolution of the drainage system and of coupling the drainage system to ice flow. Rainer Helmig IWS, University of Stuttgart, Germany Ian Hewitt Institut fur Wasserbau Mathematics Department, University of British Columbia [email protected] Vancouver, Canada [email protected] Ivar Aavatsmark CIPR University of Bergen [email protected] MS28 Discretization and Solvers for the Stokes Equations Bernd Flemisch of Ice Sheet Dynamics at Continental Scale University of Stuttgart, Germany bernd.fl[email protected] Ice sheets exhibit incompressible creeping flow with shear- thinning rheology. On a continental scale, the flow is characterized by localized regions of fast flow that are sepa- MS27 rated from vast slow regions by thin transition zones. We Application of Saturation Functions and Implica- use a parallel, adaptive mesh, higher-order finite element tion of Representing Complex Dynamical Systems discretization to model in 3D the equations for ice sheet in Up-Scaled Models dynamics on a continental scale. We will address issues related to the scalable solution of the resulting equations, Compositional reservoir simulations of gas displacement with emphasis on the nonlinear rheology and addressing processes incorporating complex phase behavior and dy- the effects of a highly anisotropic discretization. namic movements of phases will be presented. Based on consistent handling of two-phase saturation functions Tobin Isaac,GeorgStadler to three-phase conditions, examples of Water-Alternating- University of Texas at Austin Gas (WAG) injection will be illustrated in 1D and 2D [email protected], [email protected] models. Saturation history development for immiscible and miscible WAG injection processes in a 2D trough Omar Ghattas cross stratified sandstone model at mesoscopic scale het- The University of Texas at Austin [email protected] GS13 Abstracts 113

MS28 Jeremie Mouginot Advances in Ice-Sheets Simulations, Models Com- University of California - Irvine parison and Parameters Estimation [email protected]

Several models of different complexity and accuracy have Eric Larour, Ala Khazendar been proposed for describing ice-sheet dynamics. We intro- Jet Propulsion Laboratory duce a parallel, finite element framework for implementing [email protected], [email protected] these models, which range from the ”shallow ice approximation” up through nonlinear Stokes flow. These models make up the land ice dynamical core of FELIX, which is be- MS29 ing developed under the Community Ice Sheet Model. We A Mixed Order Scheme for the Shallow Water present results from large-scale simulations of the Green- Equations land ice-sheet, compare models of differing complexity and accuracy, and explore different solution methods for the Learn how to use mixed order schemes for faster simulation resulting linear and nonlinear systems. We also address of the shallow water equations. This session will explain the problem of finding an optimal initial state for Green- how the use of different order schemes within the same sim- land ice-sheet via estimating the spatially varying linear- ulation can give higher numerical performance with a min- friction coefficient at the ice-bedrock interface. The prob- imal impact on accuracy. We present the implementation lem, which consists of minimizing the mismatch between of our numerical scheme on the GPU, discuss the accuracy a specified and computed surface mass balance and/or the of the approach, and benchmark how well it maps to the mismatch between observed and modeled surface veloci- underlying computational hardware. ties, is solved as an optimal control problem constrained by the governing model equations. Andr’e R. Brodtkorb SINTEF ICT, Department of Applied Mathematics Matthew Hoffman [email protected] Los Alamos National Laboratory, Los Alamos, NM, USA mhoff[email protected] MS29 Mauro Perego Lateral Coupling of 1D-2D Shallow-Water Equa- Florida State University tions [email protected] There are numerous situations in hydraulic engineering (dam breaks, flooding events...) that require numerical Stephen Price simulation. Since large domains are often considered, Los Alamos National Laboratory yielding significant computational cost, it is still remain- [email protected] ing a challenging domain.1D and 2D tools developed by Electricité De France, respectively called Mascaret and Andrew Salinger Telemac2D , are widely used to solve this kind of free sur- Applied Computational Methods Dept, Sandia National face flow problems. They are based on solution of the shal- Labs low water equations. In this study, we aim at coupling Sandia National Labs these two codes in order to benefit from their different as- [email protected] sets in the same computation.. To this end, a lateral coupling technique without overlapping has been developed.. This coupling based on transversal local Riemann solver is MS28 described and validated on academic test cases. Modeling the Response of Pine Island Glacier, West Antarctica, for the next 50 years Nicole Goutal EDF R&D & Saint-Venant Hydraulic Lab. Pine Island Glacier experienced spectacular changes over [email protected] the past decades, which are attributed to warmer ocean waters in the Amundsen Sea affecting the floating part of martin parisot Pine Island. We use ISSM and a three-dimensional higher- Saint-Venant Hydraulic Lab. order model to simulate the evolution of the glacier for the [email protected] next fifty years and assess the effect of changes in several climate forcings and model parameters, namely basal melting under the floating part, ice front position, atmospheric Fabrice Zaoui conditions and grounding line retreat, on ice dynamics. EDF R&D [email protected] Helene Seroussi Jet Propulsion Laboratory [email protected] MS29 Coupling 1-D and 2-D Shallow Water Equations for Mathieu Morlighem Flood Modelling University of California - Irvine Rubar 3 and Rubar 20 developed by Irstea solved respec- [email protected] tively 1-D and 2-D shallow water equations using similar finite volume Godunov type second order schemes. Their Eric Rignot coupling is built on a calculation of the exchange terms University of California - Irvine using the 2-D method. Two examples are shown: an ex- Jet Propulsion Laboratory - Caltech periment in which a pipe is connected with one street sim- [email protected] ulating the calculation unit for urban flood and the annual 114 GS13 Abstracts

flood in the Inner delta of the Niger River. MS30 Towards Improvement of Climate Models Using AndréPaquier Data Assimilation Irstea [email protected] The data assimilation problem is traditionally a state estimation problem, combing observational data with a nu- Bazin Pierre-Henri merical model to create an improved estimate of the cur- Irstea,UR HHLY rent state from which to make forecasts. We will look at [email protected] the inverse problem of using observational data coupled with state-of-the-art data assimilation techniques to incre- Gilles Belaud mentally improve the forecast model. This will include Ecole Nationale Supérieure d’Agronomie estimation of non-global parameters as well as stochastic [email protected] parameterization of unseen dynamics. Lewis Mitchell MS29 The University of Vermont Computational Methods for Coupling 1D channels Department of Mathematics and Statistics in Complex Shallow Water Networks [email protected]

We present two methods for coupling 1D channels in complex shallow water networks. In the first method, 1D chan- MS30 nels are connected through local 2D unstructured mesh Assimilation and Model Error for a 3D Ocean Pro- patches. The second technique replaces the 2D patch by cess Model a single, specially chosen 2D element. Both methods work well for all flow regimes, including bores, with CPU-time A simple kinematic model of a wind-forced three dimen- savings of two orders of magnitude relative to a full 2D sional ocean eddy can illuminate complex dynamics of the treatment. fluid flow. However, a kinematic model alone cannot hope to perfectly describe reality or the data one may collect. Eleuterio F. Toro As such we propose modeling the difference between the Department of Civil and Environmental Engineering kinematic model and data as a random function which we University of Trento, Italy refer to as a bias. Once the random function is fit, we [email protected] use the now bias-corrected kinematic model to explore the eddy dynamics. Francesca Bellamoli Elaine Spiller Laboratory of Applied Mathematics, University of Trento Marquette University Italy [email protected] [email protected] DW Han Lucas Mueller University of Massachusettes University of Trento, Italy [email protected] [email protected] Lawrence Pratt MS30 Woods Hole Oceanographic Institution En-Route Data Assimilation [email protected] Assimilation of data collected by Lagrangian or pseudo- Tamay Ozgokmen Lagrangian instruments such as drifters, gliders, or floats, University of Miami/RSMAS and in particular subsurface data, is of great interest, but [email protected] difficult because the subsurface paths are unknown. Our recent work introduces an observation operator which allows us to express these en-route observations as a func- MS30 tion of the state vector of the model at the measurement Pseudo-Orbit Gradient Descent for Lagrangian time. We show the efficacy of this en-route data assimila- Data Assimilation tion scheme. A nonlinear approach to data assimilation, known as Amit Apte pseudo-orbit gradient descent, is presented and illustrated TIFR Centre for Applicable Mathematics in the context of assimilating Lagrangian tracer trajec- Bangalore, India tories in two-dimensional flows of point-vortex systems. [email protected] The approach centers on minimizing a cost function in sequence space, initialized with the noisy observations. The Elaine Spiller tracer advection equations augment the point vortex model Marquette University equations, allowing the observed tracer positions to up- [email protected] date the state information about unobserved vortex positions. Pseudo-orbit gradient descent has been successfully Christopher Jones demonstrated for the case of both full and partial observa- University of North Carolina tions. [email protected] Emma Suckling Centre for Analysis of Time Series London School of Economics GS13 Abstracts 115

[email protected] Applied Mathematics SINTEF ICT [email protected], [email protected] MS31 Modeling Coupled Hydro-Mechanical Phenomena Ivar Aavatsmark in the Near Field of a High-Level Radioactive CIPR University of Bergen Waste Repository in Clay Formations [email protected] Clay/shale formations are being investigated as potential host rock for geological disposal of high-level radioactive Helge Dahle waste throughout the world. This presentation discusses Department of Mathematics advanced computational methods for modeling the cou- University of Bergen pled hydro-mechanical processes occurring near repository [email protected] tunnels as a result of tunnel excavation, ventilation, waste emplacement, and gas production. We also touch on how MS31 these methods are being tested against in situ experimental data from underground research laboratories. Lifetime of Carbon Capture and Storage as a Cli- mate Change Mitigation Technology Jens T. Birkholzer Lawrence Berkeley National Laboratory In carbon capture and storage (CCS), CO2 is captured (LBNL) at power plants and then injected underground into reser- [email protected] voirs like deep saline aquifers for long-term storage. While CCS may be critical for the continued use of fossil fuels in a carbon-constrained world, the deployment of CCS has Daisuke Asahina, James Houseworth, Hui-Hai Liu, Jonny been hindered by uncertainty in geologic storage capacities Rutqvist and sustainable injection rates, which has contributed to Lawrence Berkeley National Laboratory (LBNL) the absence of concerted government policy. Here, we clar- [email protected], [email protected], [email protected], ify the potential of CCS to mitigate emissions in the United [email protected] States by developing a storage-capacity supply curve that, unlike current large-scale capacity estimates, is derived MS31 from the fluid mechanics of CO2 injection and trapping and incorporates injection-rate constraints. We show that Can CCS Find Synergies with Geothermal Energy storage supply is a dynamic quantity that grows with the and Shale Gas Production? duration of CCS, and we interpret the lifetime of CCS as Currently, the only realistic path forward for implementa- the time for which the storage supply curve exceeds the tion of large-scale Geological Carbon Storage is through storage demand curve from CO2 production. We show synergistic activities that can provide positive economic that in the United States, if CO2 production from power drivers for CO2 storage. Two such possibilities are CO2 in- generation continues to rise at recent rates, then CCS can jection as part of a geothermal production strategy, and in- store enough CO2 to stabilize emissions at current lev- jection of CO2 into depleted shale gas formations. Compar- els for at least 100 years. This result suggests that the ison of simulation approaches for these two systems with large-scale implementation of CCS is a geologically viable simulation approaches for CO2 injection into deep saline climate-change mitigation option in the United States over aquifers highlights the challenges associated with these al- the next century. ternate strategies. Michael Szulczewski Michael A. Celia MIT Princeton University Civil and Environmental Engineering Dept of Civil Engineering [email protected] [email protected] Christopher W. MacMinn MIT MS31 Mechanical Engineering Coupled Thermal Models with Vertical Equilib- [email protected] rium Howard Herzog Coupled thermal and fluid flow processes should be con- MIT sidered when modeling CO2 injection and storage. Often, MIT Energy Initiative CO2 is injected at a different temperature than geothermal [email protected] conditions, leading to significant density differences within the plume. This impact is particularly important for injec- Ruben Juanes tion sites near the critical point. We couple heat transfer MIT within the vertical equilibrium framework for fluid flow, Civil and Environmental Engineering which requires an upscaled representation of thermal pro- [email protected] cesses. Simulations are performed for realistic geological storage sites. MS32 Sarah Gasda University of North Carolina at Chapel Hill Multicore Aware Parallel Simulations of Co2 Geo- [email protected] logical Storage We enhance the parallel scalability of the general-purpose Odd Andersen, Halvor Nilsen Tough2-MP code to consider complex modeling. This talk 116 GS13 Abstracts

will focus and the required adaptations of the assembly and ulation of CO2 Sequestration the solve phases considering the impact of the mapping of the processes on the physical cores. We will also comment Carbon Capture and storage is simulated with a two-phase on the extra-costs inferred by the memory hierarchy and two-component flow model employing a special set of pri- the bandwidth limitation. Some illustrative examples of mary variables (capillary pressure / phase pressure) to deal long-term fate of CO2 stored in reservoirs will also be de- with the (dis-)appearance of the nonwetting phase. The tailed. implementation is based on DUNE PDELab. Numerical results of massive parallel simulations for test cases with Fabrice Dupros millions of unknowns on hundreds of cores on the super BRGM computer HERMIT (Cray X6) are presented and discussed. ORLEANS, FRANCE [email protected] Rebecca Neumann Interdisziplinäres Zentrum für Wissenschaftliches MS32 Rechnen (I Assessment of An Hpc Two-Phase Flow Solver in Universität Heidelberg, Germany Porous Media for Realistic Cases [email protected]

In this presentation we address the developments and per- Olaf Ippisch formance of a two-phase flow solver for porous media. The Interdisziplinary Center for Scientific Computing software library implements the IMplicit Pressure/Explicit University of Heidelberg Saturation (IMPES) algorithm. To address realistic cases, [email protected] with millions of degrees of freedom and physical properties with strong variations, a parallel implementation is needed, Peter Bastian along with a suitable choice of preconditioners. We present Interdisciplinary Center for Scientific Computing here some tools and techniques that can be used to achieve University of Heidelberg good performance on modern supercomputers. [email protected] Alessio Fumagalli MOX, Department of Mathematics MS33 Politecnico di Milano, Italy [email protected] Discontinuous Galerkin Multiscale Methods for El- liptic Problems Antonio Cervone A discontinuous Galerkin multiscale method for flow in MOX, Department of Mathematics Politecnico di Milano, porous media is proposed. Convergence results are pre- Italy sented both for diffusion and convection dominated prob- [email protected] lems, with heterogeneous data without any assumption on scale separation or periodicity. The multiscale method uses Luca Formaggia a corrected basis that is computed on patches/subdomains. Department of Mathematics Linear convergence in energy norm is obtained indepen- Politecnico di Milano, Italy dently of the data. Numerical experiments confirms the [email protected] theoretical rates of convergence. Daniel Elfverson MS32 University of Uppsala (Sweden), Div. Scientific Improving the Scalability of Reservoir Simulation Computing on Multicore Architecture Dept. Information Technology [email protected] Today, reservoir simulators have difficulties to fully har- ness the power of modern supercomputers: a simulation Axel M˚alqvist of several million of active cells barely scales over a few Uppsala University hundred cores when large supercomputers count hundreds [email protected] of thousands of cores. In this presentation, we discuss our research to improve the scalability of a reservoir simula- Daniel Peterseim tor by using a fine grain parallelization in an MPI/thread Humboldt-Universitaet zu Berlin framework. We will focus on the linear solver part which Institut für Mathematik is the bottle-neck of such an approach. [email protected] Pascal Henon EP/DEV/GIS/SIM MS33 Total France [email protected] Discontinuous Galerkin Multiscale Methods for Advection-Diffusion Problems with Highly Hetero- geneous Data Corentin Rossignon TOTAL In this talk, we introduce a discontinuous Galerkin het- [email protected] erogeneous multiscale method (DG-HMM) for advection- diffusion problems with highly heterogeneous data. We discuss the stability of the method for both advection and MS32 diffusion dominated problems and for general data. Fur- Compositional Two-Phase Flow with Disappearing ther, we present fully discrete a priori error estimates for Nonwetting Phase - Modeling and Numerical Sim- locally periodic data. Moreover, we show that under scale GS13 Abstracts 117

separation assumption (e.g., local periodicity) the compu- MS34 tational work is independent of the smallest scale in the Effect of Heterogeneous Earthquake Slip on medium. Tsunami Run-Up Uncertainty Assyr Abdulle We first review investigations of tsunami propagation due EPFL - Ecole Polytechnique Federale de Lausanne to heterogeneous slip, with emphasis on uncertainty and assyr.abdulle@epfl.ch predictability. A systematic study of plane wave propagation and uncertainty propagation due to heterogeneous slip Martin Huber from earthquake slip scaling laws all the way to run-up is Ecole´ Polytechnique Fédérale de Lausanne (Switzerland) then presented. Non-hydrostatic hydrodynamic effects are Mathematics Institute of Computational Science & given particular attention. Finally, the effect of heteroge- Engineering neous slip from real cases such as the 2011 Tohoku tsunami martin.huber@epfl.ch is briefly discussed. Finn Lovholt MS33 Norwegian Geotechnical Institute (NGI) On Oversampling for the Multiscale Finite Element fi[email protected] Method

In this talk, we review several oversampling strategies as MS34 performed in the Multiscale Finite Element Method (Ms- Modelling Tsunamis and Problems Constraining FEM). Common to those approaches is that the oversam- the Slip in Mega-Thrust Earthquakes pling is typically performed in the full fine scale space restricted to a patch. We suggest, by contrast, to perform Mega-thrust earthquakes and tsunamis cause untold de- local computations with additional constraints. The new struction. In this talk a new finite volume unstructured setting gives rise to a general fully discrete error analy- grid tsunami model is presented. The model is a finite P nc P sis for the proposed multiscale method with oversampling volume analogue of the 1 - 1 finite element, in which without suffering from resonance effects. mass conservation is guaranteed not only in a global sense, but within each cell. The model conserves momentum, and Patrick Henning accurately handles flooding and drying problems. Results University of Münster, from the Indian Ocean and Japanese Tsunami compare Institut für Numerische und Angewandte Mathematik well with flooding and run-up data. [email protected] Julie Pietrzak Faculty of Civil Engineering and Geosciences Daniel Peterseim Delft University of Technology Humboldt-Universitaet zu Berlin [email protected] Institut für Mathematik [email protected] H Cui, G.S. Stelling Delft University of Technology MS34 [email protected], [email protected] Probabilistic Models of Earthquake Slip for Tsunami Hazard Assessment MS34 Probabilistic Tsunami Hazard Assessment (PTHA) for a Modeling Dynamic Rupture with Implications for community requires sampling the earthquake parameter An Alaskan-Aleutian Megathrust Earthquake and space of possible seismic events that may cause tsunamis. Resulting Tsunami The distribution of slip on a given fault geometry can greatly affect the resulting inundation, particularly in the We investigate the effects of rate-strengthening-like fric- nearfield. Recent work will be presented on the use of tion (e.g., Dieterich, 1992) and heterogeneous fault pre- Karhunen-Loeve expansions to represent slip on the Cas- stress on rupture propagation, slip, free surface deforma- cadia Subduction Zone, and use of these models together tion, and the resultant tsunami in time (Shuto, 1991; Sa- with GeoClaw for PTHA on the coast of California and the take, 2002). Using time-weakening friction as a proxy for Pacific Northwest. rate-strengthening friction, and given fault data along the Alaska-Aleutian megathrust assembled from the Science Randall J. LeVeque Application for Risk Reduction team (SAFRR), we are Applied Mathematics able to dynamically model a Mw9 earthquake and resul- University of Washington (Seattle) tant tsunami on a similar megathrust. [email protected]; [email protected]; rjl@washingt Kenny J. Ryan Department of Earth Sciences Knut Waagan, Frank I. González University of California, Riverside University of Washington [email protected] [email protected], fi[email protected] David D. Oglesby Guang Lin Department of Earth Sciences, Univ. of CA, Riverside Pacific Northwest National Laboratory 900 University Ave. Riverside, CA 92521 [email protected] [email protected]

Eric L. Geist US Geological Survey 118 GS13 Abstracts

[email protected] media, using an upscaling approach to recently derived phase ﬁeld models. To this aim, we combine rational thermodynamics, i.e. the assumption of maximum rate of en- MS35 tropy production by Rajagopal and Srinivasa, with for- A Multilevel Domain Decomposition Algorithm for mal asymptotic expansion. The result will be a family of Fluid-structure Interaction in Porous Media twoscale models for several types of microscopic regimes.

In this talk we consider multilevel domain decomposition Martin Heida algorithms for the numerical solution of fluid structure in- Universität Heidelberg teraction problems for flows in porous media. From the [email protected] physical point of view, the use of this class of algorithms is motivated by the need to solve fluid filtration problems in porous media which are characterized by a high hetero- MS35 geneity in terms of length scale, as it occurs for instance Water Transport in Partially-molten Ice - A Multi- in the case of fractured porous media with complicated phase Theory Approach geometries. From the numerical point of view, multilevel domain decomposition algorithms are defined with the pur- We present a two-phase model for thermo-mechanical evo- pose of combining the advantageous features of both geo- lution of partially molten ice and gravity-driven water ex- metric multigrid and domain decomposition methods, such traction. We perform scale analysis and associated model as optimal computational complexity and parallelizable im- reduction in a physical setting relevant for conditions in plementation. We investigate the performances of the al- the ice layers of moons of outer planets in the solar sys- gorithm in terms of accuracy and computational efficiency tem (Europa, Enceladus). We revisit the traditional zero by considering the results of some numerical tests for fluid- compaction length approximation, obtained by omission of structure problems naturally arising in the study of porous the coupling effects between melt flow and ice deformation. media fluid flows. We numerically investigate the relation between the shock- like solutions of the zero compaction length model and the Giorgio Bornia wave-train solutions of the full model and examine the ef- Dept. of Mathematics and Statistics Texas Tech fects of the zero compaction length approximation on the University character of the water transport. [email protected] Ondrej Soucek Soucek Sandro Manservisi Charles University Laboratory of Montecuccolino [email protected]ff.cuni.cz DIN, University of Bologna [email protected] MS36 Using the Gibbs-Helmholtz Constrained Eos in MS35 Reservoir Simulation Realistic Scale Simulations of Sedimentary Basins This talk will provide an overview of a general framework A parallel implementation for the development and evolu- for multi-component, multi-phase equilibrium flash calcu- tion of sedimentary basins is proposed. Rocks are modeled lations, which uses the multi-scale Gibbs Helmholtz Con- as highly viscous fluids in creeping flow regime. When deal- strained (GHC) equation, and discuss the reliability and ing with realistic scales, the number of degrees of freedom efficiency of the flash algorithm, how they are measured, becomes huge, and the solution of the discretized problem and their relationship to reservoir simulator performance. becomes challenging, especially in the presence of high vari- The multi-scale GHC equation flash algorithm, GFLASH, ations in the physical parameters. In particular, precondi- has been coupled to the Stanford University reservoir sim- tioners that scale well with respect to parallel processes, ulator, AD-GPRS. Reservoir simulation examples and geo- viscosity ratios and dofs are analyzed. metric illustrations are presented to elucidate key concepts.

Antonio Cervone Angelo Lucia MOX, Department of Mathematics Politecnico di Milano, Department of Chemical Engineering Italy University of Rhode Island [email protected] [email protected]

Nur A. Fadel Denis Voskov Politecnico di Milano - MOX - Dipartimento di Energy Resources Engineering Department Matematica Stanford Univeristy [email protected] [email protected]

Luca Formaggia MS36 Department of Mathematics Calculation of Phase Equilibrium: Status and Per- Politecnico di Milano, Italy spectives [email protected] The talk presents an overview of selected computational methods for calculation of phase equilibrium. Topics are MS35 equilibrium calculations of relevance for compositional sim- Modeling Mulitscale and Multiphase Flow in ulation with the classical cubic equation of state. In ad- Porous Media dition the computational aspects of implementing complex equations of state like SAFT are discussed. For such equa- We consider multiphase ﬂow, e.g. water and air, in porous GS13 Abstracts 119

tions, formulation in terms of volume rather than pressure points in its favor. First, it is straightforward to use new may be preferable. meshes as a simulation progresses. Second, it is natural to construct a geometric multigrid solver for the stress- Michael L. Michelsen balance equations. Thirdly, domain decomposition is easy. Technical University of Denmark [email protected] Stephen Cornford University of Bristol MS36 [email protected] Gibbs Free Energy Minimization for Reactive Flow in Porous Media Daniel Martin Lawrence Berkeley National Laboratory The modeling of CO2 injection for enhanced oil recovery [email protected] in carbonate reservoirs entails complex interplay of flow, geochemical reactions and hydrocarbon phase behavior. A new framework for compositional simulation is introduced MS37 that integrates reactions and phase behavior using local Grounding Line Migration in a Full-Stokes Model: equilibrium assumption. The equilibrium composition is from Processes to Applications solution to the constrained nonlinear optimization of the Gibbs free energy function for the system. Two applica- We examine here the possibility of modeling Antarctic tions are discussed – acid gas solubility and hydrocarbon outlet glaciers using the full-Stokes finite-element model phase changes in presence of reactions. Elmer/Ice. Process studies of the grounding line dynamics on synthetic regular bedrocks are first discussed and com- Ashwin Venkatraman, Larry Lake pared with analytical results. Further simulations showing The University of Texas at Austin the evolution of actual systems are presented and compared [email protected], [email protected] with obserbations.

Russell Johns Gael Durand Penn State University Laboratoire de Glaciologie et de G´eophysique [email protected] de l’Environnemt, Grenoble, France [email protected]

MS36 Olivier Gagliardini, Lionel Favier Multi-Linear Representation of Phase Behavior for LGGE Large Scale Gas Injection Simulation [email protected], [email protected] We describe an Adaptive Compositional Space Parametrization (ACSP) method for Thomas Zwinger compositional flow simulation. The method is based on CSC casting the nonlinear governing equations in terms of the zwinger@csc.fi tie-simplex. The tie-simplex space is directly discretized using a limited number of tie-simplexes. The coefficients in Anne-Sophie Drouet, Jean Krug, Fabien Gillet-Chaulet the governing system of equations, including the composi- LGGE tion, density, and mobility of the phases, are computed us- [email protected], [email protected], gillet- ing multilinear interpolation in the discretized space. The [email protected] ACSP completely replaces all the standard EOS computations MS37 Rustem Zaydullin Mesh-adaptive Approaches to Numerical Ground- Stanford University ing Line Migration [email protected] Central to the evolution of marine ice sheets that could po- Denis Voskov tentially make large contributions to sea level rise in com- Energy Resources Engineering Department ing centuries is the evolution of grounding lines, a process Stanford Univeristy difficult to represent numerically, largely due to issues of [email protected] resolution. I will show numerical results of several mesh- adaptive approaches that attempt to deal with these issues. I will discuss the strengths of weaknesses of each approach, Hamdi Tchelepi and compare with an existing quasi-analytical approach. Stanford University Energy Resources Engineering Department Daniel Goldberg [email protected] Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology, Cambridge, USA MS37 [email protected] Block-Structured Adaptive Mesh Refinement in the Bisicles Ice Sheet Model MS37 The BISICLES ice sheet model employs a block-structured Review of Adaptive Methods for Marine Ice Sheet mesh of rectangular cells to obtain high resolution at the Models grounding line. In some ways that is restrictive compared to (say) an unstructured mesh of triangles, but it has three Adaptive mesh refinement methods are required to account 120 GS13 Abstracts

for the sharp changes of the dynamical regime of ice in the University of Cassino and Southern Lazio transition zones between ice sheets and ice shelves. The [email protected] empirical criterion, which consists of strongly reﬁning close to the grounding line, is easy to implement but not opti- Michele Iervolino, Andrea Vacca mal. In contrast, a new family of methods based on error Second University of Naples estimates has appeared in recent years. This talk aims to [email protected], [email protected] give a comparative overview of such methods.

Guillaume Jouvet MS38 Freie Universität Berlin Local Adaptive Mesh Refinement on the GPU Institut für Mathematik [email protected] We present the implementation of adaptive mesh refinement (AMR) for shallow water simulation on the GPU. AMR significantly increases accuracy, with little impact MS38 on computational cost compared to increasing grid resolu- One-Dimensional Finite-Volume Modelling of the tion for the entire domain. Mapping the AMR algorithm Flow and Morphological Processes During the 1996 to the GPU, however, is non-trivial. Our implementation Lake Ha!Ha! Dyke Break Event targets the second-order accurate Kurganov-Petrova central scheme. We present implementation details, difficul- The Lake Ha!Ha event is chosen as an example of extreme ties, key insights, and performance benchmarks. flow to highlight two key issues in numerical simulations of real events: the discretisation of topographical source Martin L. Stra terms in very irregular and evolving cross-sections, and Centre of Mathematics for Applications the representation of morphological processes when ero- University of Oslo sion affects the river banks as well as the river bed. A [email protected] finite-volume modelling framework is used to conduct the analysis first from a pure hydrodynamical point of view, and secondly by including morphological processes. MS38 A GPU Implementation of High-Order PVM Finite Sandra Soares-Frazao Volume Schemes for Shallow Flows on Triangular Institute of Mechanics, Materials and Civil Engineering Meshes Ecole Polytechnique de Louvain [email protected] In this work we present a CUDA implementation of the high-order WENO reconstruction operator proposed by M. Fabian Franzini Dumbser and M. Käser for triangular meshes. We use Ecole Polytechnique de Louvain this reconstruction operator in combination with the PVM- [email protected] IFCP sheme in order to simulate one an two-layer shallow water flows achieving second and third order accuracy. Fi- Olivier Carlier,YvesZech nally, we perform an analysis of the obtained precision and Institute of Mechanics, Materials and Civil Engineering efficiency with respect to CUDA implementations of the Ecole Polytechnique de Louvain first order PVM-IFCP scheme for one and two-layer shal- [email protected], [email protected] low water systems. Marc de la Asuncion,JoseM.Mantas MS38 University of Granada 2D Depth Integrated Modeling of Morphodynami- [email protected], [email protected] cal Processes: A New Algorithm for Unstructured Grids Manuel J. Castro University of Malaga In recent years many complex multi-phase or multi-layer [email protected] models were proposed for modeling water and sediment flows in unsteady conditions. Moreover representation of complex geometries can be achieved using a unstructured MS39 mesh. In the present paper an ad-hoc algorithm for un- Targeting Observations and Parameter Estimation structured triangular cells is proposed. It is demonstrated Techniques Within Ensemble Data Assimilation that the algorithm is globally mass-preserving. Effective- ness of the proposed approach is demonstrated by the nu- We explore novel data assimilation techniques for two merical integration of the morphodynamic model proposed model problems of potential meteorological interest. Using by Greco et Al. (2012). the local ensemble transform Kalman Filter (LETKF), our main result demonstrates LETKF with targeted observa- Angelo Leopardi tions based on largest ensemble variance is skillful by out- DIPARTIMENTO DI INGEGNERIA CIVILE E performing LETKF with randomly located observations. MECCANICA We implement the parameter estimation method SPEEK Università di Cassino, Italy to further improve state estimation. We also determine [email protected] the effect that number of observations, ensemble size, and localization radius have on state estimation. Massimo Greco University of Naples Thomas Bellsky [email protected] Arizona State University [email protected] Stefania Evangelista GS13 Abstracts 121

Eric J. Kostelich University of New South Wales Arizona State University [email protected] School of Mathematical & Statistical Sciences [email protected] Christian Horenkamp Chair of Applied Mathematics Alex Mahalov University of Paderborn departement of mathematics, [email protected] Arizona State University [email protected] Adam Monahan School of Earth and Ocean Sciences University of Victoria MS39 [email protected] The Onset of Desertification: the Dynamics of Veg- etation Patterns under Slowly Varying Conditions Vincent Rossi In this talk we introduce a conceptual model for vegeta- UNSW, Australia, tion patterns in semi-arid ecosystems on sloped terrains. [email protected] We consider the onset of pattern formation through a Turing/Turing-Hopf bifurcation by varying the parameter Alex Sen Gupta (A) that measures yearly rainfall. We numerically con- UNSW, Australia struct Busse balloons to follow the family of stable spa- [email protected] tially periodic (vegetation) patterns into the realistic area of localized vegetation patterns. Next, we assume that A Erik van Sebille is a slowly decreasing function and study the trajectory University of New South Wales of the patterns through the Busse balloon. We find that [email protected] the vegetation patterns undergo ‘mini-catastrophes’ as the trajectory approaches the boundary of the Busse balloon before they reach the final catastrophe of desertification. MS40 Experimental Investigation of Shale Gas Produc- Arjen Doelman tion Impairment Due to Spontaneous Imbibition of Mathematisch Instituut Fracturing Fluid Following Wellbore Stimulation. [email protected] A series of laboratory experiments were conducted to mimic spontaneous imbibition of water-based fracturing MS39 fluid into fractured shale formations and investigate its im- Pseudo-Orbit Data Assimilation for Atmospheric pact on gas production impairment. The imbibing front Gcms was monitored using X-ray computed tomography, which allowed us to map saturation at controlled time intervals. Data assimilation for nonlinear models such as weather Results are compared against similar experiments in tight forecasting models is a challenging task. A promising al- sand and Berea sandstone samples in terms of regained ternative approach is proposed to produce more consistent permeability and evolution of saturation profiles. estimates of the model state, and to estimate the (state dependent) model error simultaneously, using the Pseudo- Zuleima T. Karpyn,LuisAyala orbit Data Assimilation method with a stopping criteria. Energy and Mineral Engineering This method is shown to be more efficient and more co- The Pennsylvania State University herent than the variational method and outperform the [email protected], [email protected] Ensemble Kalman Filter in nowcast on large scale models.

Hailiang Du MS40 Centre for Analysis of Time Series Competitive Usage of Sub-Surface Systems: How London School of Economics Can Modeling Help to Quantiﬁy Potential Impacts [email protected] and Risks?

Global climate change, shortage of resources and the grow- MS39 ing usage of renewable energy sources has lead to a growing Automatic Identification of Oceanic and Atmo- demand for the utilization of subsurface systems. Among spheric Coherent Structures As Minimal Flux Re- these competing uses are Carbon Capture and Storage gions Using Transfer Operators (CCS), geothermal energy, nuclear waste disposal, ”renewable” methane or hydrogen storage as well as the ongoing Optimally coherent sets are the most efficient transporters production of fossil resources like oil, gas and coal. Addi- of geophysical flow mass (eg. water mass or air mass). We tionally, these technologies may also create conflicts with describe a recent numerical method that uses Lagrangian essential public interests such as water supply. For ex- information to detect and track optimally coherent sets in ample, the injection of CO2 into the subsurface causes an time-dependent geophysical flows. We illustrate the new increase in pressure reaching far beyond the actual radius approach by tracking Agulhas rings, and accurately deter- of influence of the CO2 plume, potentially leading to large mining the locations of the Antarctic polar vortex. The amounts of displaced salt water. In order to be able to method works naturally in two- and three-dimensions, and asses the large scale impacts of different technologies it is can handle both advective and advective/diffusive dynam- necessary not only to consider the reservoir itself but also ics. the regional hydrogeology. This is especially important for the vertical migration of displaced formation fluids or con- Gary Froyland taminants. Structures such as fault zones or salt domes are 122 GS13 Abstracts

considered as potential pathways for displaced fluids into lems in Geoscience for New Hybrid Architecture shallow systems and their influence has to be taken into account. Industrial simulation software have to manage: (i) the complexity of the underlying physical models, (ii) the Holger Class complexity of numerical methods used to solve the PDE Universitaet Stuttgart systems, and finally (iii) the complexity of the low level Scientist computer science services required to have efficient soft- [email protected] ware on modern hardware. Nowadays, some frameworks offer a number of advanced tools to deal with the com- Alexander Kissinger plexity related to parallelism in a transparent way. How- Universitaet Stuttgart ever, high level complexity related to discretization meth- [email protected] ods and physical models lack of tools to help physicists to develop complex applications. Generative programming and domain-specific languages (DSL) are key technologies MS40 allowing to write code with a high level expressive language Simulation of Coupled Flow and Reactive Trans- and take advantage of the efficiency of generated code for port in Porous Media by MFEM with Application low level services. In our paper, we present a C++ Domain to Concrete Carbonation Specific Embeded Language (DSEL) to implement multiscale methods for elliptic problems in porous media with a We discuss a prototypical reaction-diffusion-flow scenario high level of abstraction allowing to separate the low level in saturated/unsaturated porous media. The special fea- layer necessary to have performance on new hybrid het- tures of our scenario are: the reaction produces water and erogeneous mutiprocessors architecture with data-parallel therefore the flow and transport are coupled in both direc- accelerators. We focus on the capability of the language tions and moreover, the reaction may alter the microstruc- to design complex multi-scale methods and we present the ture. This means we have a variable porosity in our model. abstract object oriented runtime system model allowing to For the spatial discretization we propose a mass conser- adress heterogeneous architecture. We present some per- vative scheme based on the mixed finite element method. formance results on various hybrid platforms. The scheme is semi-implicit in time. Error estimates are obtained for some particular cases. We apply our finite Jean Marc Gratien element methodology for the case of concrete carbonation IFP – one of the most important physico-chemical processes [email protected] affecting the durability of concrete.

Florin A. Radu,FlorinA.Radu MS41 Institute of Mathematics Scalability of a Multi-Phase Code for Performance University of Bergen Assessment of a Radioactive Waste Disposal in ﬂ[email protected], ﬂ[email protected] Porous Media

Adrian Muntean The French National Radioactive Waste Management Department of Mathematics and Computer Science Agency (Andra) runs numerical simulations to assess per- TU Eindhoven formance of radioactive waste disposal in geological me- [email protected] dia. Parallel mpi based code TOUGH2-MP has been used for years to perform multi-phase simulations on this topic.According to grid of millions cells and long time sim- Iuliu Sorin Pop ulated, scalability of TOUGH2-MP has been studied on Dept of Mathematics and Computer Sciences Linux clusters (Intel and AMD) up to 2048 cores for vari- TU Eindhoven ous physical situations and results are presented here. [email protected] Bernard Vialay Andra MS41 France Gampack (gpu Algebraic Multigrid Package) [email protected] Algebraic multigrid (AMG) has become the preconditioner of choice for solving the pressure subblock of multiphase MS41 flow matrices. The serial and irregular nature of traditional Multi-GPU Parallelization of Nested Factorization AMG algorithms has made accelerating them on massively Linear Solver parallel processors difficult. We discuss the approaches we have used to successfully accelerate AMG on multi- We describe a massively parallel Nested Factorization (NF) ple GPUs by employing algorithms with sufficient fine- linear solver. The key features are: 1) a special ordering of grained parallelism. We then compare the performance of the matrix elements that maximizes coalesced memory ac- our GAMPACK solver with CPU-based AMG solvers for cess, 2) application of twisted factorization, which doubles matrices arising from reservoir simulation. concurrent threads at no additional cost, and 3) extension to multiple GPUs by overlapping memory transfer between Vincent Natoli, Kenneth Esler GPUs with solution of the interior regions. The 6-GPU so- Stone Ridge Technology lution of a 26.9M-cell model is more than five times faster [email protected], than the single-GPU solution. [email protected] Yifan Zhou Stanford University MS41 (Now with Chevron Energy Technology Company) Arcfvdsl, a Dsl in C++ to Develop Diffusive Prob- [email protected] GS13 Abstracts 123

Hamdi Tchelepi Media Stanford University Energy Resources Engineering Department The governing equations for porous media problems con- [email protected] sist of coupled processes that can vary over multiple scales. Because of disparity of scales, the direct numerical simulations of these processes are prohibitively expensive. This MS42 presents the need to develop simplified models to signifi- The Localized Reduced Basis Multiscale Method cantly reduce the number of degrees of freedom while ne- glecting irrelevant details of the involved physics. In this We present the Localized Reduced Basis Multiscale work, we apply dynamic mode decomposition (DMD) and (LRBMS) method for parameter dependent heterogeneous proper orthogonal decomposition (POD) on compressible elliptic multiscale problems [F. Albrecht, B. Haasdonk, flows in highly heterogeneous porous media to extract the S. Kaulmann, and M. Ohlberger. The Localized Re- dominant coherent structures and derive a reduced-order duced Basis Multiscale Method. In A. Handloviˇcová model. Different permeability fields are considered to in- and Z. MinarechováandD.Sevˇˇ coviˇc (editor(s)): AL- vestigate the capability of these techniques to capture the GORITMY 2012 - Proceedings of contributed papers and main flow characteristics and reconstruct the flow field posters (2012), 393–403]. This method brings together within a certain accuracy. In most of the cases, DMD- ideas from both Reduced Basis methods to efficiently solve based approach showed a better predictive capability. parametrized problems and from multiscale methods in order to deal with complex heterogeneities and large do- Mehdi Ghommem mains. We present recent developments of the method and King Abdullah University of Science and Technology applications in the two-phase flow context. (KAUST) Division of Physical Sciences & Engineering (PSE) Felix Albrecht [email protected] University of Münster (Germany) Institute for Computational und Applied Mathematics Yalchin Efendiev, Michael Presho [email protected] Department of Mathematics & ISC Texas A&M University Bernard Haasdonk, Sven Kaulmann [email protected], [email protected] University of Stuttgart [email protected], Victor M. Calo [email protected] King Abdullah University of Science and Technology (KAUST) Mario Ohlberger Division of Physical Sciences & Engineering (PSE) Universität Münster [email protected] Institut für Numerische und Angewandte Mathematik [email protected] MS42 Computation of Eigenvalues by Numerical Upscal- MS42 ing Analysis of a Control Volume Hmm for Multi- PhysicsProblemsinPorousMedia We present a numerical upscaling technique for computing eigenvalues of selfadjoint elliptic operators with multiscale We discuss conservative methods based on the heteroge- coefficients. We compute a low-dimensional generalized fi- neous multiscale methodology. The key ingredients are lo- nite element space that preserves small eigenvalues in a su- cally conservative control volume methods on the coarse perconvergent way. The approximate eigenpairs are then scale, coupled with local solvers for the fine scale prob- obtained by solving the corresponding low-dimensional al- lems, thus providing proper effective relationships among gebraic eigenvalue problem. The rigorous error bounds are coarse scale parameters. We place particular emphasis on provided. proper handling of coarse-scale heterogeneities. Axel M˚alqvist Sergey Alyaev Uppsala University University of Bergen [email protected] Department of Mathematics [email protected] Daniel Peterseim Department of Mathematics Jan M. Nordbotten Humboldt-Universität zu Berlin Department of Mathematics [email protected] University of Bergen [email protected] MS43 Eirik Keilegavlen Discontinuous Galerkin Unsteady Discrete Adjoint University of Bergen Method for Real-Time Efficient Tsunami Simula- [email protected] tions An unsteady discrete adjoint implementation for a discon- MS42 tinuous Galerkin model solving the shallow water equa- Coupled Local-Global Model Reduction for Com- tions on the sphere is presented. Its use for tsunami sim- pressible Flows in Highly Heterogeneous Porous ulations is introduced to reconstruct the initial condition automatically from buoy measurements. Based on this feature, a real-time tsunami model is developed, using several 124 GS13 Abstracts

numerical tools such as a high-order discretization, hp- are discretized by the finite-difference method and inte- refinement, parallel dynamic load balancing and adjoint- grated on a rectangular grid, which is the map of the curvi- based data assimilation. The model is able to reconstruct linear grid generated by the elliptic method. Verification the tsunami source and accurately forecast its far-field and validation of numerical model is performed against the propagation in a computational time 20 times faster than laboratory experiment by Heller (2007) and megatsunami the physical propagation time. The work presented consti- Lituya Bay event. tutes a step towards an efficient nonlinear tsunami warning model. Additional features could be added for more com- Natalja Rakowsky plete realistic forecasts. Alfred-Wegener-Institute for Polar and Marine Research Am Handelshafen 12, 27570 Bremerhaven, Germany Sebastien Blaise [email protected] Institute of Mechanics, Materials and Civil Engineering Université catholique de Louvain Alexey Androsov [email protected] AWI [email protected] Amik St-Cyr Computation and Modeling, Sven Harig Shell International E&P, Inc. Alfred-Wegener-Institute for Polar and Marine Research [email protected] [email protected]

Dimitri Mavriplis Department of Mechanical Engineering MS43 University of Wyoming Implementation of Triangular Galerkin Type [email protected] Adaptive Tsunami Propagation and Inundation Schemes Brian Lockwood University of Wyoming A tsunami simulation framework is presented, which is [email protected] based on adaptive triangular meshes with finite element Galerkin type discretizations. This approach allows for high local resolution and geometric accuracy, while main- MS43 taining the opportunity to simulate large spatial domains. Quadrilateral-Based Discontinuous Galerkin Meth- Within this framework, different discretizations are imple- ods with Adaptive Mesh Refinement for the mented and compared concerning efficiency and accuracy. Oceanic Shallow Water Equations Furthermore, the whole evolution of a tsunami event is investigated, from the excitation to the inundation event at In recent years, we have been working on a triangle-based the coast. discontinuous Galerkin shallow water model for simulating tsunamis. This model, DGCOM, is a semi-automated Stefan Vater system that allows a user to build a grid along any coastal University of Hamburg, KlimaCampus region and then run the problem. However, DGCOM never [email protected] included any type of adaptive mesh refinement (AMR). Re- cently, we have developed a quadrilateral-based discontin- Jörn Behrens uous Galerkin AMR code for various applications includ- KlimaCampus, University of Hamburg ing the 1) nonhydrostatic atmosphere and 2) shallow water [email protected] on the sphere, and more recently 3) shallow water on the plane. In this talk I will describe this new model which we call NUMACOM and will show some benchmark test cases MS44 and discuss the addition of inundation algorithms for this The Multidimensional Muskat Inial Boundary high-order quadrilateral-based DG AMR model. Value Problem Francis X. Giraldo, Michal A. Kopera We consider the Muskat Problem for a generalized formu- Naval Postgraduate School lation to Darcy’s law equation (Darcy-Brinkman’s law). [email protected], [email protected] We follow our original idea established in previous work, which is to perturb the Darcy law equation with a positive Shivasubramania Gopalakrishnan (small as needed) viscosity term. The mathematical model Indian Institute of Technology is formulated as [email protected] ∂tρ + v ·∇x ρ = 0,∂tν + v ·∇x ν = 0, h(t, x,μ) v − divx μ Dv = −∇xp + ρf, divxv = 0, MS43 Modeling of Tsunami Generation by An Underwa- where v is the velocity field, ρ−the density, ν−the effective ter Landslide viscosity and μ = ρν−the dynamic viscosity. The generalized Muskat Problem is posed in a bounded domain of RN A high-resolution model solving for dynamics of a stack of for two-phase flow (oil-water), that seems more realistic shallow layers in curvilinear co-ordinates has been devel- from the physical point of view. We show the solvability oped for simulating landslides that can serve as source of of the initial boundary value problem for the system. This tsunami waves. The model relies on the reduced-gravity is primarily joint work with Wladimir Neves (Institute of approximation and solves nonlinear, hydrostatic or non- Mathematics, Federal University of Rio de Janeiro). hydrostatic equations for horizontally inhomogeneous, viscous fluid layers on an f-plane. The dynamical equations Nikolai Chemetov Center of Mathematics, Universidade de Lisboa GS13 Abstracts 125

[email protected] [email protected]

MS44 MS45 Blow-up and Vanishing Properties for a Class of Simplified Mineralization Dynamics in Long-Term Doubly Degenerate Parabolic Equations with Vari- CO2 Storage able Nonlinearity Geological CO2 storage relies upon long-term trapping of Anisotropy and variable nonlinearity lead to certain prop- CO2 within the storage formation. Knowledge of the effi- erties intrinsic for the solutions of doubly degenerate ciency of trapping mechanisms, of which the most perma- parabolic equations of this type. We discuss the influence nent is carbon mineralization, is essential for risk analysis. of anisotropy on the blow-up and vanishing of solutions Timescales of mineralization may be comparable to the and show that for equations with variable nonlinearity the timescales of dissolution trapping due to convective mixing. effects of finite time vanishing and blow-up may happen We present results regarding the interaction between disso- even if the equation becomes linear at time infinity. lution trapping and mineralization trapping. We use simplified mineralization dynamics to efficiently explore sensi- Sergey Shmarev tivity regarding the rate of mineralization. Universidad de Oviedo [email protected] Maria Elenius Uni Research [email protected] MS44 Regularity of Solutions to Weighted Equations of Helge Hellevang Porous Medium Type University of Oslo [email protected] We establish the Harnack inequality and continuity for nonnegative solutions of nonlinear parabolic equations of porous medium type in the presence of weight. This work Sarah Gasda incorporates the recent improvements brought to regularity University of North Carolina at Chapel Hill theory by Di Benedetto, Gianazza and Vespri and greatly [email protected] simplifies the proofs obtained by Ivanov in 80s. Ivar Aavatsmark Mikhail D. Surnachev Center for Integrated Petroleum Research Insitute of applied mathematics, University of Bergen Russion Academy of Science, [email protected] [email protected] MS45 MS44 A New Flow-Reactive-Transport Numerical Mod- Geometric PDE Models for Secondary Structure in eling Framework and Application to Co2 Mineral Proteins Carbonation This report represents a small part of an extensive research Surveys of carbon reservoirs suggest that mineral carbon- project regarding elastic membranes which occur in molec- ation is a stable long-term storage mechanism for CO2 ular structures. It applies to the mathematical study of in geologic formations. Simulation of carbonation entails the beta-sheet models which appear in the protein fold- modeling the coupled phase equilibrium, multiphase flow, ing. The β sheet (sometimes called β-pleated sheet) is a species transport, and reaction processes. This presenta- form of regular secondary structure in proteins (as the most tion describes a fully-coupled procedure for general flow well-known form is the alpha helicoidal sheet). The exist- and reactive-transport problems in a compositional sim- ing literature approximates the β sheet models by mini- ulation framework, based on element conservations. The mal surfaces (catenoidal surfaces). We will prove that the procedure, accomplished within Stanford General Purpose existing model is neither mathematically nor chemically Research Simulator, enables field-scale simulation of CO2 appropriate, and we will propose a different model based carbonation in deep saline aquifers. on surfaces whose mean curvatures lie in intervals of the form (h − , h + ). Mathematical tools involved are based Yaqing Fan on differential geometry, calculus of variations, numerical Shell Oil Company methods and special functions. [email protected] Magdalena Toda Department of Mathematics and Statistics. MS46 Texas Tech University On the Transport of Particles in Oceanic Flows: [email protected] Modeling, Theory, and Experiments

We study reduced models for transport of particle pollu- MS45 tants in the ocean. The particles transported by the ﬂuid Modeling Coupled Gas Compositional Flow, Geo- are modeled by another continuum phase, with models re- chemical, and Thermal in Porous Media sembling dusty-gas or Eulerian ones adapted to the incompressible setting. Theoretical results and some numerical Abstract not available at time of publication. experiments will be shown. Mojdeh Delshad Luigi C. Berselli University of Texas at Austin Dipartimento di Matematica Applicata ”U. 126 GS13 Abstracts

Universita’diPisa sure. [email protected] Henrik Kalisch Matteo Cerminara University of Bergen Scuola Normale Superiore, Pisa [email protected] Istituto Nazionale di Geofisica e Vulcanologia [email protected] MS46 Numerical Modeling of Oceanic Turbulent Mixing- MS46 Layers Progresses and Challenges in Spectral Multido- We introduce elements for the mathematical and numerical main Simulations of Small-Scale Oceanic Stratified analysis of turbulence models for oceanic surface mixing Flow Processes layers. Turbulent mixing-layer models are usually verti- Following an overview of spectral multidomain penalty cal first-order closure models, depending on the gradient method (SMPM) fundamentals, we discuss the physical Richardson number. We propose a model that allows to insights enabled by application of a singly non-periodic manage mixing layer flows with horizontal perturbations version of SMPM to the simulation of select small-scale of the initial conditions. We perform a theoretical and nu- oceanic stratified flow processes. We then present a recent merical analysis of the model, and a comparison with a modification of SMPM for quadrilateral subdomains. Em- general model, based on the Primitive Equations. phasis is placed on the challenges, in terms of consistency Samuele Rubino and preconditioning, resulting from the non-symmetric ma- Universidad de Sevilla trix in the iterative solution of the discretized pressure [email protected] Poisson equation.

Peter Diamessis MS47 Department of Civil and Environmental Engineering Cornell University Multiscale Simulation of Reactive Flow and Trans- [email protected] port in Porous Media In this work we model single, multiphase, reactive, and MS46 non-Newtonian flow at the pore and sub pore scales but develop multiscale techniques to bridge the pore and macro- Central-Upwind Schemes for 2D Shallow Water scales. A more efficient, novel domain decomposition Equations method is used for upscaling. The medium is decomposed In this talk we will discuss central-upwind schemes for the into hundreds of smaller networks (sub-domains) and then shallow water equations. These equations are widely used coupled with the surrounding models to determine accurate in many scientific applications related to modeling of wa- boundary conditions. Finite element mortars are used as a ter flows in rivers, lakes and coastal areas. Furthermore, mathematical tool to ensure interfacial pressures and fluxes many real world engineering applications require the use of are matched at the interfaces of the networks boundaries. triangular meshes due to the complicated structure of the The results compare favorably to the more computation- computational domains of the problems being investigated. ally intensive (and impractical) approach of upscaling the Therefore the development of robust and accurate numer- media as a single model. ical methods for the simulation of shallow water models in Matthew Balhoff complex domains is an active challenging problem. In our ICES talk we will discuss the recently developed central-upwind The University of Texas at Austin schemes for such models. We will demonstrate the perfor- balhoff@mail.utexas.edu mance of the proposed methods in a number of numerical examples. This is joint work with J. Albright, S. Bryson, A. Kurganov and G. Petrova. MS47 Yekaterina Epshteyn Adaptive Hybrid Models of Reactive Transport in Department of mathematics Porous Media University of Utah Continuum-scale models of flow and transport in porous [email protected] media rely on sets of assumptions and simplifications, and fail to describe experimentally observed phenomena when- MS46 ever such conditions are not satisfied. This is particularly true for highly localized phenomena, e.g. (bio-) geochem- Reconstruction of the Pressure in Long-Wave Mod- ical reactive processes, in which poor mixing at the pore- els with Constant Vorticity scale often leads to a localized breakdown of macroscopic The effect of constant background vorticity on the pres- equations. In such systems the use of hybrid models, which sure beneath steady long gravity waves at the surface of a solve pore-scale equations in a small portion of the com- fluid is investigated. Using an asymptotic expansion for the putational domain and use their continuum counterparts streamfunction, we derive a model equation given in terms everywhere else, become imperative. A desirable feature of the vorticity, the volume flux, total head and momentum of hybrid models is their ability to track where and when flux. It is shown that for strong vorticity, the maximum in space and time to use pore-scale simulations, i.e. their pressure is not located under the wave crest, and the fluid adaptability to time- and space-dependent phenomena. In pressure near the surface can be below atmospheric pres- this work, we construct criteria for adaptive hybridization, based on macroscopic dimensionless numbers. This approach allows one to dynamically establish whether or not hybridization is needed at any instances in space and time, GS13 Abstracts 127

by evaluating continuum-scale quantities only. Finally, we mum Reynolds numbers. implement the proposed adaptive hybridization scheme to reactive flow through a chemically heterogeneous planar Jannes Kordilla fracture. Geoscientific Centre University of Goettingen Ilenia Battiato [email protected] Department of Mechanical Engineering, Clemson University Alexandre M. Tartakovsky [email protected] Pacific Northwest National Laboratory [email protected] MS47 Tobias Geyer On the Origin of Non-Fickian Transport in Porous Geoscientific Centre Media University of Goettingen The exact relationship between structure, velocity field and [email protected] non-Fickian transport in heterogeneous media has not been fully understood. A novel methodology is developed that MS48 predicts transport on micro-CT images by using probability density functions (PDFs) of displacement and transit Multiscale Simulation of Flow and Heat Transport times between image voxels, and relates it to PDF of lo- in Fractured Geothermal Reservoirs with Improved cal velocity. A key determinant for non-Fickian transport Transport Upscaling is the spread in velocity distribution, as demonstrated on We present a framework for modeling and simulation of beadpack, sandstone and a range of complex carbonate flow and heat-transport in fractured geothermal reservoirs, rock. where fractures impact flow and transport at multiple Branko Bijeljic scales. Flow in large-scale fractures are simulated explic- Department of Earth Science and Engineering itly in the computational model, while flow in small-scale Imperial College London fractures and the porous media is upscaled. The link to [email protected] the fine-scale solution is kept to enable computation of approximate fine-scale solutions. Based on the approximate fine-scale solutions, upscaling of the transport is improved. Martin J. Blunt Department of Earth Science and Engineering Imperial College Tor Harald Sandve [email protected] University of Bergen Norway [email protected] MS47 Pore-Network Modeling of Electrokinetic Flow and Inga Berre, Eirik Keilegavlen Transport in Microcapillaries University of Bergen Electrokinetic transport porous media is a complex cou- [email protected], [email protected] pled phenomenon, which is highly influenced by surface chemistryaswellastransportoftheionsinthemicrocap- Jan M. Nordbotten illaries. After derivation of analytical relations for flow and Department of Mathematics transport in a micro-capillary that include gradients of con- University of Bergen centration, pressure and electric potential, these relations [email protected] are solved numerically in a complex network. Effects of heterogeneity of pore geometry and zeta potential on flow and transport have been studied. MS48 Title Not Available at Time of Publication Vahid Joekar-Niasar Department of Earth Sciences Abstract not available at time of publication. University of Utrecht [email protected] Alifio Grillo Polythecnic of Turin, Italy alfi[email protected] MS47 Simulation of Film and Droplet Flow on Smooth MS48 and Rough Wide Aperture Fractures using Smoothed Particle Hydrodynamics Space-Time Domain Decomposition For Transport In Porous Media With Fractures Gravity-driven flow in fractured porous media exhibits highly dynamical interfaces and a wide range of intermit- We consider nonoverlapping domain decomposition meth- tent flow processes ranging from adsorbed films to droplets, ods for transport problems in porous media with frac- rivulets and wavy surface films. We present a free-surface tures. The first approach uses the time dependent Steklov- Smoothed Particle Hydrodynamics model to simulate cap- Poincaré operator and the second uses the optimized illary forces dominated droplet and film flow on dry and Schwarz waveform relaxation. Each method enables different time steps in the subdomains. Both d-dimensional and prewetted wide aperture fracture surfaces. We demon- d − d strate the various effects of wettability on the flow dynam- ( 1)-dimensional fractures (for a -dimensional domain) ics and show the influence of surface roughness on maxi- are considered. Numerical results in 2D will be presented. 128 GS13 Abstracts

Alessio Fumagalli MOX, Department of Mathematics Thi Thao Phuong Hoang Politecnico di Milano, Italy INRIA Paris-Rocquencourt, France [email protected] Phuong.Hoang Thi [email protected]

Jerome Jaffre MS49 INRIA-Roquencourt Compressibility of Porous Materials with Com- 78153 Le Chesnay cedex France pressible Fluids Using Thermodynamics Jerome.Jaff[email protected] There are a variety of compressibilities for porous materi- Caroline Japhet als: jacketed, unjacketed, and pseudo-bulk are a few ex- Paris 13 university, France amples. The relationship between these compressibilities [email protected] traditionally do not account for the volume fraction. Here we present how thermodynamics can be used to determine the relationship between these compressibilities, the vol- Michel Kern ume fraction, and the compressibility of each phase. INRIA [email protected] Lynn S. Bennethum University of Colorado Denver Jean E. Roberts [email protected] INRIA Paris-Rocquencourt France [email protected] MS49 Modeling Transport of Charged Colloids Including Electrochemically Induced Adhesive Interactions MS48 Modeling Subsurface Fractures Using Enriched Fi- In this talk, we present a pore scale model describing the nite Element Method transport of charged colloids in a porous medium. Despite diffusion, convection and electrophoretic transport mecha- Enriched finite element method (EFEM) allows us to accu- nisms, the considered model includes electrochemically in- rately model fractures without having to construct mesh to duced adhesive interactions. The talk focuses on how to honor geometries of fractures. In this talk, we will present model these additional adhesive interactions which play an two applications of EFEM with improved formulations. important role in many applications. The first one concerns rapid evaluation of well productiv- ity with fractured completions. Examples will be given on Matthias Herz how to use the new method to quantify the impact of non- Department of Mathematics Darcy effect for different configurations of fractured stimu- University of Erlangen lation. The second application concerns predicting natural [email protected] fracture patterns under geological loading. The method to model fracture interaction in EFEM will be discussed. MS49 Hao Huang, Jichao Yin, Rodrick Myers, Richard Albert Multiscale Modeling of Colloid and Fluid Dynamics ExxonMobil Upstream Research Company in Porous Media including an Evolving Microstruc- [email protected], [email protected], ture [email protected], [email protected] We describe colloidal dynamics and fluid flow within a porous medium at the pore scale. The model consists of the NernstPlanck and Stokes equations including a forcing MS48 term. Surface reactions result in an evolution of the mi- A Numerical Method for Two-Phase Flow in Frac- crostructure which is captured by a level set function. Ap- tured Porous Media with Non-Matching Grids plying an averaging procedure in this framework, we obtain Darcys law and a convectiondiffusion equation with time- Two-phase flows in porous media are influenced by the and space-dependent coefficients. The results are comple- presence of fractures in many relevant applications. In- mented by simulations of a heterogeneous multiscale sce- stead of refining the grid to capture the fractures, we rep- nario. resent them as immersed interfaces, using a reduced model for the flow and suitable coupling conditions. We allow Nadja Ray for non matching grids between the porous matrix and the University of Erlangen-Nuremberg fractures to obtain a flexible method for realistic configu- [email protected] rations. Numerical fluxes that yield an entropic and conservative scheme are discussed. Tycho van Noorden, Florian Frank, Peter Knabner Department of Mathematics Anna Scotti University of Erlangen Politecnico di Milano [email protected], [email protected], [email protected] [email protected]

Luca Formaggia Department of Mathematics MS49 Politecnico di Milano, Italy Multiscale Adaptive Simulations of Concrete Car- [email protected] bonation Taking into Account the Evolution of the GS13 Abstracts 129

Microstructure Colorado School of Mines [email protected] Concrete carbonation is a chemical degradation mechanism compromising the service life of reinforced concrete structures. Using a homogenization approach to upscale MS50 the associated reaction–diffusion system given in a porous Mixing Entropy and Reactive Solute Transport medium, whose microstructure undergoes an evolution in time, an effective macroscopic limit model is obtained. To Mixing processes affect reactive solute transport in fluids. lower the complexity of numerical simulations further, an In this work the transport equation for the entropy of a effiŒcient adaptive øfinite element scheme for the limit reactive compound is derived and we show that the expo- problem is presented. The approach is generally applica- nential of the Shannon entropy is an appropriate metric ble to reaction–diffusion problems in porous media. to quantify the interplay between mixing and reactive processes. The degree of uniformity of the solute distribution Claus-Justus Heine for a reactive species and its rate of change are informative University of Stuttgart measures of physical and (bio)chemical processes and their [email protected] complex interaction.

Christian Moeller, Malte A. Peter Gabriele Chiogna University of Augsburg University of Trento, Italy [email protected], [email protected] [email protected] David Hochstetler Kunibert Siebert Stanford University University of Stuttgart [email protected] [email protected] Alberto Bellin Universita de Trento MS49 [email protected] Conceptual Multiscale Models for Flows in Layered Deforming Media Peter K. Kitanidis Dept. of Civil and Environmental Engineering We present sveral approaches to reduce computational Stanford University complexity of flow and deformation simulations in dou- [email protected] ble porous media featured by local periodicity which is assumed in the “horizontal directions’ for each layer. Homog- enized models are obtained which result in the 3D-to-2D Massimo Rolle dimensional reduction of the associated PDEs, while the Stanford University microstructure is fully 3D. We develop coupling conditions [email protected] which enable us to combine models for several homoge- nized layers to approximate a 3D structure. Applications MS50 in tissue perfusion are discussed. Characterization and Modeling Non-Fickian Dis- Eduard Rohan persion Triggered by Matrix-Diffusion in Porous Dept. of Mathematics, Faculty of Applied Sciences Media University of West Bohemia [email protected] Mobile-immobile mass transfer model implicitly states that large scale non-Fickian dispersion is controlled by the microscale properties of the media. This model has been ap- Vladimir Lukes plied successfully to interpret tracer tests at many scales University of West Bohemia, Pilsen using a memory function (MF) as a sink/source term in the [email protected] ADE equation for describing the transient diffusive mechanisms in the immobile domain. The MF is an intrinsic MS50 characteristic of the medium that can be calculated using high-resolution 3D representation of the pore structure. Modelling Chemical Reactions in Porous Media with Particle Based Methods Phillipe Gouze University of Montpellier We use a particle-tracking method to simulate several one- [email protected] dimensional bi-molecular reactive transport experiments. In our numerical scheme, the reactants are represented by particles: advection and dispersion dominate the flow, MS50 and molecular diffusion dictates, in large part, the reac- Diffusion and Reaction in Heterogeneous Media: A tions. When compared to the solution of the advection- Continuous Time Random Walk Approach dispersion-reaction equation (ADRE) with the well-mixed reaction experiments and the particle-tracking simulations Reaction kinetics in heterogeneous systems are different agreed well showing 20% to 40% less overall product, which from the ones observed in well-mixed reactors. We present is attributed to poor mixing. The poor mixing also leads to an approach to model reactive transport in complex me- higher product concentrations on the edges of the mixing dia based on a transport representation in terms of con- zones, which the particle model simulates more accurately tinuous time random walks. In this framework, linear ki- than the ADRE. netic sorption-desorption reactions are modeled as compound Poisson processes. More general chemical reactions David A. Benson are quantified using a kinetic Monte-Carlo approach. This 130 GS13 Abstracts

method allows studying the impact of heterogeneity on the time derivative of the in-plane Laplacian of the vertical anomalous diﬀusion and reaction behavior. deﬂection.

Dentz Marco Andro Mikelic Spanish National Research Council (CSIC) Institut Camille Jordan, Departement de Math´ematiques [email protected] Universit´eLyon1 [email protected]

MS50 Anna Marciniak-Czochra The Architecture of Random Mixtures University of Heidelberg Germany The principles of scalar mixing in randomly stirred media, [email protected] aiming at describing the overall concentration distribution of the mixture, its shape, and rate of deformation as the mixture evolves towards uniformity are reviewed. Then MS51 we consider the fine structure of a scalar mixture advected Geomechanical Coupling Between Poroelastic in a random, interconnected, frozen network of paths, i.e. Reservoirs and Viscoelastic Cap Rocks: Applica- a porous medium. We describe in particular the relevant tion to Pre-Salt Geological Formations scales of the mixture, the kinetics of their evolution, the nature of their interaction, and the scaling laws describing We construct locally conservative numerical methods for the coarsening process of the concentration field as it pro- two-phase immiscible flow in a strongly heterogeneous gresses through the medium, including its concentration poroelastic rock underneath a saline formation composed of distribution. halite and anydrite displaying creep behavior with the viscous strain ruled by a nonlinear constitutive law of power- Emmanual Villermaux law type. Numerical simulations are presented of a water- Univ de Provence, IRPHE flooding problem in a strongly heterogeneous carbonated Marseille, France rock overlain by a salt dome lying between a two-well verti- [email protected] cal arrangement showing the effects of viscoelasicity upon breakthrough curves.

MS51 Marcio A. Murad Modeling Arterial Walls As Multi-Layered Poroe- National Laboratory of Scientific Computation lastic Structure and Their Interaction with Pul- LNCC/MCT satile Blood Flow [email protected] We present a new model and two novel loosely coupled schemes modeling fluid-structure interaction between an Jesus Obregon incompressible, viscous fluid and a multi-layered structure, National Laboratory of Scientific Computing consisting of a thin elastic shell and a poroelastic medium. LNCC/MCT Elastodynamics of the thin shell is described by the linearly [email protected] elastic Koiter shell model, while the poroelastic medium is modeled as a Biot system. We present the analysis and Marcio Borges comparison of the two methods, and numerical results. National Laboratory of Scientific Computation LNCC/MCT Martina Bukac Petropolis University of Pittsburgh [email protected] Department of Mathematics [email protected] Maicon R. Correa, Luiz Radtke National Laboratory of Scientific Computing Ivan Yotov LNCC, Brazil Univeristy of Pittsburgh [email protected], [email protected] Department of Mathematics [email protected] MS51 Paolo Zunino Multiscale Modelling and Analysis of Flow, Chem- University of Pittsburgh ical Reactions and Mechanical Processes in Elastic Department of Mathematics Porous Media [email protected] Microscopic descriptions (at the pore scale) of flow, transport and reactions of substances, and their interaction with MS51 mechanics of the solid phase in porous media, lead to cou- A Rigorous Derivation of the Equations for the pled systems of partial differential equations in complex Biot-Kirchhoff-Love Poroelastic plate geometric structures. We derive an effective description given by the quasi-static Biot system, coupled with the We rigorously study limit behavior of the solution to quasi- upscaled reactive flow. Effective Biot’s coefficients depend static Biots equations in thin poroelastic plates as the on the reactant concentration. Additionally to the weak thickness in x3 direction tends to zero. At Terzaghis time two-scale convergence results, convergence of the energies scale we obtain the norm convergence. The bending and is proved. the pressure equations are coupled. Bending equation contains Laplacian of the pressure bending moment. The pres- Maria Neuss-Radu sure equation has derivatives only in t and x3 and contains University of Erlangen-Nürnberg Mathematics Department GS13 Abstracts 131

[email protected] [email protected]

Willi Jäger Bader Michael University of Heidelberg Technische Universität München [email protected] Department of Informatics, Scientific Computing [email protected] Andro Mikelić University of Lyon 1 Christian Pelties [email protected] Ludwig-Maximilians-Universitaet Muenchen University Munich [email protected] MS51 A High-order, Fully-coupled, Upwind, Compact Discontinuous Galerkin Method for Modeling of MS52 Viscous Fingering in Compressible Porous Media Large-Scale Dynamic Earthquake Rupture Simula- tions with the Ader-Dg Method: Towards Simula- We present a new approach for high-fidelity porous media tion Based Seismic Hazard Assessment flow simulation, based on a fully coupled, upwind, high- order discontinuous Galerkin formulation of miscible (com- We aim to understand ground-motion generation from pressible) displacement transport. The proposed method large-scale dynamic earthquake scenarios in 3D Earth is flexible on complex subsurface geometries and captures structure using the ADER-DG scheme. The method solves the strong interaction between pressure and transported the spontaneous rupture problem with high-order space- concentrations in highly compressible media. It also shows time accuracy on unstructured tetrahedral meshes. To this very low sensitivity to mesh orientation and its robustness end, geometrically complex faults can be accurately dis- and accuracy are demonstrated in a number of compress- cretized and a high frequency content may be generated. ible and incompressible multiphase flow problems. The physical problem is challenging for current numerical methods with respect to both algorithmic and computa- Guglielmo Scovazzi tional complexity, and thus requires advanced optimization Duke University strategies. [email protected] Alice A. Gabriel Hao Huang LMU Muenchen ExxonMobil Upstream Research Company [email protected] [email protected] Christian Pelties Ludwig-Maximilians-Universitaet Muenchen MS52 University Munich Hardware-aware optimization of SeisSol, an un- [email protected] structured ADER-DG code. Atanas Atanasov In this talk we give an insight into advanced hardware- Technical University Munich aware optimizations applied to SeisSol, a package for sim- [email protected] ulation of seismic wave phenomena on unstructured grids, based on the discontinuous Galerkin method combined with ADER time discretization. We show how a rigorous Vipin Sachdeva enriched pre-compile phase leads to significant speedups. IBM Research, Austin Especially code generation for small sparse matrix ker- IBM nels, typical for discontinuous Galerkin schemes, is a key [email protected] point enabling usage of advanced features on state-of-the- art hardware, such as the AVX-instruction set. We also Luca Passone discuss memory access patterns for unstructured grids used King Abdullah University of Science and Technology in SeisSol, such as element orders or grid-dependent access [email protected] frequencies to a small number of flux matrices. Finally we give an outlook to optimizations introducing hardware Kirk E. Jordan requirements already in the numerical method, which is IBM T.J. Watson Research crucial to prepare SeisSol for next-generation supercom- [email protected] puters. Geoffrey Ely Alexander Breuer Argonne National Laboratory Technische Universität München [email protected] Department of Informatics [email protected] Martin Mai KAUST Alexander Heinecke [email protected] TU München [email protected] MS52 Sebastian Rettenberger Tsunami Alert and Forecast Using a Massive Par- Technische Universitaet Muenchen Department of Informatics, Chair of Scientific Computing 132 GS13 Abstracts

allel Multiscale Model over French Polynesia Department of Informatics [email protected] Over the last four years, one widespread tsunami occurred each year in Pacific Ocean which were observed on Martin Kaeser tide gages and coasts of polynesian islands. The French Geo Risk Research, Munich Reinsurance Polynesia Tsunami Warning Center (CPPT), located on [email protected] Tahiti, used these last events to improve the accuracy of the tsunami height estimation. In this context, the last tsunamis have been modelled over Pacific ocean to test MS53 the accuracy and validate our new local forecast system Comparison of Open Source Porous Media Simula- of tsunami height based on our model using a parallel im- tors for Reservoir Engineering Applications plementation and our new computational capabilities (2.5 Tflops). The water surface initialization has been com- Open-source code provides a chance for sustainable soft- puted from Okada’s formulation, using seismic parameters ware development in the geosciences, being attractive for evaluated by CPPT. Tsunami propagation has been mod- academic institutions and industry. Recently, several open- elled by a finite-difference numerical model solving shallow source simulators have been developed for flow in porous water equations. The model is implemented using the do- media. This talk presents a detailed comparison of some main decomposition technique in conjunction with message of these simulators for reservoir engineering applications. passing interface (MPI). The values of tsunami amplitudes, By means of realistic field-scale scenarios, robustness, ef- flow velocities and arrival times are compared to the ob- ficiency and accuracy are compared by means of various served data in French Polynesia. measures. All participating simulators are part of the Open Porous Media Initiative, opm-project.org. Anthony Jamelot, Dominique Reymond CEA/LDG Pamatai, Tahiti, French Polynesia Bernd Flemisch [email protected], [email protected] University of Stuttgart, Germany bernd.fl[email protected] Helene Hebert CEA,DAM,DIF F-91297 Arpajon France Kristin Flornes [email protected] IRIS, Bergen, Norway [email protected] MS52 Knut-Andreas Lie The SeisSol Software Package for Tsunamigenic SINTEF ICT, Dept. Applied Mathematics Earthquake Simulations [email protected] We will present the SeisSol software package for the simulation of tsunamigenic earthquakes. The dynamic earth- MS53 quake faulting and the subsequent seismic wave propaga- Fully Implicit Solvers for Matlab Reservoir Simu- tion is solved simultaneously by a high order ADER-DG lation Toolbox (MRST) method implemented on unstructured tetrahedral meshes. The package provides a workflow with a concept for mesh We present a framework for development of fully implicit generation, pre- and postprocessing tools and solutions solvers based on automatic differentiation (AD) in the for visualization. To demonstrate the advantages of the open-source toolbox MRST. With an AD-class for auto- scheme we will present a subduction earthquake scenario. matically generating Jacobians, solver prototyping basi- cally boils down to writing down the residual equations. Christian Pelties It also facilitates easy manipulation of Jacobians, essen- Ludwig-Maximilians-Universitaet Muenchen tial for preconditioning. As example we use the code for University Munich adjoint-based optimization of net-present-value for a real- [email protected] istic case using the black-oil model.

Alexander Breuer Stein Krogstad,OlavMøyner Technische Universit¨at M¨unchen SINTEF ICT Department of Informatics [email protected], [email protected] [email protected]

Sebastian Rettenberger MS53 Technische Universitaet Muenchen Ensemble Kalman Filter Toolbox in Mrst Department of Informatics, Chair of Scientiﬁc Computing [email protected] An open source Ensemble Kalman Filter (EnKF) module was developed for use with the Matlab-based reservoir toolbox MRST. The module can be used for rapid testing and Alice A. Gabriel prototyping of new algorithms and workﬂows for history LMU Muenchen matching reservoir models to production or seismic data. [email protected] This presentation will discuss the functionality included in the module and show examples on both synthetic grids and Alex Heinecke Eclipse corner point grids. TU Muenchen [email protected] Olwijn Leeuwenburgh TNO, The Netherlands Michael Bader [email protected] Technische Universitaet Muenchen GS13 Abstracts 133

MS53 Hamdi Tchelepi Flow Diagnostics on Stratigraphic Grids Stanford University Energy Resources Engineering Department We present a set of simple flow diagnostic tools that can [email protected] be used to assess the quality of upscaling and quantify uncertainty in reservoir characterization. The tools are based on the computation of time-of-flight and stationary tracer MS54 distribution using an Eulerian rather than a streamline for- Theory and Software Concepts mulation. The tools are available as a module in the open- source Matlab Reservoir Simulation Toolbox. Based on a mathematical abstraction layer for multiscale methods such as the heterogenous multiscale method, mul- Knut-Andreas Lie tiscale finite element methods and the localized reduced SINTEF ICT, Dept. Applied Mathematics basis multiscale (lrbms) method [Albrecht, F. et al., 2012. [email protected] The Localized Reduced Basis Multiscale Method. In A. Handlovicová, Z. Minarechová, & D. Sevcovic,ˇ eds. Algo- ritmy 2012. Publishing House of STU, pp. 393–403.] we MS54 introduce an interface-based software framework enabling Upscaling of Fine Scale Geological Models for Non- exascale computing for multiscale methods. Additionally Linear Flow Simulations we present recent results for the lrbms method.

In this work some classical upscaling methods are extended Sven Kaulmann to the non-linear Forchheimer law. We consider the in- University of Stuttgart compressible and slightly compressible single phase steady [email protected] state filtration in anisotropic heterogeneous porous media. Our approach is local: the fine grid problem is solved independently on each subregion covering the coarse cell with MS54 suitable boundary conditions. The fine solution is then Conditional Numerical Simulations of Flow and used to determine the coarse cell parameters locally on a Transport in Porous Media single coarse cell. In this talk we compare the solutions of flow and transport Eugenio Aulisa models obtained by conditional simulations with Monte Department of Mathematics and Statistics. Carlo and stochastic collocation methods. We show that Texas Tech University for both methods the conditioning helps to reduce the un- [email protected] certainty of the solutions. We discuss a method of simulating the conditional random fields based on the uncondi- Lidia Bloshanskaya tional representation and provide the error estimates asso- Texas Tech University ciated with the simulation of conditional random fields. Department of Mathematics and Statistics [email protected] Veronika S. Vasylkivska Department of Mathematics Oregon State University Akif Ibragimov [email protected] Texas Tech [email protected] Mina E. Ossiander Math Dept Yalchin Efendiev Oregon State University Dept of Mathematics [email protected] Texas A&M University [email protected] Malgorzata Peszynska Department of Mathematics MS54 Oregon State University Multiscale Finite Volume Method For High- [email protected] Contrast Heterogeneous Media We study the mathematical properties of the MSFV MS54 method and detect the cause of its failure in presence of Multiscale Parameterization of Geologic Uncer- highly heterogeneous transmissibility fields. Local grid- tainty and stencil-based treatments are proposed to resolve this limitation in a general way. For several problems we show Abstract not available at time of publication. that the results of our conservative MSFV are accurate and Xiao-Hui Wu, Larisa V. Branets, Yahan Yang monotone with no nonphysical peaks. ExxonMobil Upstream Research Company Hadi Hajibeygi [email protected], Delft University of Technology [email protected], Dept. of Geoscience and Engineering [email protected] [email protected] MS55 Yixuan Wang A Finite-volume Approach for Coupled Simula- Stanford University [email protected] 134 GS13 Abstracts

tions of Ice, Sediment, and Melt-water Transport phy and Mass-Balance

We present a finite-volume approach for simulating coupled We present an inverse approach to estimate the ice thick- ice-related flow processes. The method employs explicit ness distribution within a mountain glacier, given transient time marching and discrete cell interactions. Ice flow is surface geometry and mass-balance. It is based on the min- computed using a second-order shallow-ice approximation imization of the surface topography misfit in the shallow (iSOSIA). The inherent benefit of the method relates pri- ice approximation. Neither filtering of the surface topogra- marily to the ease with which several types of earth surface phy nor interpolation of the basal shear stress is involved. processes may be simulated simultaneously. We illustrate Novelty of the method is the use of surface topography and the potentials of the approach by simple model scenarios mass-balance only within a time-dependent Lagrangian ap- related to the long-term dynamics of alpine glaciers. proach for moving-boundary glaciers. David Lundbek Egholm, Christian Braedstrup, Anders Laurent Michel Christensen Ecole Polytechnique Fédérale de Lausanne Department of Geoscience, Aarhus University, Denmark Lausanne, Switzerland [email protected], [email protected], laurent.michel@epfl.ch [email protected] Marco Picasso EPFL, Switzlerand MS55 marco.picasso@epfl.ch Inverse Modeling of the Greenland Ice Sheet Flow Dynamics: from Local Sensitivity to Large-Scale Daniel Farinotti, Andreas Bauder, Martin Funk Model Initialisation VAW, ETHZ, Switzerland Over the last two decades, the Greenland Ice Sheet has [email protected], [email protected], been losing mass at an increasing rate, with an impor- [email protected] tant contribution coming from acceleration and thinning of numerous outlet glaciers. Representing these changes in Heinz Blatter flow models is a challenge requiring the development of (i) Institute for Atmospheric and Climate Science grid refinement strategies to capture individually the nar- ETHZ, Switzerland row outlet glaciers, (ii) efficient numerical schemes to solve [email protected] the appropriate flow equations and (iii) inverse methods to constrain poorly known parameters. Here, we will present details and applications of these recent developments from MS56 local sensitivity analysis to large-scale model initialisation Dynamic Effects and Hysteresis in Two-Phase Flow in Porous Media

Fabien Gillet-Chaulet We consider a model describing two-phase flow in porous Laboratoire de Glaciologie et de Géophysique media, where dynamic effects are taken into account in the de l’Environnemt, Grenoble, France difference of the phase pressures(’tau term’).We investigate [email protected] the existence and uniqueness of weak solutions, starting with the non-degenerate case and then extending to the Olivier Gagliardini degenerate case . Then we study the convergence of nu- LGGE,Grenoble,France merical approximation schemes and the error estimates in IUF,France the two cases. [email protected] Xiulei Cao Department of Mathematics and Computer Science Jerome Monnier TU Eindhoven, NL Mathematics Institute of Toulouse [email protected] [email protected] nathan martin MS56 IMT CNRS/INSA/UPS, Toulouse, France. Hysteresis and Trapping in Two-Phase Flow in [email protected] Porous Media

Catherine Ritz The parameters and parameter functions of classical for- LGGE,Grenoble,France mulations of two-phase flow in porous media - the relative [email protected] permeability saturation relationship, the capillary pressure - saturation relationship, and the associated residual saturations - show path dependence, i.e. their values depend Maelle Nodet not only on the state variables but also on their drainage LJK / Université Joseph Fourier Grenoble (France) and imbibition history. In my talk I will focus on hysteresis INRIA Rhône Alpes, France of the standard model and illustrate mathematical impli- [email protected] cations, modeling challenges and possible applications. Florian Doster MS55 Dep. of CEE, Princeton University Estimating the Ice Thickness of Mountain Glaciers Dep. of Mathmatics, University of Bergen with An Inverse Approach Using Surface Topogra- [email protected] GS13 Abstracts 135

MS56 jects of this space and with an inverse function we rebuild A Componnt-Based Eulerian-Lagrangian Formu- the facies distribution. We present two examples with dif- lation for Multiphase Multicomponent Flow in ferent types of complexity, both channelized reservoirs. Porous Media Bogdan Sebacher Abstract not available at time of publication. TU Delft [email protected] Hong Wang University of South Carolina Remus Hanea Department of Mathematics [email protected] [email protected] tu delft

MS57 Arnold Heemink Delft University of Technology Estimation of Discrete Geologic Facies Distribu- [email protected] tions from Production Data Using Probability Maps MS57 Conditioning complex geologic facies models to nonlinear flowdataleadstoadiscreteparameter estimation problem. Multi-Level Estimation of a Layered Subsurface We introduce a probability conditioning method (PCM) from Sea Floor Electromagnetic Data that, instead of directly estimating facies distribution, uses We aim to identify large-scale geological structures with the flow data to infer spatial facies probability maps. The different electric conductivities using seafloor electromag- probability maps are then used to guide facies simulation. netic data. An implicit representation of the parameter We extend the proposed PCM approach to a Bayesian mix- structure related to level-set parameterization is applied to ture model formulation for conditional simulation under reduce the number of parameters while maintaining struc- multiple plausible prior facies connectivity models. tural flexibility. To quantify the model uncertainties we Behnam Jafarpour use ensemble-based estimation methods. We balance data Chemical and Electrical Engineering fit and stability using a multi-level regularization, while a University of Southern California new technique called shape priors is applied to incorporate [email protected] geological realism. Svenn Tveit Morteza Khodabakhshi Uni CIPR Texas A&M University Dept. of Mathematics, U. of Bergen khodabakhsh. @ mail.com [email protected]

MS57 Shaaban Ali Bakr, Martha Lien Uni CIPR Updating Large-Scale Geological Structures and [email protected], [email protected] Application to Shallow-Marine Environments Accurate description of dominant large-scale geological Trond Mannseth structures in petroleum reservoirs are essential for im- Centre for Integrated Petroleum Research proved hydrocarbon recovery. In this talk we discuss chal- University of Bergen, Norway lenges related to updating of these features. Further, we [email protected] show an application where the ensemble Kalman filter is used to update facies boundaries and petrohpysical parameters in a field with shallow-marine environment character- MS58 istics. The methodology is based on a parameter transfor- Vanishing Cap- mation that ensures better agreement with the necessary illarity Solutions of Buckley-Leverett Equation in Gaussian assumptions. Multi-Layer Porous Medium and Their Approxi- mation by a Convergent Phase-by-phase Upstream Rolf Lorentzen,GeirNævdal Scheme. IRIS [email protected], [email protected] We present mathematical and numerical tools for approximating two-phase flow models in porous media that con- Ali Shafieirad sist of different rock types. We study situations where the Statoil capillary effects can be neglected within each rock; but [email protected] at the junctions between rocks, capillarity effects should be carefully taken into account. From the mathematical viewpoint, Buckley-Leverett equation with neglected MS57 capillarity admits many different weak solutions. Follow- Channelized Reservoir Estimation using EnKF. A ing Kaasschieter (Comput. Geosci., 1999), using a theory Probabilistic Approach for discontinuous-flux conservation laws we deeply investigate vanishing capillarity limits in dimension one and point In this study we estimate the locations of facies types that out some wrong interpretations of the Kaasschieter’s re- occur in the reservoir domain. We introduce a new object sult that appeared in the literature. We derive a simple named ”signed probabilities field”, and probabilities are used as distances from two instances represented by 1 and procedure that selects the physical solution. We use it to 0. Then, the ensemble Kalman filter is applied for the ob- design efficient finite volume schemes in multiple space dimensions. In particular, we claim that the phase-by-phase 136 GS13 Abstracts

upstream scheme can be adapted to the heterogeneous set- Robert Eymard ting in such a way that it does converge to the physically University Paris East relevant vanishing capillarity solution. [email protected]

Boris Andreianov Cindy Guichard Laboratoire de Mathématiques University of Nice Sophia Antipolis Université de Franche-Comté [email protected] [email protected] Raphaele Herbin Konstantin Brenner University of Aix-Marseille Laboratoire Jean-Alexandre Dieudonné [email protected] UniversitédeNice [email protected] MS58 Clément Cancès Discontinuous Galerkin Method for Two-phase Lab. Jacques-Louis Lions Flows in Heterogeneous Porous Media with Cap- Paris 5ème, France illary Barriers [email protected] We present an accurate discontinuous Galerkin method with low numerical dispersion for two-phase immiscible in- MS58 compressible flows in heterogeneous porous media with a Multi-Phase Multi-Component Flow in Heteroge- discontinuous capillary field. Implicit Euler scheme is used neous Porous Media for the saturation equation and the total velocity is reconstructed from the discontinuous Darcy flux in a RTN Natural porous media often show a pronounced heterogene- space. The non-linear interface conditions are enforced ity, which not only influences the permeability but also rel- weakly through an adequate design of the penalties on ative permeability and capillary pressure saturation curves. jumps of the global pressure and the saturation at inter- This is of particular importance for applications like soil face. physics. We present an approach for the numerical solution of Richards’ equation and of multi-phase multi-component Igor Mozolevski flow based on a capillary pressure – phase pressure formu- Federal University of Santa Catarina lation. Application relevant test cases are solved with a [email protected] self-centred Finite-Volume scheme and the results are discussed. Alexandre Ern Universite Paris-Est Olaf Ippisch CERMICS, Ecole des Ponts Interdisziplinary Center for Scientific Computing [email protected] University of Heidelberg [email protected] Luciane Schuh Federal University of Santa Catarina Rebecca Neumann luciane fl[email protected] Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (I Universität Heidelberg, Germany MS59 [email protected] Nonlinear and Nonlocal: Combined Effects on Re- actions Peter Bastian Interdisciplinary Center for Scientific Computing Many transport processes in the subsurface have been University of Heidelberg shown to be well modeled by equations that are nonlocal [email protected] in space and or time. Further, many processes, including chemical reactions require a nonlinear modelling approach. In this talk we explore the influence of nonlocal phenomena MS58 in nonlinear systems as they pertain to chemical reactions Finite Volume Discretizations of Two Phase Darcy in porous media. Flows with Discontinuous Capillary Pressures Diogo Bolster This talk deals with the extension of the finite volume ver- Department of Civil Engineering and Geological Sciences tex approximate gradient scheme to take into account dis- University of Notre Dame continuous capillary pressures for two phase Darcy flows [email protected] on general meshes. Our approach is based on the choice of the phase pressures as primary unknowns at the vertices which allows for discontinuous saturations at the interface MS59 between different rocktypes. The scheme is shown to con- Multiscale Methods for Fluid-Structure Interaction verge on a simplified model and numerical tests exhibit its with Applications to Poroelasticity efficiency on general meshes. Modeling Fluid-Structure Interaction (FSI) is a compli- Roland Masson cated task in its own right, but when dealing with com- University of Nice Sophia Antipolis plicated microstructure with many scales direct numeri- [email protected] cal simulation is often impossible. To circumvent this difficulty, using a two-scale homogenization approaches, we are able to obtain a nonlinear effective poroelastic model. GS13 Abstracts 137

Unlike in the linear poroelastic setting, the effective coeffi- Tanguy Le Borgne cients are nonlinearly coupled to micro-scale cell equations. University of Rennes, France We present computational techniques to deal with comput- [email protected] ing the effective coefficients off-line. Marco Dentz Donald Brown IDAEA, Spanish National Research Council (CSIC) Texas A&M University [email protected] [email protected]

Victor Calo MS60 KAUST A Water-Hydrogen Gas-Liquid Flow Formulated [email protected] As a Complementarity Problem

Yalchin Efendiev We consider a two-phase –liquid-gas– two-component – Dept of Mathematics hydrogen-water– system in a porous media ﬂow. Water Texas A&M University is only in the liquid phase and hydrogen can be in the [email protected] gas phase or dissolved following Henry’s law. This problem arose from the simulation of the migration of hydrogen Peter Popov produced by the corrosion of metallic containers in a deep Bulgarian Academy of Sciences underground repository of nuclear waste. It is solved using [email protected] a complementarity formulation and a Newton-min method.

MS59 Ibtihel Ben Gharbia, Jean Charles Gilbert INRIA-Rocquencourt Langevin Model for Anomalous Reactive Transport ibtihel.ben [email protected], [email protected] Under certain conditions, effective transport equations fail to describe accurately reactive transport. In this presenta- Jerome Jaffre tion, a stochastic reduction model based on the Langevin INRIA-Roquencourt approach will be presented. Numerical discretization and 78153 Le Chesnay cedex France accuracy of the resulting stochastic equations will be dis- Jerome.Jaff[email protected] cussed in the context of anomalous transport with mixing controlled bimolecular reactions. MS60 Alexandre M. Tartakovsky Presence of Fluid Phases as a Non-Linear Comple- Pacific Northwest National Laboratory mentarity Problem [email protected] Partly because of phase transitions, miscible fluid flows in porous media tend to be numerically difficult. This talk MS59 will present an approach to explicitly deal with phase tran- Quantifying Mixing of Passive Scalars in Heteroge- sitions in the system of equations. For this, the transition neous Porous Media Flow using Lagrangian Statis- conditions are formulated as a set of local inequality prob- tics lems. We will briefly discuss how this approach can be used for numerical models and flash calculations and compare The role of kinematics in increasing mixing efficiency has it to previous approaches by means of several numerical been topic of intense research in the past. Mixing con- examples. sists of stretching and folding of material lines and surfaces, which serve to homogenize the scalar distribution. Andreas Lauser Mapping these kinematical properties onto mixing mea- Universität Stuttgart, Germany sures can help to further our understanding of the system [email protected] and provide better predictions. In this talk, we quantify mixing measures as a function of the kinematical mechanisms such as straining and shearing on large-scale trans- MS60 port. Our work differs from previous ones in the sense A General Model for Two-Phase Flow in Terms of that we focus on investigating the Lagrangian statistics of Multiple Complementarity Conditions the spatially variable kinematical measures experienced by solute parcel in enhancing the overall mixing. We map We present the formulation and examine the properties of mixing and transport patterns with the spatial structure a general mathematical model for compositional two-phase of velocity fields in terms of its deformation counterparts. flow in porous media. We discuss the proper choices of Our results illustrate the appearance of coherent structures principal variables and subsequent static (flash) equations when we map the spatially varying velocity field onto the allowing for any (dis)appearance of one of the phases with- kinematical measures. We hypothesize that analyzing the out the need of variable switching or unphysical quantities. Lagrangian statistics of kinematical measures and its cor- The formulation in terms of complementarity conditions al- relation properties can help understand their consequences lows for an efficient and stable solution by the semismooth in mixing of passive scalar. In particular, quantify the cor- Newton’s method. relation properties (auto-correlation and cross-correlation) Estelle Marchand of the different deformation components. Department Mathematik, AM1 FelipedeBarros Friedrich-Alexander-Universitaet Erlangen-Nuernberg Politecnica de Catalunya [email protected] [email protected] 138 GS13 Abstracts

Peter Knabner University of Warwick Friedrich-Alexander University Erlangen-Nurenberg, [email protected] Germany Department of Mathematics [email protected] MS61 Discontinuous Galerkin Methods for Adaptive At- Torsten Müller mospheric Flow Universitaet Erlangen-Nuernberg [email protected] We present higher order discontinuous Galerkin (DG) methods for adaptive atmospheric flow problems. Adap- tive DG methods will be applied to standard test cases MS60 for atmospheric flow and different adaptation indica- Analysis and Numerical Approximation of tors will be discussed. The implementation of the DG Methane Hydrates Model methods is based on the software package DUNE-FEM (dune.mathematik.uni-freiburg.de) which is a module of Modeling of formation and dissociation of methane hy- DUNE (www.dune-project.org). The numerical results will drates is important for energy and climate studies. The be accompanied by a short presentation of implementation nonlinear degenerate PDE model has to account for multi- details such as dynamic load balancing. ple phases and solubility constraints. An appropriate formulation using monotone operator techniques leads to well- Robert Kloefkorn posedness results extending those for a porous-medium University of Freiburg equation and Stefan problem. In turn, we can take ad- [email protected] vantage of complementarity constraints to get convergence results comparable to those for Stefan problem but with a MS61 superior solver performance. A Semi-Implicit, Semi-Lagrangian, P-Adaptive Ralph Showalter, Malgorzata Peszynska, Nathan L. Discontinuous Galerkin Method for the Rotating Gibson, F. Patricia Medina Shallow Water Equations on the Sphere Department of Mathematics Oregon State University As a first step towards construction of a DG based dy- [email protected], namical core for high resolution atmospheric modelling, a [email protected], semi-implicit and semi-Lagrangian Discontinuous Galerkin [email protected], method for the SWE is proposed and analysed. The [email protected] method is equipped with a simple p-adaptivity criterion, that allows to adjust dynamically the number of degrees of freedom employed. Numerical results in the framework MS61 of standard idealized test cases prove the accuracy and ef- Adaptive Discontinuous Galerkin Simulations of fectiveness of the method even at high Courant numbers. Shallow Water Flow Building on the work of Giraldo et al. (2002), we intro- Giovanni Tumolo duce an adaptive triangular Discontinuous Galerkin model ICTP, Trieste, Italy for solving the two-dimensional shallow water equations. [email protected] Accurate Riemann solvers and limiters ensure a correct handling of interfaces between wet and dry cells, while MS62 the adaptive mesh, which is created using the library am- atos (Behrens et al. (2005)), reduces computational costs DuMux As a Versatile Tool for Special Core Anal- without effecting the precision. Several idealized testcases ysis demonstrate the method’s accuracy and efficiency. An important problem in the interpretation of special Nicole Beisiegel,Jörn Behrens core analysis (SCAL) laboratory data is that during rela- KlimaCampus, University of Hamburg tive permeability measurements a strong interference exists [email protected], [email protected] with the capillary forces. To unravel this interference, simulations of the experiments are necessary. The presentation highlights how DuMux has been adapted to simulate SCAL MS61 experiments, significantly improving the business impact of Comparing a DG Dynmaic Core for Local Area SCAL measurements. A web-based user interface to Du- Weather Prediction with the Operational COSMO Mux is made available that can be used free of charge. Model Jos G. Maas We introduce a dynamic core based on the Discontinuous TNO, The Netherlands Galerkin method, implemented within the Dune software [email protected] framework (www.dune-project.org/fem). Special mechanisms are included for advection dominated flow and for Bernd Flemisch including local grid adaptation. We first study the effi- University of Stuttgart, Germany ciency, and scalability of the code. To further investigate bernd.fl[email protected] the effectiveness and efficiency of the code, we compare it with the operational COSMO model in cooperation with Albert Hebing the German Weather service. PanTerra GeoConsultants [email protected] Andreas Dedner GS13 Abstracts 139

MS62 MS63 Multiscale Simulation of Flow in Fractured Porous Intercomparison Eﬀorts: An Overview Media using MRST Abstract not available at time of publication. Flow and transport in fractured porous media involves processes on a continuum of scales, and a successful simulation Stefan Kollet strategy requires an adequate representation of the scales. Meteorological Institute We propose a two-level method, where dominating frac- University of Bonn tures deﬁne the coarse model. Then the long-range corre- [email protected] lations in the problem are represented in the coarse model and, moreover, fractures give a physical interpretation of the tangential approximation often applied to determine MS63 boundary conditions for localized problems providing the Intercomparison of Integrated Hydrologic Models basis functions. Abstract not available at time of publication. Tor Harald Sandve University of Bergen Reed M. Maxwell Norway Department of Geology and Geologic Engineering [email protected] Colorado School of Mines [email protected]

MS62 MS63 Opm Simulation of Polymer Injection Intercomparison of Geochemical Reactive Trans- The Open Porous Media (OPM) Initiative provides a set of port Models open-source GPL licensed tools centered around the simulation of flow and transport of fluids in porous media. In Abstract not available at time of publication. this talk we will give an overview of the capabilities of OPM Carl Steefel and focus on the Enhanced Oil Recovery module. We will Lawrence Berkeley National Laboratory show simulation of polymer injection into a reservoir with [email protected] heavy oil. Numerical results will be compared with output from commercial tools. MS63 Ove Svareid IRIS, Bergen, Norway Intercomparison of Coupled Hydrologic Atmo- [email protected] spheric Models Abstract not available at time of publication. Atgeirr F. Rasmussen SINTEF Mauro Sulis [email protected] Meterological Institute Bonn University Kristin M. Flornes [email protected] IRIS kristin.fl[email protected] MS64 Weak Galerkin Methods for Darcian flow: Hetero- MS62 geneity and Anisotropy MPFA on Adaptive Parallel Grids with Applica- tions to Reservoir Engineering Abstract not available at time of publication. Large scale simulation of flow through porous media with Guang Lin high spatial resolution of materials and processes require Pacific Northwest National Laboratory accurate but efficient numerical solvers. One development [email protected] branch in the simulator DuMux addresses this problem by a bundle of sequential (IMPET) solvers which allow the use MS64 of non-conforming adaptive and/or parallel grids. Accurate flux approximation on hanging nodes is achieved by MPFA Connection and Differences of WGFEMs and methods and efficient solution of the linear system by a Other Finite Element Methods parallel AMG solver. Abstract not available at time of publication. Markus Wolff James Liu University of Stuttgart Department of Mathematics Germany Colorado State University markus.wolff@iws.uni-stuttgart.de [email protected]

Benjamin Faigle University of Stuttgart [email protected] 140 GS13 Abstracts

MS64 Applied Mathematics and Computational Science Title Not Available at Time of Publication King Abdullah University of Science and Technology [email protected] Abstract not available at time of publication. Yalchin Efendiev Guowei Wei Dept of Mathematics Department of Mathematics Texas A&M University Michigan State University [email protected] [email protected] Oleg Iliev MS64 Fraunhofer Institute for Industrial Mathematics Weak Galerkin Finite Element Methods for Germany Helmholtz Equations [email protected] Abstract not available at time of publication. MS65 Shan Zhao Hybrid Multiscale Methods in Porous Media Department of Mathematics University of Alabama One of the most significant challenges facing hydrogeologic [email protected] modelers is the disparity between those spatial and temporal scales at which fundamental processes can best be understood and quantified (e.g., microscopic to pore scales, MS65 seconds to days) and those at which practical model pre- Pore-Scale Modeling of Multiphase Reactive dictions are needed (e.g., plume to aquifer scales, years to Transport with Phase Transitions and Dissolu- centuries). We review a range of approaches to this chal- tion/precipitation Reactions lenge, focusing on methods that directly integrate models defined at multiple distinct scales. We present a pore-scale model for simulating multiphase reactive transport processes including phase transi- Timothy D. Scheibe tions and dissolution/precipitation reactions. The model Pacific Northwest National Laboratory is based on the lattice Boltzmann method (LBM) and [email protected] combines the single-component multiphase Shan-Chen LB model, the mass transport LBM, and the dissolution/precipitation model. Additional schemes are devel- MS65 oped to handle reactive and moving boundaries with com- Accounting for Saturation History in Image-Based plex geometries, to account for liquid/vapor phase transi- Pore-Scale Modeling of Two-Phase Flow tion, and to guarantee mass and momentum conservation in a closed system. Multiphase flow behavior depends on saturation history in many situations, which poses problems for traditional Qinjun Kang Darcy-scale models (which treat the parameters as state Division of Earth and Environmental Sciences functions of saturation) and also for pore-scale models that Los Alamos National Laboratory employ periodic boundary conditions (saturation cannot [email protected] evolve naturally from the physics). In this paper we present a pore-scale algorithm for dynamic two-phase flow that op- Bruce Robinson erates on non-periodic domains using pressure gradient and Los Alamos National Laboratory inlet fractional flow as boundary conditions. This enables [email protected] the model to be used to study a wider variety of multiphase flow conditions and to couple the algorithm to continuum models. Li Chen Xi’an Jiaotong University Karsten Thompson [email protected] Dept Petroleum Engineering Louisiana State University [email protected] MS65 Pore Scale and Multiscale Modeling Using LBM MS65 We use GeoDict to generate geometries for representative Large-Scale Computations of Flows with Inertia elementary volumes of real porous medias. The pore-scale and Anisotropy Based on Micro-Imaging Data flows inside those geometries are simulated by the efficient LBM based on the N-S equation and macroscopic proper- Based on computational solutions of Navier-Stokes equa- ties are calculated. An efficient upscaling strategy is em- tions in geometries representing porous media at a pore ployed to reduce the CPU time of micro- and macro-scale scale, we study flows for a wide range of velocities. Our computations. main focus is on performing simulations on voxel-based micro imaging real 3D data sets. Compared to synthetic Jun Li geometries, this brings challenges due to size, data resolu- King Abdullah University of Science and Technology tion, and complexity of structures. We propose a practical Center for Numerical Porous Media power-based fully anisotropic non-Darcy model at corescale [email protected] with parameters computed by upscaling. Victor M. Calo Anna Trykozko GS13 Abstracts 141

ICM - Interdisciplinary Centre for Mathematical and Bruno Lombard Computat LMA [email protected] [email protected]

Malgorzata Peszynska St´ephane Operto Department of Mathematics GEOAZUR Oregon State University CNRS [email protected] [email protected]

Aleksander Serdyukov MS66 IPGG Local Time-Stepping and High-Order Discretiza- [email protected] tion for Wave Propagation

We present a local time-stepping method combined with a MS66 high-order spectral element spatial discretization, for seis- High-Order High-Throughput Numerical Methods mic wave propagation on locally refined meshes. This for High-Contrast Seismic Imaging space-time discretization is fully explicit. Local time- stepping methods however reduce the severe stability re- We will discuss numerical and computational issues driv- striction of explicit time-stepping scheme. The coarse and ing research into high-resolution methods for accurately refine part of the mesh is here determined by the relation solving wave propagation in high-contrast media. In par- among the mesh-size h and the polynomial order N. Nu- ticular we will compare accuracy and efficiency of mass merical experiments illustrate the efficiency of the proposed lumped finite elements, spectral elements, and discontin- method. uous Galerkin based solvers for acoustic and elastic wave scattering problems. We will discuss the structure of the Loredana Gaudio methods and how this relates to their parallel scalability University of Basel on modern hardware accelerators. [email protected] Timothy Warburton Marcus J. Grote Department of Computational And Applied Mathematics Universität Basel Rice University [email protected] [email protected]

David Medina MS66 Rice University Seismic Elastic Modeling for Seismic Imaging [email protected] We shall discuss the pros and cons for forward modeling of elastic waves considering volumetric methods, boundary Amik St-Cyr integral approaches and asymptotic formulations. Finite Computation and Modeling, difference methods are efficient. However, they suffer from Shell International E&P, Inc. limitations not met by finite element methods. Boundary [email protected] integral approaches are quite efficient especially using fast moment methods although simple heterogeneities should MS67 be considered between boundaries. Asymptotic methods have not met too much attention when considering full Modeling Biofilm Formation Within Microfluidic waveform inversion. We may see why. Channels Jean Virieux Despite multiple diseases causing widespread damage to ISTerre the citrus, wine, and other fruit industries, there has been University Joseph Fourier little attention paid to modeling biofilm development and [email protected] progression of many plantal bacterial infections. A multiphase modeling framework will be used to examine the dynamic behavior and fluid/structure interactions of biofilm Romain Brossier colonization within microfluidic channels. Linear stability ISTerre analysis will be used to determine potential causes and ten- [email protected] dencies of a robust, regular spatial patterning visualized in a laboratory setting. Stephanie Chaillat POems-ENSTA Matthew Donahue, Nick Cogan [email protected] Department of Mathematics Florida State University Anton A. Duchkov [email protected], [email protected] IPGG SB RAS and Novosibirsk State University [email protected] Leonardo de La Fuente Department of Entomology and Plant Pathology Vincent Etienne Auburn University GEOAZUR [email protected] University Nice - CNRS [email protected] Mark E. Whidden Florida State University 142 GS13 Abstracts

[email protected] taxis and Bioclogging

We model the degradation of pollutants in porous media MS67 by chemotactically moving bacteria that react with the Modeling of Bacterial Growth, Adhesion and contaminants. Chemotaxis describes the influence of the Transport in Porous Media locomotion of organisms toward or away from the concentration gradient of a chemical species. A second species of We introduce a numerical simulator for multiphase multi- bacteria can form strong biofilms which can be used as bio- component reactive flow in porous media, which is able to barriers to restrict the flow of the pollutants. Concerning consider simultaneously multiphase flow, component trans- the corresponding system of PDEs we discuss some analyt- port, phase exchange and microbiological processes. The ical results and numerical simulations. observed behaviour of Escherichia coli like growth, adhesion and biofilm formation onto sand grains was added to Raphael Schulz the simulator. The results of numerical simulations of E. Department of Mathematics coli growth and transport in the capillary fringe, with nu- University of Erlangen trient supply under steady-state and transient flow condi- [email protected] tions are finally compared to the experimental data.

Pavel Hron MS67 IWR Interaction of Reactive Flow with Solid Phase, University of Heidelberg Leading to Changes in Volume and Mechanical [email protected] Properties - Mathematical Modelling and Simula- tion Peter Bastian Interdisciplinary Center for Scientific Computing The interaction of reactive flow with solid phase is an im- University of Heidelberg portant aspect in various applications, e.g. plaque forma- [email protected] tion in blood vessels. In this talk, we formulate a model to describe this process. This includes the interaction between flow and solid, and the penetration of chemical species in Olaf Ippisch the solid phase. Numerical simulations illustrate changes Interdisziplinary Center for Scientific Computing in volume of the solid phase, and increase stress values. University of Heidelberg [email protected] Yifan Yang IWR Daniel Jost University of Heidelberg Karlsruhe Institute of Technology [email protected] [email protected] Maria Neuss-Radu University of Erlangen-Nürnberg MS67 Mathematics Department Upscaling of Thin Layer Flows Involving Reactions [email protected] at Moving Solid-Fluid Interfaces

We consider pore scale models for reactive porous media MS68 flows, with particular focus on the case when the reaction Miscemetry in Reactive Transport product deposits in layers having non-negligible thickness when compared to the pore size. This leads to models Simulation of groundwater flow and transport relies on up- involving moving interfaces between the fluid and the de- scaling fluid dynamics and linked reactive processes spec- posited layer. After addressing some modeling details, we ified at pore- or column-scales. Upscaling failure has led consider a simplified geometry for which we derive upscaled many to refocus on ”mixing measures” as proxies for re- models. These results are further extended to transport actions. I review this approach as one of calculating the dominating diffusion, and to biofilm growth. exposure-time of one solute to another, and develop (eulerian) equations governing the evolution of a solute over Iuliu Sorin Pop space, time, and mixing extent. Limitations associated Dept of Mathematics and Computer Sciences with transition state theory are introduced. TU Eindhoven [email protected] Tim Ginn University of California at Davis Kundan Kumar [email protected] University of Texas at Austin [email protected] MS68 Tycho van Noorden Scaling of Convective Mixing in Porous Media Comsol B.V. t.l.v.noorden@gmail,com Convective mixing in porous media results from a Rayleigh–Bénard-type instability resulting from a higher density fluid mixture overlaying a light fluid. Here we study MS67 the scaling of dissolution fluxes by means of the variance Remediation in Porous Media by Bacterial Chemo- of concentration and the scalar dissipation rate. The fundamental relations among these three quantities allow us to show that the classical model of convective mixing in porous media exhibits, in the regime of high Rayleigh num- GS13 Abstracts 143

ber, a dissolution flux that is constant and independent of MS69 the Rayleigh number. Our findings point to the need for Domain Decomposition for alternative explanations of recent nonlinear scalings of dis- Poroelasticity-Elasticity Systems solution flux observed experimentally. A domain decomposition framework is discussed, which is Juan J. Hidalgo applicable for large systems that dynamically couple poroe- MIT, Boston, USA lasticity and elasticity. Mortar finite elements are used to [email protected] impose physically meaningful interface conditions. Benjamin Ganis MS68 The University of Texas at Austin Probability Density Function of Concentration in Center for Subsurface Modeling Porous Media [email protected]

We study the mixing of a scalar line transported in a two- Ivan Yotov dimensional porous media under heterogeneous advection Univeristy of Pittsburgh and diffusion. We propose a theoretical framework to quan- Department of Mathematics tify the overall concentration distribution, predicting its [email protected] shape and rate of deformation as it progresses towards uniformity. Analytical expression for the temporal scaling of the concentration moments and the scalar dissipation rate Mary F. Wheeler are derived for all times. High resolution numerical simula- Center for Subsurface Modeling tions of flow and transport in heterogeneous permeability University of Texas at Austin fields provide a detailed quantification of concentration dis- [email protected] tribution, which validates the theory. Tanguy Le Borgne MS69 University of Rennes, France Darcy vs Brinkman [email protected] Different laws for describing filtration of a fluid through a porous medium can be found in the literature. We focus MS68 on Darcy’s law and Brinkman’s law. They have different Magnetic Resonance Measurement of Transport mathematical structure, but they can both be derived from Dynamics and Mixing in Biogeochemical Precipi- the Navier-Stokes system using homogenization in periodic tation model of porous medium, depending on the magnitude of permeability. Geoengineering the subsurface to sequester carbon dioxide is a current topic of societal and technological interest. Eduard Marusic-Paloka Significant theoretical advances in modeling and simula- Department of Mathematics, tion of reactive transport processes in porous media have University of Zagreb, Croatia occurred recently. Noninvasive magnetic resonance (MR) [email protected] measurement of the water phase molecular displacement length and time scale dependent dynamics due to hydro- MS69 dynamic dispersion in porous media characterize transport and mixing. The use of MR data in testing and analyzing Full Finite Volume Discretization for Poroelasticity reactive transport models is considered. The standard approach to discretization of coupled flow Joseph D. Seymour and mechanics in geological porous media is to apply fi- Univesity of Montana nite volume methods to the Darcy flow equation and fi- [email protected] nite element methods to the deformation equations. We propose an alternative approach where both flow and deformation are discretized using finite volume methods. We MS68 construct a novel finite volume discretization for linear elas- Anomalous Kinetics of Reactive Fronts in Porous ticity, and highlight the coupling between the flow and de- Media formation discretizations. Convergence is established for homogeneous cases. The dynamics of reactive transport phenomena in porous media derive from the interaction of microscopic mass Jan M. Nordbotten transfer and reaction processes. The understanding of ob- Department of Mathematics served reaction behavior requires the quantification of these University of Bergen microscale processes and their impact on the large scale re- [email protected] action and transport behavior. Here we study the mixing limited (fast) reaction A + B –¿ C at the pore-scale, and MS69 its effective behavior on the mesoscale, as a paradigmatic case that allow us to provide a connection between local Coupling Biot and Navier-Stokes Equations for mixing properties and global reaction kinetics Modelling Fluid-Poroelastic Media Interaction

Pietro de Anna We focus on a fluid-poroelastic structure interaction prob- MIT, Boston, USA lem arising in hemodynamics. The finite element approxi- [email protected] mation of such a problem is involved because both subproblems are indefinite. Thanks to stabilization techniques, we use the same finite element spaces for all the variables, sim- 144 GS13 Abstracts

plifying the discretization and the enforcement of the cou- [email protected] pling conditions. To solve the associated linear system we propose both a monolithic approach and partitioned procedures. We compare all the methods on a test problem. MS70 Hybrid Tree-Based Approach to Block-Structured AMR for Finite Volume Methods on the Sphere Santiago Badia International Center for Numerical Methods in Skepticism persists as to whether the use of adaptive mesh Engineering refinement (AMR) can improve atmospheric flow simula- Universitat Politècnica de Catalunya, Barcelona, Spain tions. Model developers are reluctant to engage in AMR [email protected] code development amid concerns that multi-resolution grids are ineffective in the absence of precise error esti- Annalisa Quaini mators or can damage numerical solutions. We propose University of Houston a highly scalable, spatially adaptive code to test modern [email protected] finite volume discretizations on Cartesian grids, and establish their effectiveness on several benchmarks in atmo- Alfio Quarteroni spheric flows. Ecole Pol. Fed. de Lausanne Donna Calhoun Alfio.Quarteroni@epfl.ch Boise State University [email protected] MS69 Hierarchical Multiscale Method for Elastic Me- Carsten Burstedde chanical Deformation of Naturally Fractured Rocks Institut fuer Numerische Simulation Universitaet Bonn A multiscale finite-element method (MSFEM) is developed [email protected] for solving the elliptic mechanics equation for heterogeneous porous media. Heterogeneity and anisotropy in the elastic properties may be due to the presence of fractures, MS70 as well as, geometric complexity of the reservoir architec- Wavelet-Based Dynamic Adaptivity for the ture. The basis functions, coarse-scale operator, and re- Shallow-Water Equations on Staggered Meshes construction kernels are described in detail. We show that relatively small-scale features can affect the global defor- This talk presents a dynamically adaptive wavelet method mation and stress fields quite significantly, e.g., fault acti- for the shallow water equations on a staggered hexago- vation and large-scale formation instabilities. We analyze nal C-grid, designed so it can be extended easily to the the MSFEM method for naturally fractured systems, both icosahedral subdivision of the sphere. Distinct biorthog- in terms of the quality of the coarse-scale (upscaled) oper- onal second generation wavelet transforms are developed ator and overall computational efficiency. for the pressure and the velocity, together with compatible restriction operators ensuring mass conservation and Karine Levonyan no numerical generation of vorticity. The conservation and Stanford error control properties of the method are verified by apply- [email protected] ing it to a propagating inertia-gravity wave packet and to rotating shallow water turbulence. Even in the latter case Hamdi Tchelepi significant savings in the number of degrees of freedom are Stanford University achieved. Energy Resources Engineering Department Thomas Dubos [email protected] LMD Ecole Polytechnique MS70 [email protected] Hybrid Tree-based Approach to Block-structured AMR for Finite Volume Methods Nicholas Kevlahan Department of Mathematics & Statistics Block-structured adaptive meshes have a long tradition in McMaster University the numerical solution of hyperbolic PDEs. In contrast, the [email protected] development of non-overlapping, strictly tree-based AMR methods has been motivated predominantly by low- and high-order finite element discretizations. We present an MS70 approach that uses the p4est octree algorithms to drive Imex Methods for Continuous and Discontinu- the parallelization of Clawpack-based numerics for conser- ous Galerkin Methods for the Compressible Euler vation laws. We will outline differences and similarities to Equations: Applications to Nonhydrostatic Atmo- structured AMR methods and close with presenting pre- spheric Modeling liminary numerical studies. We have been developing 3D fully parallel compressible Carsten Burstedde Euler solvers using high-order continuous (CG) and dis- Institut fuer Numerische Simulation continuous Galerkin (DG)methods. The focus of this Universitaet Bonn model is towards numerical weather prediction at both the [email protected] limited-area and global scale. In order to improve the efficiency of these models, we construct Implicit-Explicit time- Donna Calhoun integrators whereby the slow modes (advection) are treated Boise State University nonlinearly and explicitly while the fast modes (acoustics) GS13 Abstracts 145

are treated linearly and implicitly. In this talk, I will de- University of Notre Dame scribe the challenges we have faced in constructing IMEX [email protected] methods for both CG and DG methods. For example, in order to increase the eﬃciency of the methods requires ex- Andrew Kennedy tracting the Schur Complement of the IMEX system which University of Notre Dame is non-trivial for DG methods. I will report on the ideas [email protected] that have proven successful and those that have not for both CG and DG. MS71 Francis X. Giraldo Title Not Available at Time of Publication Naval Postgraduate School [email protected] Abstract not available at time of publication. Ethan Kubatko MS71 The Ohio State University A Discontinuous Galerkin Scheme for a 2-Equation [email protected] Vertical Eddy Viscosity Parameterization

Vertical eddy viscosity parametrizations are one of the key MS72 components of ocean models affecting the model skill and From a Geological to a Numerical Model for Earth- its performance. Here we discuss our implementation of the quake Generation (and fluids reaction) 2-equation generic turbulence length scale parametrization (Umlauf, Burchard, 2003) within UTBEST3D – a 3D dis- We model the state of stress and the circulation of fluids continuous Galerkin simulator. A specialty of our approach in faults cross-cutting the brittle-ductile transition (BDT). is the discretization of the turbulence unknowns with the The fault is assumed have stickslip behavior in the brittle help of a 1D discontinuous Galerkin method on vertical crust and to deform by steady-state shear in the ductile segments. crust. These contrasting behaviors determine a stress and strain gradient at the BDT that is dissipated during the Vadym Aizinger earthquake. Changes in porosity and permeability at the University of Erlangen BDT from interseismic to coseismic stages control fluid dis- [email protected] charge. Eugenio Carminati MS71 Dept. of Earth Sciences, UniversitàlaSapienza Adaptive Galerkin Type Methods for Inundation Rome, Italy Computations [email protected]

Tsunami as well as storm surge simulation requires accu- Carlo Doglioni rate and robust simulation techniques capable of resolv- UniversitàLaSapienza ing the large scale features (in deep ocean) and the small [email protected] scale phenomena (usually near the shore). This is achieved by using Galerkin-type (finite element and discontinuous Galerkin) numerical approximations on adaptively refined Salvatore Barba, Federica Riguzzi meshes. In this presentation we focus our attention to effi- Istituto Nazionale di Geofisica e Vulcanologia, Rome, ciency and accuracy of the numerical schemes in inundation Italy applications. [email protected], [email protected] Jörn Behrens KlimaCampus, University of Hamburg MS72 [email protected] Surface Water Enables Subduction on Earth: Pre- dictions from Self-Consistent Models

MS71 Fully coupled solid-fluid numerical models demonstrate Green-Naghdi solutions to the Pressure Poisson that the presence of surface water controls both initia- equation with Boussinesq-type scaling tion and style of subduction via local brittle/plastic rock strength reduction. Although subduction fails to initiate One of the most challenging aspects of numerically mod- under fluid-absent conditions, it can naturally start and eling near shore wave dynamics is balancing computa- become self-sustaining when porous water is present in- tional cost and accuracy. One approach to reducing cost is side oceanic crust and along the plate boundaries. Fluid through Boussinesq–type scaling, however the irrotation- percolation localizes along spontaneously forming fractures ality assumption is often invalid for near–shore physics. A where high fluid pressure compensates lithostatic pressure, Boussinesq–type scaling without the assumption of irrota- thus dramatically decreasing friction along the subduction tionality is presented. Solutions to the Pressure Poisson zone. equation using a Green-Naghdi approach are shown to be advantageous in terms of cost and order of the solution. Taras Gerya Geophysical Institute Aaron Donahue ETH-Zurich University of Notre Dame [email protected] [email protected] MS72 Joannes Westerink Department of Civil Engineering and Geological Sciences Consequences of Viscous Anisotropy in Partially 146 GS13 Abstracts

Molten Rocks MS73 Title Not Available at Time of Publication In partially molten regions of Earth, rock and magma co- exist as a two-phase aggregate in which the solid grains of Abstract not available at time of publication. rock form a viscously deformable matrix. Liquid magma resides within the permeable network of pores between Knut Waagan grains. Deviatoric stress causes the distribution of con- University of Washington tact area between solid grains to become anisotropic; this [email protected] causes anisotropy of the matrix viscosity. The anisotropic viscosity tensor couples shear and volumetric components of stress/strain rate. This coupling, acting over a gradient MS73 in shear stress, causes segregation of liquid and solid. Liq- Weak Galerkin Finite Element Methods for Elliptic uid typically migrates toward higher shear stress, but under Problems speciﬁc conditions, the opposite can occur. Furthermore, in a two-phase aggregate with a porosity-weakening vis- Abstract not available at time of publication. cosity, matrix shear causes porosity perturbations to grow into a banded structure. We show that viscous anisotropy Junping Wang reduces the angle between these emergent high-porosity National Science Foundation features and the shear plane. This is consistent with lab [email protected] experiments.

Richard F. Katz MS73 University of Oxford Wgfem for Biharmonic Problems [email protected] Abstract not available at time of publication.

Yasuko Takei Xiu Ye Earthquake Research Institute University of Arkansas, Little Rock University of Tokyo [email protected] [email protected]

MS74 MS72 Bayesian Uncertainty Quantiﬁcation of Subsurface Improved Rheological Models for the Description Flow Models Using Nested Sampling and Sparse of Rift Dynamics Polynomial Chaos Surrogate

Oceanic rift processes are due to diverget plate tectonics, An accelerated Bayesian uncertainty quantification method these zones represent the fundamental areas where to inves- based on the nested sampling (NS) algorithm and tigate lithosphere/mantle interactions. The development non-intrusive stochastic collocation method is presented. of a mathematical model is required in order to exploit Nested sampling is an efficient Bayesian sampling algo- modern numerical tools to give a detailed description of rithm that builds a discrete representation of the posterior the structures developed in rift areas. In this talk a set distributions by iteratively re-focusing a set of samples to of novel mathematical models (in accordance with mod- high likelihood regions. The main difficulty of the nested ern geological observations) to describe the rift processes sampling algorithm is in a constrained sampling step which is presented. is commonly performed using a random walk Markov chain Monte-Carlo (MCMC) algorithm. In the current work, we Marco Cuffaro utilize a two-stage MCMC sampling using a polynomial Istituto di Geolgia Ambientale e Geoingegneria (IGAG) chaos response surface to filter out rejected samples in the Consiglio Nazionale delle Ricerche (CNR) Markov chain Monte-Carlo method. The combined use of marco.cuff[email protected] the nested sampling algorithm and the two-stage MCMC provides significate computational gains in terms of the Edie Miglio number of simulation runs. The proposed algorithm is ap- Politecnico di Milano (Italy) plied for calibration and model selection of subsurface flow MOX, Dept. of Mathematics models. [email protected] Ahmed H. ElSheikh Mattia Penati, Marco Vigan Center for Subsurface Modeling, ICES MOX, Dept. of Mathematics, Politecnico di Milano University of Texas at Austin, TX, USA Milano, Italy [email protected] [email protected], [email protected] Mary F. Wheeler Center for Subsurface Modeling, ICES MS73 University of Texas at Austin Wgfem for Elliptic Interface Problems [email protected]

Abstract not available at time of publication. Ibrahim Hoteit Lin Mu King Abdullah University of Science and Technology Michigan State University (KAUST) [email protected] [email protected] GS13 Abstracts 147

MS74 Problems in Random Media Toward An Expectation-Maximization Method for Parameter Estimation and Its Application to Rate Partial differential equations (PDEs) with random coeffi- Estimation in Oil Wells cients are used in computer simulations of physical processes in science, engineering and industry applications Information of flow rates in individual wells is crucial with uncertain data. The goal is to obtain quantitative for production optimization and reservoir management. statements on the effect of input data uncertainties for a To obtain this information, a framework has been devel- comprehensive evaluation of simulation results. However, oped consisting of a transient wellflow model, a stochas- these equations are formulated in a physical domain cou- tic flowrate model, and estimation methods. The stochas- pled with a sample space generated by random parameters tic flowrate model used in the framework needs to specify and are thus very computing-intensive. We outline the the variances of the driving noise terms. In this talk, an key computational challenges by discussing a model elliptic Expectation-Maximization (EM) based method is adopted PDE of single phase subsurface flow in random media de- to automatically estimate these parameters in an online scribed by correlated lognormal distributions. In this appli- fashion. cation the coefficients are often rough, highly variable and require a large number of random parameters which puts Xiaodong Luo a limit on all existing discretisation methods. To overcome International Research Institute Of Stavanger (IRIS) these limits we employ multilevel Monte Carlo (MLMC), [email protected] a novel variance reduction technique which uses samples computed on a hierarchy of physical grids. A rigorous con- Rolf Johan Lorentzen, Andreas Stordal, Geir Naevdal vergence and complexity analysis of MLMC requires the International Research Institute Of Stavanger (IRIS) estimation of the error introduced by the finite element Bergen 5008, Norway discretisation. We extend recent works on the analysis of [email protected], [email protected], standard nodal finite elements to mass-conservative low- [email protected] est order Raviart-Thomas mixed finite elements. This is very important since the use of mass-conservative discretisation schemes is highly desirable in realistic groundwater MS74 flow problems. As in the standard case, the analysis is Multiple Criteria Optimization of CO2 Sequestra- non-trivial due to the limited spatial regularity and the tion Strategy Under Geological Uncertainty Using unboundedness of the employed lognormal random fields. Adaptive Sparse Grid Surrogates This is joint work with Andrew Cliffe (Uni Nottingham), Mike Giles (Uni Oxford), Ivan Graham (Uni Bath), Minho The key to successful CO2 sequestration depends on eco- Park (Uni Nottingham), Robert Scheichl (Uni Bath) and nomic efficiency, capacity and long-term security of CO2 Aretha Teckentrup (Uni Bath). storage. Making decisions in injection strategies under multiple objectives become a challenging task due to ge- Elisabeth Ullmann ological uncertainty and conflicting objectives. In the cur- University of Bath rent work, we used Non-dominated Sorting Genetic Algo- [email protected] rithm (NSGA-II) based on Adaptive Sparse Grid Interpo- lation (ASPI) to maximize sweep efficiency, economic cri- MS75 teria, and simultaneously minimize risks associated to CO2 injection. Numerical results showed that a Pareto-optimal An Adaptive Fast Multipole Accelerated Boundary front of the injection strategies is essential to making a Element Method for 3D Elastodynamics decision in CO2 sequestration projects. The Boundary Element Method is well suited to the com- Rachares Petvipusit putation of elastic wave propagation as only the domain QCCSRC, Department of Earth Science and Engineering boundaries are discretized. This advantage is offset by Imperial College London the fully-populated matrix. Considerable speedup of so- [email protected] lution time and decrease of memory requirements are achieved with the Fast Multipole Method. This speeds up the matrix-vector product computation at each itera- Ahmed H. ElSheikh tion. Then, additional gains in CPU time and accuracy Center for Subsurface Modeling, ICES are reached by using a dedicated mesh adaptation proce- University of Texas at Austin, TX, USA dure. [email protected] Stephanie Chaillat Martin Blunt POems-ENSTA Dept. Earth Science and Engineering [email protected] Imperial College London [email protected] Adrien Loseille INRIA Paris-Rocquencourt Peter King [email protected] Imperial College London Department of Earth Science & Engineering [email protected] MS75 Up-scaling 3D Complex Geological Media for the Elastic Wave Equation MS74 Multilevel Monte Carlo for Groundwater Flow Seismic waves propagating in the Earth are affected by different sizes of heterogeneities. When modelling these waves, taking into account small heterogeneities is a chal- 148 GS13 Abstracts

lenge because it often requires important meshing efforts MS76 and leads to high numerical costs. In the recent years, An Efficient Numerical Approach for Reactive this problem has been overcome by applying the homoge- Multiphase Multicomponent Flow in Porous Me- nization technique (originally developed in solid mechanics dia for periodic media) to the elastic wave equation in non- periodic media (Capdeville et al 2010a,b; Guillot et al We present an efficient numerical model for the simulation 2010). This technique allows to upscale the small het- of partially miscible two-phase multicomponent flow with erogeneities and yields a smooth effective medium and ef- chemical reactions. The choice of primary variables is suit- fective equations. In this presentation we first recall the able to deal with phase transitions which are handled by a theory of the homogenization, then we describe its imple- complementarity approach. A model-preserving reformu- mentation in the 3D case, and we finally show applications lation technique is applied to eliminate unknowns and the which validate our code. remaining system is solved by a global-implicit approach using Newton’s method. Paul Cupillard IPG Paris Fabian Brunner [email protected] University of Erlangen [email protected] Yann Capdeville CNRS Peter Knabner [email protected] Department of Mathematics University of Erlangen [email protected] MS75 Forward and Inverse Problems in Acoustics and Seismic Modeling: An Optimized-Spectral Ele- MS76 ment Approach Efficient Numerical Simulation of 2D and 3D Mul- ticomponent Reactive Transport Spectral-element methods for adjoint/inverse problems have evolved significantly in recent years. We will dis- We present complex scenarios of multicomponent reactive cuss recent improvements that have been implemented in transport in 2-D and in 3-D. These scenarios are further the SPECFEM3D package, namely coupling with a re- developments of the setting given by the MoMaS bench- gional quasi-analytical solution, wavelet compression, and mark. We show how to solve the equations using a global source encoding. We will also show a real application implicit approach in an efficient way, and we present the to seismological data obtained in the Pyrenees region in derived computational results. Southern France in the context of the ANR PYROPE / TOPOIBERIA transportable recording array experiment Serge Krautle, Alexander Vibe that has been carried out in recent years. Department of Mathematics University of Erlangen-Nuremberg, Germany Dimitri Komatitsch [email protected], [email protected] CNRS Research Director (DR CNRS) [email protected] Joachim Hoffmann University of Erlangen-Nuremberg Zhinan Xie Department of Mathematics CNRS & Universite de Marseille hoff[email protected] [email protected] Peter Knabner Friedrich-Alexander University Erlangen-Nurenberg, MS75 Germany Dicontinuous Galerkin Approximation of Seismic Department of Mathematics Wave Propagation Problems [email protected] In this talk we present SPEED-SPectral Elements in Elas- todynamics with Discontinuous Galerkin- a high perfor- MS76 mance open-source numerical code for seismic wave prop- Importance of Non-Negative Numerical Solution agation problems. Based on the Discontinuous Galerkin for Mixing-Controlled Reactive Transport paradigm, allows the treatment of non-uniform polynomial degree distribution as well as a locally varying mesh size. Conventional numerical methods for reactive transport can We show validation benchmarks that demonstrate the ac- produce non-physical values, particularly for heterogeneous curacy, stability, and performance of the parallel kernel as flow fields, irregular grids and full tensor dispersion. Nega- well as applications of SPEED for simulating realistic mul- tive concentrations cannot be tolerated for nonlinear reac- tiscale wave propagation phenomena. tions. We present several computational strategies to address these issues for mixing-controlled reactions. The flux Ilario Mazzieri, Paola F. Antonietti corrected transport framework is a flexible method that Politecnico di Milano can be used with existing simulators. We also present a [email protected], [email protected] FEM formulation that uses optimization to strictly enforce maximum principles and the non-negative constraint. Alfio Quarteroni Ecole Pol. Fed. de Lausanne Albert J. Valocchi Alfio.Quarteroni@epfl.ch University of Illinois at Urbana-Champaign [email protected] GS13 Abstracts 149

Kalya Nakshatrala Center for Wave Phenomena Department of Civil and Environmental Engineering Colorado School of Mines University of Houston [email protected] [email protected] Paul C. Sava Colorado School of Mines MS76 [email protected] Isotopic Management in the Reactive Transport Code Hytec : Isotopic Fractionation and Radioac- tive Decay MS77 Renormalization of Scattering Series and the Im- HYTEC is a coupled reactive transport code used for a provement of Convergence Property wide variety of applications in geosciences. This work presents a new functionality : the isotopic management. It is well known that the forward or inverse Born scattering This new option allows to take into account any even com- series is of the Fredholm type and its convergence is limited plex radioactive decay chains and chemical isotopic frac- to a region of weak scattering regime. The current status tionation at equilibrium. The effective implementation of in application of the higher order Born series is to calculate the new option is presented as well as two illustrative ex- only a few terms and see the improvement compared with amples with comparison to analytical solutions: one for the the first order term. In this work, we apply the De Wolf se- radioactive decay, and the other for isotopic fractionation. ries method (De Wolf transform) to reorder and renormal- ize the Born series, and hence transform the Fredholm type Caroline de Dieuleveult, Vincent Lagneau into a Volterra-type series which has a guaranteed conver- Geosciences Center gence. Numerical examples are given to demonstrate the MINES ParisTech convergence and efficiency of the De Wolf approximation caroline.de [email protected], for multiple forward-scattering. [email protected] Ru-Shan Wu University of California, Santa Cruz MS77 [email protected] Autofocusing of Internal Multiples and Application to Multidimensional Deconvolution Lingling Ye We describe a method that reconstructs the wavefield from Univ of California, Santa Cruz a virtual source inside a medium without needing a re- [email protected] ceiver at the virtual-source location. An estimate of the direct arriving wavefront is required in addition to reflec- MS77 tion data. This method allows us to decompose the reconstructed wavefield in up- and down-going components. Interferometric Imaging of the Leading-order In- We illustrate the method with numerical examples in loss- ternal Multiples less acoustic media. This method is a basis for techniques We develop a three step imaging procedure, which would relying on Multi Dimensional Deconvolution. image the first order internal scattering. This approach Filippo Broggini, Roel Snieder mainly utilizes the background Green’s function from the Colorado School of Mines surface to each image point. We first back propagate of the [email protected], [email protected] recorded surface data using the background Green’s function down to the image point. Next, we cross-correlate the back-propagated data with the recorded surface data. Fi- Kees Wapenaar nally, we cross-correlate the result of second step with the Department of Geoscience and Engineering background Green’s function form surface to image point. Delft University of Technology This would give us the image of the point from which sin- [email protected] gle scattering has not been recorded. Note that this internal multiple imaging procedure will image only the points Joost van der Neut which has taken part in a single order internal scattering CITG, Delft University of Technology and single scattering points will be suppressed. We add [email protected] this image to those obtained from any of the many single scattering based imaging procedure, for example, Kirchhoff migration, to give the total image. Application to synthetic MS77 data with reflectors illuminated by multiple scattering only Wavefield Tomography Based on Local Image Cor- demonstrates the effectiveness of the approach. We shall relations also show that the first order internal scattering is imaged by the conventional Reverse Time Migration (RTM), but A smooth model of the subsurface is necessary to map is very weak compared to single scattering image and cause waves recorded at the surface where contrasts in physi- possible crosstalk. In our method, by cross-correlating the cal parameters exist. The model is unknown and must be back propagated field with the data we manage to sepa- estimated from the data. Contrast interfaces are described rate the second order term in the Born scattering series by position and orientation. If the model is accurate, the (first order internal scattering), which enhances the image reflector positions are invariant with respect to an exten- corresponding to that term. sion parameter (e.g., shot index). Our inversion procedure is based on similarity of the reflector orientations and re- Mohammad A. Zuberi quires fewer images. KAUST [email protected] Francesco Perrone 150 GS13 Abstracts

Tariq Alkhalifah [email protected] King Abdullah University of Science and Technology [email protected] MS78 A Posteriori Error Estimates, Stopping Criteria, MS78 and Adaptivity for Two-Phase Flows A Numerical Study of Splitting Schemes and Im- plicit Solution Methods for Biot’s Equation We show how computable a posteriori error estimates can be obtained for the two-phase porous media flow problem. The stability of splitting schemes for Biot’s equation has Iterative linearizations by, e.g., the Newton method and recently been studied by Mikeli`c and Wheeler [1], and oth- iterative solutions of the arising linear systems are typi- ers. We will investigate the performance of these stable cally involved in the numerical approximation procedure. splittings, and compare them with a fully implicit solu- We show how the corresponding error components can be tion method on two cases which are numerically difficult. distinguished and estimated separately. A fully adaptive We will also look at a reformulation of the most promising solution procedure, with adaptive choices of the number of splitting scheme as a block preconditioner for a fully im- nonlinear and linear solver steps, the time step size, and plicit solver. [1] A. Mikeli`c, M. F. Wheeler: Convergence the computational mesh, is presented. of iterative coupling for coupled flow and geomechanics, Martin Vohralik Computational Geosciences, 2012. DOI: 10.1007/s10596- Université Pierre et Marie Curie 012-9318-y Paris, France Joachim B. Haga,KentMardal [email protected] Simula Research Laboratory [email protected], [email protected] Mary F. Wheeler Center for Subsurface Modeling Jan M. Nordbotten University of Texas at Austin Department of Mathematics [email protected] University of Bergen [email protected] Clement Cances University Paris VI Eirik Keilegavlen Laboratoire J.L. Lions University of Bergen [email protected] [email protected] Sorin Pop CASA MS78 Eindhoven University of Technology Inexact Linear Solvers for Control Volume Dis- [email protected] cretizations

We discuss the construction of inexact linear solvers for MS79 control volume discretizations of elliptic problems. The A Multilevel Time Integrator for Large-scale At- methods are formulated as multi-level discretizations which mospheric Flows preserve the conservation structure of the continuous problem, and conservative flux fields are produced even for We present a numerical scheme aimed at simulating mul- inexact pressure solutions. Thus the linear solver allows tiscale atmospheric flows in the low Mach number regime. for significant computational savings while still producing Compressible flow equations are discretized with a second- physically meaningful solutions. The iterations are con- order accurate projection method. Results obtained with trolled by error estimates. Numerical experiments verify the advection of a vortex, an acoustic wave and a ris- the viability of our approach. ing warm air bubble showcase the method’s performance. With a multilevel time integration approach based on Eirik Keilegavlen, Jan M. Nordbotten multigrid ideas, the scheme can handle multiscale features University of Bergen around balanced regimes in a controlled fashion. [email protected], [email protected] Tommaso Benacchio Freie Universitaet Berlin MS78 [email protected] Multiscale Methods: Tools to Balance Accuracy and Efficiency Rupert Klein Freie Universität Berlin In the description of flow through porous media, approx- [email protected] imate solution based on upscaling procedures have been widely employed. Recent advances in adaptive multiscale techniques offer a general framework that enables great MS79 flexibility in balancing accuracy and efficiency. However, Exponential Integrators for Applications to Envi- an optimal choice is possible only if the objectives are ronmental Fluid Dynamics clearly defined and the particular application specified. We discuss this topics in relation to the MsFV method. The accuracy and performance of some kinds of exponential time integrators are assessed for the time discretization Ivan Lunati, Laureline Josset, Rouven Kuenze of hyperbolic problems. In particular, their potential for University of Lausanne applications to environmental fluid dynamics problems is [email protected], [email protected], assessed by comparison with more common time discretiza- GS13 Abstracts 151

tion techniques. Possible extensions of the standard expo- University of Texas at Austin nential methods discussed in the ODE literature will also [email protected] be discussed. Corey Trahan Luca Bonaventura DRC MOX Politecnico di Milano Vicksburg, MS USA Milan, Italy 20133 [email protected] [email protected]

MS80 MS79 Pressure Forcing and Dispersion Analysis for Dis- Comparison of Adaptive and Uniform DG Simula- continuous Galerkin Approximations to Oceanic tions Fluid Flows

Adaptive mesh refinement generally serves to increase com- This work is part of an effort to study the potential applica- putational efficiency without compromising the accuracy of tion of DG methods to the numerical modeling of the gen- the numerical solution significantly. However it is an open eral circulation of the ocean. One step performed here is to question in which regions the spatial resolution can actually develop an integral weak formulation of the pressure forc- be coarsened without affecting the accuracy of the result ing that is suitable for usage with a DG method and with a significantly. This question is investigated for the simula- generalized vertical coordinate that includes level, terrain- tion of warm air bubble test cases. For this purpose a novel fitted, and isopycnic coordinates as examples. This formu- numerical model is developed that is tailored towards this lation is then tested, in special cases, with some compu- specific meteorological problem. A method is introduced tational experiments and with analyses of well-balancing, which allows one to compare the accuracy between differ- dispersion relations, and numerical stability. ent choices of refinement regions. For a rising warm air bubble the additional error by using adaptivity is smaller Robert L. Higdon than 1% of the total numerical error if the average number Oregon State University of elements used for the adaptive simulation is about 50% [email protected] smaller than the number used for the simulation with the uniform fine-resolution grid. MS80 Andreas Mueller Adaptive Vertical Coordinates for Modeling Strat- Institute for Atmospheric Physics ified, Coastal Seas Mainz University [email protected] An adaptive strategy for the vertical gridding in terrain- following 3D ocean models is presented here, which is designed for reducing discretisation errors in ocean models. MS80 With this, internal flow structures such as pycnoclines can Multiresolution Ocean Simulations with Fesom be well resolved and followed by the grid. A set of examples is presented, which show that the adaptive grid strat- Unstructured meshes offer geometric flexibility. In the con- egy reduces pressure gradient errors and numerical mixing text of large-scale ocean modeling they enable simulations significantly and improves the representation of physical with a regional focus in an otherwise global setup. The processes, nutrient fluxes and plankton growth. Finite-Element Sea ice-Ocean circulation Model (FESOM) offers such functionality. A brief review of current FESOM- Richard Hofmeister assisted research will be given, to illustrate the utility of the Helmholtz-Zentrum Geesthacht approach. New developments include a global cell-vertex [email protected] finite-volume setup which is compared to FESOM in global ocean simulations. Jean-Marie Beckers Sergey Danilov University of Liège, MARE-GHER-AGO, Belgium Alfred Wegener Institute [email protected] [email protected] Ulf Gräwe Leibniz Institut for Baltic Sea Research, Warnem{ MS80 Germany Local Timestepping in the Discontinuous Galerkin [email protected] Method for Shallow Water Systems Hans Burchard Coastal models discretized explicitly in time on unstruc- Leibniz Institut for Baltic Sea Research, Warnemünde, tured meshes can give rise to severe global CFL timestep Germany constraints. This constraint is in fact local, depending on [email protected] the local eigenvalues of the system and the element mesh size. By allowing the timesteps to vary spatially, one can significantly improve computational efficiency. In this talk, MS81 we describe a parallel local timestepping approach which Aspect: An Advanced Solver for Problems in Earth conserves mass and has been observed to be second order Convection accurate. Applications to storm surge modeling will be presented. Simulating convection in Earth’s mantle is challenging for many reasons: the vastly varying scales, nonlinear material Clint Dawson behavior, advection dominated transport, and long time Institute for Computational Engineering and Sciences spans of interest. We present an overview of the open 152 GS13 Abstracts

source code ASPECT that uses modern numerical meth- tle. Such calculations make predictions that can be com- ods for adaptive mesh reﬁnement, solvers and stabilization pared to observations from seismology, geochemistry, pale- to solve convection problems in Earth. It is written with omagnetism and geology. We are also applying such models a particular focus on extensibility and scales to very large to other planets, both in our own solar system and around computations. other stars (super-Earths).

Wolfgang Bangerth Paul Tackley Texas A&M University Department of Earth Sciences [email protected] ETH Zurich Institute fuer Geophysik [email protected] Timo Heister Texas A&M University Department of Mathematics MS82 [email protected] Methods to Determine the Eﬀective Resolution of Dynamical Cores

MS81 The effective resolution of a model is the smallest scale Flexible Finite Element Methods for Geodynamics that is fully resolved. We present theoretical methods and idealized test cases to determine the effective resolution of The FEniCS Project is an open source solution for the dynamical cores. Investigating the dissipative and disper- automated solution of differential equations and is largely sive properties of a scheme determines which wavenumbers developed at Simula. Recently, we have applied FEniCS to are resolved for linear systems. Using baroclinic wave tests, mantle convection problems and tested it against published we can numerically determine which scales are resolved for benchmarks. FEniCS as a generic solver can complement the nonlinear system. We present results for NCAR’s Com- existing purpose built software for rapid deployment, community Atmosphere Model finite-volume core. plex and adaptive meshes and adjoint problems. James Kent Stuart R. Clark, Lyudmyla Vynnytska University of Michigan Simula Research Laboratory [email protected] [email protected], [email protected] MS82 MS81 Adaptive Mesh Re- Improved Thermo-Tectonic Basin Reconstruction finement for the Non-Hydrostatic Unified Model with P-T Dependent Gravimetric Calibration of the Atmosphere (NUMA) Source rock maturity depends on the thermal evolution The Adaptive Mesh Refinement algorithm was designed for of sedimentary basins. Modeling this requires a tectonic the Discontinuous Galerkin (DG) method in frame of a 2D model that resolves the basin and the lithospheric scale. mesoscale version of the Non-hydrostatic Unified Model of Unfortunately, no unique solution exists. This can be im- the Atmosphere. An investigation of the algorithm and proved by including datasets usually not considered in the its interaction with IMEX time-stepping was performed. basin-modeling context. Here we show that calibration The implementation was extended to include the Contin- with the gravity signal leads to better-constrained thermo- uous Galerkin (CG) method formulation. We present the tectonic basin models. This approach also improves grav- behavior of both DG and CG methods for non-conforming ity modeling, as the thermal state of the lithosphere can adaptive simulations on a suite of test cases employing both be included. statically and dynamically refined grids. Dani Schmid Michal A. Kopera, Francis X. Giraldo Geomodelling Solutions Gmbh Naval Postgraduate School Zurich, Switzerland [email protected], [email protected] [email protected] MS82 Lars Ruepke GeoModelling Solutions GmbH The Endgame Dynamical Core: Test Results Using [email protected] a Switchable Discretisation ENDGame is the next dynamical core for the Met Office’s Matilde Dalla Rosa, Matteo Gilardi Unified Model to be used for weather and climate predic- ENI S.p.A. tion across a range of time and space scales. ENDGame [email protected], [email protected] employs a flexible discretisation of the deep atmosphere nonhydrostatic equations allowing a number of simplifications to be made. The effects of a number of these for- MS81 mulation switches in ENDGame are investigated using a Simulating Mantle Convection, Plate Tectonics and variety of idealised tests - results and the lessons learnt the Thermo-Chemical Evolution of Planetary Inte- will be discussed. riors in a 3-D Spherical Shell on High-Performance Computers Thomas Melvin Met Office It is now possible to perform global 3D spherical models thomas.melvin@metoffice.gov.uk of solid Earth evolution that span 4.5 billion years, include self- consistently generated plate tectonics and magmatism that produces crust and chemically differentiates the man- GS13 Abstracts 153

MS82 King Abdullah University of Science and Technology Potential Vorticity Anomalies: Dynamic Or Nu- (KAUST) merical Artifact? [email protected] Conservation breaking anomalies in the dynamic potential vorticity (PV) field have been observed in simulations for MS83 models as simple as the Eady model. These anomalies oc- Iterative Smoothers for Subsurface Reservoir Flow cur when isentropic (constant potential temperature) sur- History Matching faces intersect the surface (in the case of the atmosphere). We make use of a dry baroclinic wave test case to investi- On Iterative Smoothers for Bayesian Estimation By: An- gate this phenomenon, and consider whether it is desirable dreas S. Stordal Abstract: Approximate solutions for for a dynamical core to capture these anomalies, and the Bayesian estimation in large scale models is a topic un- consequences of these features on the other pertinent dy- der investigation in many scientific communities with tha namical fields. main focus being on ensemble based methods such as the ensemble Kalman filter or Gaussian mixture filters. We Jared Whitehead define an iterative smoother version of the adaptive Gaus- Los Alamos National Laboratory sian mixture filter as a robust alternative to adaptive im- [email protected] portance sampling. The filter is compared to other iterative smoothers from a practical and theoretical point of view. Asymptotic properties of the new smoother are com- MS83 puted and compared with a theoretical result on random- Well Placement Optimization Using Stochastic ized maximum likelihood. We show that we have asymp- Approximated-Gradient Methods totic optimality under certain conditions, contrary to other smoothers where the sample distribution depend on the Stochastic approximated-gradient methods combine the nonlinearity and scaling of the model. The new smoother is advantages of both gradient-based and stochastic optimiza- also shown to outperform existing methods on simple prob- tion algorithms without the corresponding computation ef- lems as well as a one dimensional highly nonlinear reservoir fort. Two algorithms, EnOpt and FSP, are investigated problem. and compared for well placement optimization in this work. They do not require access to simulator code and generally, Andreas Stordal the gradient approximation is independent of the problem International Research Instititue of Stavanger (IRIS) dimensions. The results indicate that FSP tends to show [email protected] improved convergence characteristics and requires a lesser computational effort in comparison to EnOpt. MS83 Yuqing Chang, Deepak Devegowda Combining Multidimensional Scaling (MDS) with Mewbourne School of Petroleum and Geological Ensemble-Based Algorithms for Automatic History Engineering Matching University of Oklahoma [email protected], [email protected] The ensemble Kalman filtering fails to preserve non- Gaussian features of geological facies where there is a strong contrast in permeability values of channels and non- MS83 channels locations. We develop a methodology to combine Dual Ensemble Filtering for States Estimation of multidimensional scaling and the ensemble Kalman filter Coupled Subsurface Transport Models for updating models for a channelized reservoir. A dissimilarity matrix is computed using the dynamic responses Modeling contaminant evolution in geologic aquifers re- of ensemble members. This dissimilarity matrix is trans- quires coupling a groundwater flow model with a contami- formed to a lower dimensional space using multidimen- nant transport model. This coupling may provide accurate sional scaling. The responses mapped in the lower dimen- future estimates of the subsurface hydrologic state if as- sion space are clustered and based on distances between the sisted with essential flow and contaminant data through models in a cluster and the actual observed response, the data assimilation. Assuming perfect flow, an ensemble closest models to the observed response are retrieved. Up- Kalman filter (EnKF) can be directly used for data assim- dating of models within the closest cluster are performed ilation into the transport model. This is; however, a crude using EnKF equations. The results of the update are used assumption as flow models can be subject to many sources to re-sample new models for the next step. of uncertainties. If the flow is not accurately simulated, contaminant predictions will likely be inaccurate even af- Reza Tavakoli,SanjaySrinivasan ter successive Kalman updates of the contaminant with UT-Austin the data. The problem is usually better handled when both [email protected], flow and contaminant states are concurrently estimated us- [email protected] ing the traditional joint state augmentation approach. We introduce, here, an efficient dual strategy for data assimila- Ahmed H. ElSheikh tion into this one-way coupled system by treating the flow Center for Subsurface Modeling, ICES and the contaminant models separately while intertwining University of Texas at Austin, TX, USA a pair of distinct EnKFs; one on each model. [email protected] Mohamad El-Gharamti KAUST, Saudi Arabia Mary F. Wheeler [email protected] Center for Subsurface Modeling University of Texas at Austin [email protected] Ibrahim Hoteit 154 GS13 Abstracts

MS84 Dirk-Jan van Manen The Interior-Penalty Schlumberger Gould Research Discontinuous Galerkin Method for Elastic Wave [email protected] Propagation in Fractured Media Abstract not available at time of publication. MS84 Geological Complexity, Topography and Seismic Jonas D. De Basabe Wave Modelling: Are Finite-Differences Up to the Seismology Department Challenge? CICESE [email protected] The finite-difference (FD) method is still the most widely used method for modelling seismic waves in geophysics. Mrinal Sen However, it is not well-suited for modelling the effect of Institute of Geophysics the free-surface, especially in the presence of topogra- University of Texas phy. Although it is commonly inferred that high-order [email protected] finite-elements (FE) are the only affordable alternative in such scenarios, we want to show that certain modified FD Mary F. Wheeler schemes can satisfy most needs for seismic modelling, in- Center for Subsurface Modeling cluding challenging topographies and geologically complex University of Texas at Austin models. [email protected] Josep de La Puente Barcelona Supercomputing Center MS84 Spain [email protected] Higher Order Summation-by-parts Methods for Seismic Wave Propagation Miguel Ferrer, JoséMar´ıa Cela A fourth order accurate finite difference method for the Barcelona Supercomputing Center elastic wave equation in second order formulation is pre- [email protected], [email protected] sented. The numerical method satisfies the principle of summation-by-parts (SBP), which guarantees energy stability for arbitrary heterogeneous materials in bounded do- MS85 mains, with free surface or Dirichlet boundary conditions. Effective Upscaling of Kinetics in Simulation of in- Our approach generalizes to realistic topography by trans- Situ Combustion Processes forming the elastic wave equation to curvilinear coordinates before it is discretized by the SBP technique. Sustained high oil prices and growing demand have un- locked heavy oil resources. Production of such unconven- Anders Petersson tional oils typically requires thermal stimulation. In-situ Lawrence Livermore National Laboratory combustion is an attractive stimulation method as heat is [email protected] generated in the subsurface and the oil can often be up- graded. Performance prediction and optimization of ISC Bjorn Sjogreen projects require effective upscaling of reservoir rock proper- Center for Applied Scientific Computing ties, fluid properties and kinetics. We propose an effective Lawrence Livermore National Laboratory upscaling technique that is competitive in accuracy with [email protected] traditional approaches and many times faster. Margot Gerritsen MS84 Dept of Petroleum Engineering Stanford University Exact Boundary Conditions for Modelling and In- [email protected] version of Elastic Wave Propagation

Many applications of modelling elastic wave propagation Anna Nissen require the ability to recompute the wavefield after local Energy Resources Engineering model alterations. By using so-called exact boundary con- Stanford University ditions, the computational domain in for instance a finite- [email protected] difference solution can be arbitrarily truncated and the wavefield recomputed around the region of change. The updated wavefield will fully include all high-order long- MS85 range interactions between the truncated part and the full Formulation for Multiphase Multicomponent Flows model. Applications include full waveform inversion and and Stopping Criteria for Two-phase Flows seismic multiple elimination. The petroleum industry needs to model multiphase mul- Marlies Vasmel ticomponent flows in large porous domains. These com- ETH - Zurich putations are very expensive and thus one is interested in [email protected] optimizing them. The talk will first discuss a new formulation for multiphase multicomponent flow, its finite volume Johan Robertsson discretization, and efficient computer implementation. In a ETH-Zurich second part, we restrict ourselves to the two-phase setting [email protected] and present some adaptive stopping criteria for nonlinear and algebraic solvers based on a posteriori error estimates. GS13 Abstracts 155

ment points located above the air-ground interface or in a borehole arrangement . The relationship between such field Carole Heinry and the dielectric properties of the targets can be modeled Universite Pierre et Marie Curie (Paris 6), Paris, France by using a nonlinear integral operator involving the Green [email protected] function for half-space configurations. In the present work, an algorithm based on regularization in Banach spaces is considered to solve the associated inverse scattering equa- MS85 tion. With respect to previous algorithms, usually based Analysis of Mixed Finite Element Discretization for on classical Hilbert spaces, the present method in Banach Crystal Precipitation and Dissolution Model spaces is able to give a substantial reduction of the over- smoothing and ringing effects in the restored buried object. We deal with the numerical analysis of an upscaled model describing the reactive flow in a porous medium. The so- lutes are transported by advection and diffusion and un- Claudio Estatico dergo precipitation and dissolution. The reaction term, Department of Mathematics, University of Genova, Italy in particular, the dissolution term has a particular, multi- [email protected] valued character. We consider the mixed finite element discretization and prove the convergence to the continu- Matteo Pastorino ous formulation. Additionally, this also yields an existence Department of Electrical, Electronic, Telecomm. Eng. proof for the model in mixed variational formulation. University of Genoa [email protected] Kundan Kumar University of Austin [email protected] Andrea Randazzo Department of Electrical, Electronic, Telecomm. Eng. University of Genoa, Italy Iuliu Sorin Pop [email protected] Dept of Mathematics and Computer Sciences TU Eindhoven [email protected] MS86 Lp-Penalized Methods for Spatial Resolution En- Florin A. Radu, Florin A. Radu hancement of Microwave Radiometer Data Institute of Mathematics University of Bergen Microwave radiometer data are characterized by a spatial fl[email protected], fl[email protected] resolution that, although adequate for large-scale phenomena, is a severe limitation to observe small-scale features. An effective technique is first proposed to enhance the spa- MS85 tial resolution of two-dimensional radiometer data. It is Locally Mass Conservative Methods with Discon- based on the iterative regularization in Banach Spaces. It tinuous Galerkin in Time for Miscible Displace- allows reducing the over-smoothing effects and the oscil- ment in Porous Media lations that are present in standard Hilbert procedures. Experiments undertaken on actual data confirm the effec- The miscible displacement problem of a solvent fluid into a tiveness of the approach. resident fluid in porous media is characterized by a system of coupled partial differential equations. The flow of the Flavia Lenti fluid mixture is modeled by Darcy’s law, and the concen- Department of Science and High Technology tration of the solvent fluid satisfies a transport equation. University of Insubria, Como, Italy We propose a high order method in time and space, that fl[email protected] combines discontinuous Galerkin in time with locally mass conservative methods such as mixed finite element meth- Ferdinando Nunziata ods and interior penalty discontinuous Galerkin methods. department of Tecnology, University of Naples Convergence of the numerical solution is obtained under Parthenope mild regularity assumptions on the data. Boundedness of [email protected] the dispersion-diffusion matrix is not required. The analysis utilizes a generalized Lions-Aubin theorem, that can Claudio Estatico be applied to broken Sobolev spaces. Numerical exam- Department of Mathematics, University of Genova, Italy ples show that optimal rates of convergence are reached [email protected] for smooth solutions. Robustness of the method is tested for heterogeneous porous media. Maurizio Migliaccio Beatrice Riviere department of Tecnology, University of Naples Rice University Parthenope Houston, Texas, USA [email protected] [email protected] MS86 MS86 The Cylindrical Wave Approach and the Electro- Regularization in Banach Spaces for Microwave magnetic Scattering by Buried Objects Borehole Subsurface Prospection The Cylindrical-Wave Approach (CWA) is a spectral- In electromagnetic prospection of buried targets, the elec- domain method for the full-wave solution of the electro- tromagnetic scattered field is collected in a set of measure- magnetic forward-scattering problem by subsurface two- 156 GS13 Abstracts

dimensional objects. The scattered field is represented in [email protected] terms of a superposition of cylindrical waves. Use is made of the plane-wave spectrum to take into account the inter- Ciro Del Negro action of such waves with the interface between air and soil, Istituto Nazionale di Geofisica e Vulcanologia and between different ground layers. The ground losses and [email protected] all multiple-reflection and diffraction phenomena are taken into account. MS87 Fabrizio Frezza A Discontinuous Galerkin Method for the Simula- [email protected] tion of Multiphase Pyroclastic Flows

Lara Pajewski The mixture of gas and solid particles in non-equilibrium Rome conditions that compose a pyroclastic flows is described [email protected] with a set of coupled partial differential equations for the mass, momentum and enthalpy of each species. Following the methods of lines, a Discontinuous Galerkin space dis- MS86 cretization is introduced first, then different explicit time Regularized Solution of Linear and Nonlinear discretization schemes are adopted. Finally, several exam- Problems in Electromagnetic Sounding ples and comparisons between different numerical schemes are presented. Electromagnetic induction techniques are often used for non-destructive investigation of soil properties, since they Susanna Carcano allow to ascertain the presence in the ground of metals, MOX, Polimi liquid pollutants, or saline water. Maxwell equations lead [email protected] to a nonlinear model for this problem, which is sometimes transformed into an approximated linear model. In both Luca Bonaventura cases, the inverse problem is severely ill-conditioned. We MOX Politecnico di Milano will introduce the models and present the results of numer- Milan, Italy 20133 ical experiments on both synthetic and real data. [email protected] Giuseppe Rodriguez Universit‘a di Cagliari, Italy MS87 [email protected] A Second Order Finite-Difference Ghost-Cell Method for Volcano Deformation Modelling Caterina Fenu University of Cagliari, Italy We propose a novel strategy based on a second order Finite [email protected] Difference (FD) ghost-cell method for solving the elasto- static equations in an arbitrary domain described by a level-set function to compute rock deformation caused by MS87 the pressurization of magma sources. The elasto-static Lava Flow Simulation with Smoothed Particle Hy- equations are solved on a regular Cartesian grid and the drodynamics on GPU domain is defined implicitely by the level-set function. We consider two-dimensional cases to validate the method ver- We present a GPU implementation of the Smoothed Parti- sus analytical solutions and Finite Element results. cles Hydrodynamics (SPH) numerical method to solve the dynamic and thermal equations involved in the simulation Armando Coco of lava flows. Our model implements multiple rheologies Dipartimento di Geologia e Geofisica, UNIBA (newtonian, Bingham, power-law, Hershel-Bulkely), with [email protected] both fixed and thermal-dependent parameters, to allow different physical models of liquid lava to be tested; sim- Gilda Currenti ulations can be run on natural topographies, obtained for INGV, Catania example from an Digital Elevation Model of the location [email protected] of the simulated event.

Giuseppe Bilotta Giovanni Russo DMI, UNICT University of Catania [email protected] Department of Mathematics [email protected] Alexis Herault CNAM, Paris, France Ciro Del Negro [email protected] Istituto Nazionale di Geofisica e Vulcanologia [email protected] Eugenio Rustico INGV MS87 Catania Analysis of Non Equilibrium Effects in the Decom- [email protected] pression Structure of Multiphase Underexpanded Volcanic Jets Giovanni Russo University of Catania We have developed a semi-implicit, second-order accurate Department of Mathematics finite volume numerical scheme to simulate underexpanded GS13 Abstracts 157

volcanic jets by means of a N-particle Eulerian multiphase tegrates nonhydrostatic anelastic equations, suitable for flow model. We discuss the influence of the grain-size dis- simulation of small-to-mesoscale atmospheric flows. The tribution and particle load on the shock wave pattern of su- model builds on nonoscillatory forward-in-time MPDATA personic jets issuing from a narrow conduit. The problem approach using finite-volume discretization and admitting of the influence of non-equilibrium phenomena, associated unstructured meshes with arbitrarily shaped cells. Tech- to the polydisperse nature of the mixture, on the stability nical considerations are supported with canonical simula- of the volcanic column is finally addressed. tions of convective planetary boundary layer, and stably stratified orographic flows. The unstructured-mesh solu- Tomaso Esposti Ongaro tions are compared to equivalent results generated with an INGV, Pisa established structured-grid model, theory and observation. [email protected]

Augusto Neri Joanna Szmelter Istituto Nazionale di Geofisica e Vulcanologia Loughborough University Sezione di Pisa [email protected] [email protected] Piotr Smolarkiewicz NCAR MS88 MMM Simulation of Tropical-Cyclone-Like Vortices in [email protected] Shallow-Water ICON-Hex Using Goal-Oriented R- Adaptivity MS89 We build r-adapted grids to predict the tracks of two in- SLIM, A Baroclinic Discontinuous Galerkin Finite teracting tropical-cyclone-like vortices. A linear sensitivity Element Model for Marine Flows: Validation on analysis using a finite element model delivers goal-oriented Academic and Real Applications error estimates that indicate each grid cells’ contribution to the error in the cyclone tracks. These estimates are used Unstructured grids models for marine flow modelling are to optimize the grid of the hexagonal C-grid shallow-water used for many years now. These models have proved their model ICON-hex. Compared to uniform meshes, our ap- efficiency for coastal applications. A 3D baroclinic discon- proach reduces the required degrees of freedom by a factor tinuous Galerkin finite element model with split-explicit of four. time stepping, SLIM 3D, have recently been developed and applied to ideal coastal flows. This model still suf- Werner Bauer fers problems of stability. The simulation blows up easily University of Hamburg on the boundaries and non-physical behaviour can be ob- KlimaCampus served where there is a high horizontal pressure gradient. [email protected] In order to fix it without changing the physics beyond the model, a stabilized version has been developed and applied to large-scale ocean circulation test-case, where the prob- MS88 lems of stability are crucial. This model has been compared Mimetic Finite Element Methods for to other models to assess the quality of the results. This Ocean/atmosphere Modelling talk presents the SLIM model explaining its spatial and temporal discretization characteristics. Then a large-scale We present a finite element framework for the rotating shal- application in which we assess the robustness of our model low water equations on the sphere, which could be consid- is presented. This application, a baroclinic instability in ered to be an extension of the mimetic C-grid approach of a zonally re-entrant channel, gives a comparison between (Ringler, Thuburn, Klemp and Skamarock, 2010) to finite the SLIM model and other references. Eventually, some element methods. The finite element framework maintains results of different coastal academic and real applications conservation of potential vorticity and mass, absence of on which the model has been assessed are given. spurious pressure modes, the capability to preserve energy (although dissipation is required to control oscillations near Philippe Delandmeter to fronts) and stationarity of geostrophic linear modes on Ecole Polytechnique de Louvain the f-plane, but makes three extensions, namely: 1) the Université catholique de Louvain possibility of higher-order accuracy, 2) no restriction to or- [email protected] thogonal meshes, and 3) additional flexibility which can be used to alter the balance between velocity and pressure Jonathan Lambrecht, Jean-Francois Remacle degrees of freedom to remove spurious mode branches. We Univ. catholique de Louvain discuss extensions to three dimensional modelling and il- Belgium lustrate the approach with numerical tests. [email protected], jean-franois remacle Colin Cotter ¡jean-francois.remacle@uclou Imperial College [email protected]. Vincent Legat Université catholique de Louvain Belgium MS88 [email protected] An Edge-Based Model for Mesoscale Atmospheric Dynamics

A three-dimensional semi-implicit edge-based unstructured-mesh model is developed that in- 158 GS13 Abstracts

MS89 marks. The approach exploits the topology of the 3D mesh, Title Not Available at Time of Publication that is formed by stacking layers of prisms in the vertical direction. A robust mapping between the finite difference Abstract not available at time of publication. grid and the finite element function space is designed, taking into account the discontinuities in the latter. J. Casey Dietrich University of Texas at Austin Vincent Legat [email protected] Université catholique de Louvain Belgium [email protected] MS89 Modeling Three-Dimensional Processes in Coastal Engineering Applications MS90 Mantle Convection Modelling Irreducibly three-dimensional (and time-dependent) processes arise often enough in real-world coastal engineer- Mantle convection is central to understanding the large ing applications that effective tools for their solution are scale geologic evolution of our planet. In this contribution needed. These processes include interaction of waves and I will review recent progress in mantle convection modeling currents with coastal and hydraulic structures and subsur- in my group at Munich University. face air/water dynamics in heterogeneous materials. In this talk I will discuss examples of fully three-dimensional engi- Hans-Peter Bunge neering problems and methods for solving them directly in Department of Earth and Environmental Sciences, LMU three dimensions, particularly finite element and level set Munich methods on unstructured meshes. [email protected] Chris Kees U.S. Army Engineer Research and Development Center MS90 Coastal and Hydraulics Laboratory Simulations of Thermal Convection in Rotating [email protected] Spherical Shells

Matthew Farthing Di?erent implementations of several time integrators based US Army Engineer Research and Development Center on our own codes and public libraries are presented [email protected] to study their e?ciency when are applied to a three- dimensional thermal convection problem in rotating spherical geometry. The equations are discretized with pseudo- Matt Malej spectral techniques. Many geophysical and astrophysical Coastal & Hydraulics Laboratory phenomena such as the generation of the magnetic ?elds, U.S. Army Engineer Research & Development Center or the di?erential rotation observed in the atmospheres of [email protected] the major planets can be studied in this framework. Roham Bakhtyar Ferran Garcia University of North Carolina at Chapel Hill Universitat Polit`ecnica de Catalunya, Spain U.S. Army Engineer Research and Development Center [email protected] [email protected] Luca Bonaventura Steve Mattis Politecnico di Milano University of Texas at Austin MOX, Dipartimento di Matematica F. Brioschi [email protected] [email protected]

Clint Dawson Marta Net Institute for Computational Engineering and Sciences Departament Fsica Aplicada University of Texas at Austin Universitat Polit`ecnica de Catalunya [email protected] [email protected]

Juan Sanchez MS89 Universitat Polit`ecnica de Catalunya, Spain Eﬃcient and Elegant Numerical Tools for Ocean [email protected] Flows

Numerical modelling of coastal flows is a challenging topic MS90 due to complex topography, complex flow dynamics and Inverse Retrospective Problems in Geodynamics large density variations. Such phenomena are best simulated with unstructured grid models due to their highly Present geophysical and geodetic observations provide a exible spatial discretisation. A three-dimensional discon- clue to understanding the dynamics of the Earth interior tinuous Galerkin finite element marine model is presented. in the geological past. Data assimilation allows to con- The spatial discretisation and explicit mode splitting time strain the mantle flow and temperature in the past using integration scheme are described. Free surface movement dynamic models and present observations. Quantitative is accounted for by means of an arbitrary Lagrangian Eu- tools are required to solve inverse retrospective problems lerian (ALE) moving mesh method. Mass and volume are of geodynamics. The basic inversion methods (data as- conserved. The conservation properties and baroclinic ad- similation methods) and their applicability to restore the justment under gravity are tested with numerical bench- GS13 Abstracts 159

evolution of the Earth interior will be discussed. performance, and present results on recent parallel architectures. Alik Ismail-Zadeh Russian Academy of Sciences Michael Bader Moscow, RUSSIA Technische Universitaet Muenchen [email protected] Department of Informatics [email protected]

MS90 Alexander Breuer Multipole Boundary Element Method in Geody- Technische Universität München namics Department of Informatics [email protected] We illustrate advantages and difficulties associated to the use of Multipole-Boundary Element Method (MP-BEM) in geodynamics. MP-BEM complements Finite Element, Vol- Sebastian Rettenberger ume and Differences in an original way, offering solutions Technische Universitaet Muenchen to geophysical fluid-dynamic problems such as multiphase, Department of Informatics, Chair of Scientific Computing porous media and bubbly flow, exploiting its lagrangian [email protected] formulation. Applications to regional and global geodynamics are finally also shown. Mathematical and compu- PP1 tational issues are clarified in detail showing how MP-BEM is particularly suitable for parallelization on massive par- Polymer Flooding Techniques in Enhanced Oil Re- allel computers. covery Gabriele Morra Enhanced Oil(petroleum) Recovery in petroleum reservoirs School of Earth and Environmental Sciences is very important now due to depleting oil reserves.This pa- Seoul National University per elaborates at length different method of EOR.Polymer [email protected] flooding methods in depleted oil reservoirs have been enun- ciated.The mathematical equations have been developed and analysed.The analytical solutions are found.It is seen PP1 that an increase in production upto 30% is anticipated in A Reduced Fracture Model for Two-Phase Flow this method.The bypassing of water over oil is arrested and with Different Rock Types drag reduction enhances production.

In this work we are concerned with a reduced, discrete- Dr Sisir Kumar Bhowmick fracture model for two-phase flow in porous medium. We GMIT,Balarampur,Baruipur take capillary pressure into account, and use the global Kolkata-700144 pressure formulation. We consider the case that the frac- sisirkr@rediffmail.com ture and the surrounding matrix are of different rock type, that is they have different capillary pressure and relative PP1 permeability curves. Numerical results will be presented. Numerical Modeling of Stress Fields in the Earth’s Elyes Ahmed Mantle with Non-Newtonian Viscosity Inria Paris-Rocquencourt ahmed [email protected] The spatial fields of overlithostatic pressure, the vertical and horizontal stresses in the mantle are studied in 2D numerical model of mantle convection. The model viscosity Amel Ben Abda is temperature-, pressure-, and strain-dependent. The typ- Lamsin-Enit ical overlithostatic stresses in the main part of the mantle Tunisie are in the range of (7 - 9) MPa, with strong concentration [email protected] in the areas of descending slabs (up to 50 MPa). We find significant differences between the three studied fields. Jean E. Roberts Inria Paris-Rocquencourt Alexandr M. Bobrov, Alexey Baranov, Natalia Bobrova [email protected] Schmidt Institute of Physics of the Earth a m [email protected], [email protected], Jerome Jaffre a m [email protected] INRIA-Roquencourt 78153 Le Chesnay cedex France Jerome.Jaff[email protected] PP1 Render the Interpolation Library SCRIPP Conser- vative PP1 Optimizing a Cartesian Shallow Water Code on Abstract not available at time of publication. Hybrid Architectures Joel Chavas SWE is an education-oriented code to solve the shallow CEA water equations on Cartesian meshes, having tsunami sim- [email protected] ulation in mind as application. It is designed to support hybrid parallelisation with multiple GPUs or co-processors PP1 such as Intel Xeon Phi. We will demonstrate optimisation techniques (vectorisation, e.g.) required to achieve decent Inversion for Hydraulic Conductivity Using the 160 GS13 Abstracts

Unsaturated Flow Equations Dept of Civil Engineering [email protected] Hydraulic conductivity (K) is a property of the soil media and is the main regulator of groundwater flow. However, Jan Nordbotten in many hydrogeologic studies K is only known as a bulk Dep. of Mathmatics, University of Bergen average. An accurate estimate of K that is spatially consis- [email protected] tent with the media is highly valuable. Here we present an inverse problem that calculates K from time-varying saturation (or pressure head) data; the saturation data can PP1 come from geophysical imaging and is spatially extensive. Compressional Seismic Velocity Fields Parameter- Rowan B. Cockett ized by Haar Wavelet University of British Columbia Two-dimensional seismic compressional velocity fields, ex- [email protected] tracted from geological models, are parameterized by means of Haar wavelet. The coefficients of the Haar se- Eldad Haber ries are calculated using integral formulas. The primary Department of Mathematics objective of this work is to be assured that such parame- The University of British Columbia terization can represent the seismic velocity field in a satis- [email protected] factory way (reasonable accuracy and few coefficients) and, then, as secondary objective, to create appropriated conditions to estimate wavelet coefficients by some inversion PP1 procedure using seismic data. Transport Upscaling Using Coupled and Corre- lated Continuous Time Random Walks Wilson M. Figueiro Universidade Federal da Bahia We present a continuous time random walk (CTRW) Instituto de Geociencias framework for the upscaling of transport in heterogeneous fi[email protected] media. The CTRW approach describes particle motions in terms of a random walk in space and time. The challenge Helcio Perin consists in the determination of the map of the quenched Universidade do Estado da Bahia, UNEB disorder that represents spatial heterogeneity, into the [email protected] stochastic processes describing the space and time transitions. Based on stochastic models for the spatial disorder, we present two upscaling approaches: (i) for transport in a Adriano Martinez correlated random medium, which leads to a fully coupled Universidade Federal da Bahia, UFBA CTRW, and (ii) transport in correlated divergence-free ran- [email protected] dom velocity fields, which leads to a CTRW characterized by correlated random time increments. The transport be- Saulo P. Oliveira havior is discussed in terms of first-passage time distri- Universidade da Bahia butions, spatial particle distributions, and mean squared [email protected] displacement, using random walk particle tracking simulations. Both sub- and superdiffusive behavior is observed. Saulo P. Oliveira Finally, we derive the related (non-local) partial differen- Universidade Federal do Parana tial equations for the particle densities that describe the [email protected] large scale transport dynamics. Luiz Guimaraes Marco Dentz Universidade Federal do Rio de Janeiro, UFRJ IDAEA, Spanish National Research Council (CSIC) [email protected] [email protected] Paulo Cunha PP1 CENPES-PETROBRAS Scale Dependent Coupling of Hysteretic Capillary [email protected] Pressure, Trapping and Fluid Mobilities We study the impact of capillary-pressure hysteresis and PP1 CO2-trapping on vertically integrated constitutive param- Improvement of Convergence of Multigrid Method eter functions. Trapping is the dominant contributor to in Multiphase Flow Problems. hysteresis in integrated models for the initial drainage and a following imbibition. The hysteretic nature of the cap- Multigrid methods often become inefficient for solution illary fringe is of secondary importance for advective proof multiphase flow problems because the construction of cesses. The hysteretic capillary fringe plays an important coarse grid operators does not take into account inhomo- role for redistributive processess. geneous saturation distribution. This leads to inefficient residual smoothing and significantly reduces convergence Florian Doster rate. Here we examine the convergence behavior of geomet- Dep. of CEE, Princeton University ric multigrid method in case when the upscaling methods Dep. of Mathmatics, University of Bergen (incl. multiphase) are employed in construction of coarse [email protected] grid operators. The application for nonlinear multigrid method is also discussed.

Michael A. Celia Maxim Filatov Princeton University Lomonosov Moscow State University GS13 Abstracts 161

maxfi[email protected] PP1 Statistical Characteristics, Circulation Regimes Dmitry Maksimov and Unstable Periodic Orbits of Simple Atmo- Junior Researcher spheric Model KIAM RAS [email protected] The theory of chaotic dynamical systems gives a lot of tools that can be used in climate studies (Lyaunov exponents, attractor dimension etc). Another potentially useful one PP1 that could be used for the local analysis of the system PDF Numerical and Geometric Optimization Tech- involves an expansion in terms of unstable periodic orbits niques for Environmental Prediction Systems (UPOs). According to it, the system statistical characteristics are approximated as a weighted sum over the orbits. Abstract not available at time of publication. The weights are inversely proportional to the orbit instability characteristics so that the least unstable orbits make George Galanis larger contributions to the PDF. In our study we will try to Greek Naval Academy apply the idea of UPO expansion to the simple atmospheric University of Athens system based on the barotropic vorticity equation on the [email protected] sphere. We will check how well orbits approximate the system attractor, its statistical characteristics and PDF. The connection of the most probable states of the system with PP1 the UPOs will also be analyzed. Polynomial Interpolation and Quadrature on Sub- regions of the Sphere Andrey Gritsun Institute of Numerical Mathematics Using some recent results on trigonometric interpolation [email protected] and quadrature on subintervals of the period, we present a rule for numerical integration over some regions of the sphere, that include spherical caps and zones. The rule PP1 has positive weights and is exact for all spherical polyno- Capillary Fracturing in Granular Media mials of degree less or equal than n. We also construct Weakly Admissible Meshes and approximate Fekete points We study the displacement of immiscible fluids in defor polynomial interpolation on such regions of the sphere. formable, non-cohesive granular media. Experimentally, All the algorithms have been implemented in Matlab. we inject air into a thin bed of water-saturated glass beads and observe the invasion morphology. The control parame- Mariano Gentile ters are the injection rate, the bead size, and the confining Unaffiliated stress. We identify three invasion regimes: capillary finger- [email protected] ing, viscous fingering, and capillary fracturing, where capillary forces overcome frictional resistance and induce the A. Sommariva, M. Vianello opening of conduits. We derive two dimensionless numbers tba that govern the transition among the different regimes: a [email protected], [email protected] modified capillary number and a fracturing number. The experiments and analysis predict the emergence of fracturing in fine-grained media under low confining stress, a PP1 phenomenon that likely plays a fundamental role in many Space-Time Wavelet Techniques in the Reverse- natural processes such as primary oil migration, methane Time Depth Migration venting from lake sediments, and the formation of desicca- tion cracks. A method based on the well-known reverse–time depth migration and new Poincaré space-time wavelets is presented Mathias Trojer, Michael Szulczewski for a smooth layered medium. We represent the forward MIT and back-propagated fields in terms of localized solutions [email protected], [email protected] centered along rays in the medium. Initial amplitudes of these localized solutions on the surface are calculated by Ruben Juanes means of the continuous space-time wavelet analysis for the MIT seismic data. An example with seismograms calculated by Civil and Environmental Engineering the finite differences method is presented. [email protected] Evgeny Gorodnitskiy Physics Faculty, St.Petersburg University PP1 [email protected] Comparison Study of Spurious Wave Reflection Response with Staggered Finite-Volume and Un- Maria Perel staggered Element-Based Galerkin Schemes under St. Petersburg University, Russia Mesh-Refinement [email protected] Spurious wave reflections caused by different grid sizes are Yu Geng, Ru-Shan Wu examined using both 1D linear shallow water equations University of California, Santa Cruz models based on staggered finite-volume and unstaggered [email protected], [email protected] continuous/ discontinuous Galerkin (CG/DG) discretization. We test spurious wave reflection response caused by mesh refinement with both low and high wavenumber wave packets. Results indicate that unstaggered CG/DG 162 GS13 Abstracts

scheme produce less spurious wave reflection compared to modelling of fault core lens properties takes into account staggered finite-volume scheme. In particular, DG with their links to known physical constraints (i.e. host rock Lax-Friedrich numerical flux is completely free from spuri- stratigraphy and strain distribution). Particular attention ous wave reflections. is given to the statistical validation procedure of sampled realizations. Shin-Hoo Kang,Tae-JinOh Korea Institute of Atmospheric Prediction Systems Dmitriy Kolyukhin [email protected], [email protected] CIPR Bergen, Norway [email protected] PP1 A Statistical Subgrid Model for Large Eddy Simu- Jan Tveranger lations Uni CIPR [email protected] Cinlar velocity field has been shown to represent the submesoscale eddies up to 5 km in radius by an analysis of high-frequency radar observations. As a result, it is pro- PP1 posed as a subgrid model for Large Eddy Simulation (LES). New Efficient Numerical Method for Integral Equa- We consider a velocity field composed of eddies in two ditions in EM Sounding of Inhomogeneous Media mensions using Gamma distribution for their radius. In LES, the subgrid stress is modeled based on the covariance The new iterative numerical method for 3d integral equa- structure of the random velocity field. tions of electrodynamics was devised. The main challenge of using this equations in forward problems of EM sound- Rukiye Kara ing is a need to solve a high-order system of linear equa- Department of Mathematics tions with a dense matrix. The main distinctive feature of Mimar Sinan Fine Arts University the proposed method is a double integration of the elec- [email protected] tric Green’s tensor in the process of algebraization of the original equation to decrease the order of the matrix. Mine Caglar Department of Mathematics Mikhail Kruglyakov Koc University Lomonosov Moscow State University [email protected] [email protected]

PP1 PP1 Application of a Fast Algorithm to Solving the Upscaling of Density-Driven Instabilities Using Pressure Equation Efficiently Countercurrent Flow In this talk, we will present several fast methods for solving In two-phase flow models opposite flow directions are al- a non-separable elliptic pressure equation arising in porous lowed for the two phases in presence of density-driven flow. media flow modeling using Darcy’s law. All of these meth- This countercurrent flow can be seen as macroscopic de- ods use a fast algorithm for solving the elliptic equation by scription of unresolved microscopic velocities. We aim at Green’s function method. We will present numerical results extending the concept of countercurrent flow to upscale in- and compare the performance of this methods. This work stability observed in density-driven single-phase flow mod- is currently under progress. The research to be presented els that are originally described at the Darcy scale. The re- has been made possible by a grant (NPRP 08-777-1-141) sults are included in the Multiscale Finite Volume method from the Qatar National Research Fund (a member of The to improve approximation of density-driven instabilities. Qatar Foundation). Rouven Kuenze, Ivan Lunati JoungDong Kim University of Lausanne Texas A&M University [email protected], [email protected] [email protected]

Prabir Daripa PP1 Texas A&M University Upscaling of Reactive Flows in Domains Having Department of Mathematics Rough Boundaries [email protected] We consider the flow and transport of chemically reactive substances in a channel over substrates having complex ge- Craig Gin ometry (rough boundaries). At the boundaries, the precur- Texas A&M University sors undergo precipitation as well as dissolution. To over- [email protected] come the computational complexity, we replace the rough boundary by a flat one and provide an upscaled boundary PP1 condition. We do this for both situations: when the geometry is assumed fixed (rigorous) and when the geometry Statistical Simlulation of Fault Zone Structures varies due to reactions (formal asymptotics). The study demonstrates the potential use of statistical sim- Kundan Kumar ulation for describing some observed structural features of University of Austin complex faults zones. Deformation bands are sampled ac- [email protected] cording to probability distribution based on their link to distance from the fault and fault displacement. Stochastic GS13 Abstracts 163

Iuliu Sorin Pop Department of Civil and Environmental Engineering Dept of Mathematics and Computer Sciences Princeton University TU Eindhoven [email protected] [email protected]

Mark van Helvoort PP1 Eindhoven University of Technology Systems of Conservation Laws for Thermodynam- [email protected] ically Consistent Adsorption with Subscale Diffu- sion and Memory Terms Tycho van Noorden Multicomponent adsorption is typically described by a COMSOL BV system of conservation laws in which the nonlinear flux [email protected] terms come from explicit functional relationships called isotherms. The most popular extended Langmuir isotherm PP1 is thermodynamically inconsistent. We discuss analysis and numerical approximation of multicomponent ad- Modeling a Stochastic Convective Preciptation sorption system where the thermodynamically consistent Process isotherms are given only implicitly, or from a coupled mi- A simple stochastic model is used to simulate a strong con- croscopic model. We include memory terms in our model vective precipitation process. The model includes three and new examples. stochastic components: a stochastic trigger for precipi- F. Patricia Medina, Malgorzata Peszynska tation state on and off (a two-state Markov jump pro- Department of Mathematics cess based on a Poisson distribution), a stochastic mass Oregon State University flux at cloud base for a turbulence closer equation, and [email protected], another stochastic closure for neighborhood domain’s in- [email protected] fluence, such as moisture convergence/divergence. These three stochastic processes are tested for a single column model of climate. PP1 Kimberly Leung A Benchmark for Thermo-Hydrological Codes on San Diego State University Cold Regions Hydrology [email protected] Recent numerical studies proved the importance of coupled thermo-hydrological processes to study the evolution Aneesh Subramanian of water bodies in permafrost environments under climate University of California, San Diego, USA change. Such coupled systems of non-linear equations (in- [email protected] cluding phase change) are hard to solve and lack validation exercises. We present a benchmark of codes (numerical and Samuel S. Shen experimental test cases). It is further intended as a forum San Diego State University to improve the simulation performances in view of inten- [email protected] sive 3D simulations including the complexity of natural systems. Guang Zhang Scripps Institution of Oceanography Christophe F. Grenier [email protected] LSCE - UMR8212 [email protected]

PP1 Nicolas Roux Up-scaling Reaction Rates from Pore to Core Scale LSCE [email protected] We focus on the network flow simulation of up-scaling, from pore to core scale, of rates of anorthite and kaoli- Fran¸cois Costard nite reaction under acidic conditions commensurate with IDES CO2 sequestration. The simulations allow investigation of [email protected] uncertainties in our knowledge of micro-scale reaction rates under flow regime as well as the flow dependence of bulk Emmanuel Mouche reaction rates. The results reveal the susceptibility to pre- LSCE diction errors in the case of reactions close to equilibrium. [email protected]

W. Brent Lindquist PP1 Applied Mathematics and Statistics, Stony Brook University Geometric Characterization of Strata By Inverse [email protected] Scattering and Active Contours For simplicity, traditional subsurface characterization Daesang Kim methods assume ﬂat geological layers. Our approach seeks Applied Mathematics and Statistics the actual, arbitrary layer shapes that best match given Stony Brook University surface measurements of seismic waves. Through the mini- [email protected] mization of an energy functional, active contours modeling layer geometry evolve to the desired shape. The gradient Catherine Peters descent direction is derived semi-analytically for increased 164 GS13 Abstracts

computational speed. Together with the method of fun- Subsurface Flows: Application to Heterogeneous damental solutions for numerical elastodynamic wave solu- and 3D Configurations tions, we obtain a meshfree inversion algorithm. A fully integrated coupling between surface and subsurface Martin Mueller, Francesco Fedele flows has been implemented recently (Weill et al., 2009). Georgia Institute of Technology This model unifies the Richards and the diffusive wave [email protected], [email protected] equations into a single generalized Richards equation defined in a single domain composed of surface and subsurface Anthony Yezzi subdomains. This model has been applied successfully to Georgia Institute of Technology 2D configurations. We will show some improvements of the Electrical & Computer Engr Dept scheme to simulate the runon-runoff process on a hetero- [email protected] geneous soil and 3D configurations. Claude Mügler PP1 CEA / LSCE Identification of Seismic Quiescence Anomalies in [email protected] the Seismic Region of the Mexican Pacific Coast Emmanuel Mouche We used the region-time-length (RTL) and the Schreider CEA, DRN algorithms to characterize seismic quiescence anomalies in France the Mexican Pacific coast. We investigated the spatiotem- [email protected] poral variations of seismic quiescence prior to the past Mex- ican earthquakes of magnitude greater than 7.5 since 1970. Cécile Carrère We used an improved RTL algorithm with optimal pa- CNRS / LSCE rameters. To better understand these seismic quiescence [email protected] anomalies we also studied synthetic catalogues obtained with a two dimensional spring-block model that mimics the seismic faults dynamics. PP1 Large Scale Patterns in Convection: from Alejandro Munoz-Diosdado Rayleigh-Benard, Through Prandtl Problem, to UPIBI-IPN Moist Atmospheric Convection [email protected] Large scale patterns formation in dry and moist convection Adolfo Rudolf-Navarro scenarios are addressed in this paper. The first part of the ESFM-IPN talk will be devoted to the case of clustering of plumes [email protected] in Rayleigh-Benard convection: through a two-scale process, kinetic energy is transferred mainly to low horizontal wave numbers while the sizes of individual plumes remain PP1 on the scale of the boundary layer thickness. Again in a A Three-Scale Model of Charged Solute Transport direct numerical simulation framework, the study of the in Swelling Clays Including Ion Size Correlations Prandtl problem is addressed as a simpli?ed model of dry atmospheric convection, kept in statistically stationary ra- A three-scale model is developed to describe the mix- diativeconvective equilibrium. Finally the emergence and ing of two ionic contaminants in swelling clays. The temporal evolution of large-scale spatial-temporal oscillat- nanoscopic problem arises from the Statistical Mechan- ing modes in deep moist convection, for an atmosphere ics and is governed by an integral Fredholm equation for in radiative-convective equilibrium. To this end, we use the ion/nanopore correlation function coupled with Poisson cloud-resolving numerical simulations of the convective at- problem for the electric potential. Swelling of the clusters mosphere at very high resolution and on a very large do- is coupled microscopically with the diffusion of the species main, using WRF model in LES mode. in the micro-pores and the homogenization procedure is applied to up-scale the microscopic model to the macroscale. Antonio Parodi Istituto di Scienze dell’Atmosfera e del Clima [email protected] Dung Le, Christian Moyne Universite de Lorraine, LEMTA, UMR 7563, Vandoeuvre les Nancy, France PP1 [email protected], [email protected] Multiphysics, Multiscale Network Modeling of Gas Transport in Mudrocks Marcio A. Murad National Laboratory of Scientific Computation Despite recent research activity, shale petrophysics remains LNCC/MCT elusive due to the difficulties in experimental and numeri- [email protected] cal analysis of length scales below 100nm. We implement a network model with both micron and nanometer scale Sidarta Lima pores that includes effects of convection, diffusion as well Federal University Rural of Rio de as sorption of gas on pore walls. Diffusion and sorption Janeiro have a significant impact on ultimate gas permeability, and [email protected] the magnitude of the effect depends on pore connectivity, network geometry and size distribution.

PP1 Masa Prodanovic Continuum Darcy Approach for Coupling Surface- University of Texas at Austin GS13 Abstracts 165

Department of Petroleum and Geosystems Engineering DAIS [email protected] ﬂ[email protected]

Ayaz Mehmani Annamaria Mazzia, Giorgio Pini University of Texas at Austin Universita’diPadova [email protected] DICEA [email protected], [email protected]

PP1 Explicit Modeling of Fault Damage Zone Proper- PP1 ties Numerical Approximation of Reactive Flow in Porous Media with Discontinuous Reaction. This work aims to capture realistic damage zone features explicitly in reservoir models. A separate fault zone grid is We present a numerical method for the simulation of reac- generated from a conventional reservoir model and sub- tive flows in porous media characterized by a discontinuity sequently populated with damage zone properties using in the reaction term. The strategy is based on an oper- an extensive dataset of deformation band densities and ator splitting that decouples the reaction from advection permeability collected from outcrops. The resulting fault and diffusion, so that it can be approximated with tailored zone grid populated is subsequently merged with the orig- time integration schemes that guarantee accuracy even in inal conventional model, and comparison of flow behavior the case of discontinuous right hand sides. of this merged model and the conventional model is conducted. Anna Scotti Politecnico di Milano Dongfang Qu [email protected] Uni CIPR University of Bergen [email protected] PP1 A Fully Implicit Solver for Geochemical Processes Jan Tveranger in Compacting Basins. Uni CIPR [email protected] Geochemical processes such as quartz precipitation and illite-smectite transformation play a major role in deter- mining porosity and permeability in compacting basins. Per Røe We present a fully implicit method for the simulation of Norwegian Computing Centre temperature, pressure and porosity evolution in the pres- [email protected] ence of mechanical and geochemical compaction. The implicit approach is compared with an iterative decoupling of PP1 the equations to assess the better performances of the first strategy in cases characterized by strong overpressures. Applied Precipitation Nowcast Anna Scotti We present a reliable precipitation nowcasting system Politecnico di Milano which operates on radar data. The computational method [email protected] is an extension of the McGill Algorithm for Precipitation Nowcasting by Lagrangian Extrapolation (MAPLE), which provides a fast and accurate forecast by semi-Lagrangian Ilaria Imperiali advection and near-optimal wavelet filtering. Our imple- Mox, Department of Mathematics, Politecnico di Milano mentation provides near real-time computation and we ex- [email protected] tend MAPLE by using level sets for the computation of precipitation areas and optical flow methods for the com- Luca Formaggia putation of advection vector fields. Department of Mathematics Politecnico di Milano, Italy Thorsten Riess [email protected] W3 Data GmbH [email protected] PP1 Semi Lagrangian Methods in Variable Density Flow PP1 Meshless Techniques for Anisotropic Diffusion We present a 3D model for transient groundwater flow in a Problems confined aquifer based on discretized flow and solute mass balance equations. To overcome the difficulty of coupled Solving anisotropic diffusion equations is an important task nonlinear governing equations a Semi - Lagrangian method for many problems in Geosciences. We compare the effi- is implemented for the solute transport equation. This en- ciency of two meshless techniques based upon the Mesless ables to choose arbitrarily large time step without losing Local Petrov–Galerkin (MLPG) framework. The fist tech- stability, reduce numerical diffusion and also keep the sys- nique is an MLPG method with suitable test and trial func- tem mass conservative. tions; the latter is based on the Generalized Moving Least Squares method. By numerical experiments we show that Klara Steklova both methods can solve highly anisotropic problems. University of British Columbia Department of Earth, Ocean and Atmospheric Sciences Flavio Sartoretto [email protected] Universita’ Ca’ Foscari Venezia 166 GS13 Abstracts

Eldad Haber Rupert Klein Department of Mathematics Freie Universit¨at Berlin The University of British Columbia [email protected] [email protected]

PP1 PP1 Efficient Solver for Transversely Isotropic Eikonal Investigation of Instability of Displacement Front Equation Using Perturbation Theory in Flow Problems Numerical solutions of the eikonal (Hamilton-Jacobi) equa- The problem of two-phase immiscible fluid flow is consid- tion for transversely isotropic (TI) media are essential for ered, including sources and dependence of viscosity on tem- imaging and tomography applications. Such solutions, perature. Numerical calculations were achieved for differ- however, suffer from the inherent higher-order nonlinearity ent values of temperature and with increasing temperature, of the TI eikonal equation, which requires solving a quar- oil viscosity decreases exponentially and the stable state is tic polynomial at each computational step. Using pertur- possible. Additionally to the front stability there is an in- bation theory, we approximate the first-order discretized crease in the rate of displacement oil and increasing of pro- form of the TI eikonal with a series of simpler equations duction rate. Selecting optimal temperatures of injected for the coefficients of a polynomial expansion of the eikonal fluid is a way for intensification of the field development. solution in terms of the anellipticity anisotropy parameter η. In addition to achieving very high accuracy, the formu- Natalia Syulyukina lation allows tremendous cost reduction compared to the Lomonosov Moscow Sate University exact TI eikonal solver. We demonstrate these assertions [email protected] through tests on a homogeneous TI model, the VTI Mar- mousi model, and the BP TTI model.

PP1 Umair bin Waheed, Tariq Alkhalifah Pore-Scale Modeling and Experimental Investiga- King Abdullah University of Science and Technology tions of Mixing-Controlled Geochemical and Bio- [email protected], logical Reactions [email protected] Many important applications in geosciences and groundwater pollution require understanding of mixing-controlled PP1 geochemical and microbiological reactions that affect Adaptive Multi-Scale/physics Modeling of Two- porosity through mineral precipitation/dissolution and Phase Flow Including Capillary Pressure biofilm growth. We study these coupled processes using pore-scale simulation and micro-fluidics laboratory experi- Important applications in porous media require large-scale ments. We use the lattice Boltzmann method to solve for simulation. To capture important effects high spatial res- single-phase fluid flow, the finite volume method to solve olution can be necessary leading to enormous computa- for multi-species reactive transport, and a cellular automa- tional costs. One solution strategy are multi-scale meth- ton method for porosity evolution. Direct numerical simu- ods, which decrease the global degrees of freedom while lations are compared with laboratory experiments. preserving important features. We present an approach, which is applicable in a wide range of flow regimes, also if Albert J. Valocchi, Youneng Tang, Haihu Liu capillary pressure effects are significant. It combines adap- University of Illinois at Urbana-Champaign tive grid methods based on MPFA with local upscaling [email protected], [email protected], techniques. [email protected] Rainer Helmig Hongkyu Yoon IWS, University of Stuttgart, Germany Geoscience Research and Applications Institut fur Wasserbau Sandia National Laboratories [email protected] [email protected] Markus Wolff University of Stuttgart PP1 Germany A Multiscale Time Integrator for Computing Long- markus.wolff@iws.uni-stuttgart.de wave Shallow Water Flows at Low Froude Numbers Bernd Flemisch A new multilevel semi-implicit scheme for the computa- University of Stuttgart, Germany tion of low Froude number shallow water flows is presented. bernd.fl[email protected] Motivated by the needs of atmospheric flow applications, it aims to minimize dispersion and amplitude errors in the computation of long wave gravity waves. While it correctly balances ”slaved” dynamics of short-wave solution components induced by slow forcing, the method eliminates freely propagating compressible short-wave modes, which are under- resolved in time.

Stefan Vater University of Hamburg, KlimaCampus [email protected]