58 GS15 Abstracts

IP1 [email protected] The Seismic Inverse Problem Towards Wave Equa- tion Based Velocity Estimation IP5 Mathematical Modeling of Sedimentary Basins This talk will be on the inverse problem of exploration seis- mology, which aims at recovering earth parameters from There is a fundamental asymmetry in the continental crust controlled source seismic data measured at the surface of between high topography which tends to erode and low to- the earth. I will focus on retrieving the velocity function pography where sediments accumulate. As a result of this of seismic waves and discuss two approaches towards solv- asymmetry, sedimentary basins contain much of the history ing this problem, namely reflection tomography and Full of the Earths topography both high and low. Unravelling Waveform Inversion. that signal means understanding the processes in the base- ment which form the basins themselves and the erosion, Fons ten Kroode transportation and deposition of the sediments which find Shell themselves in the basin. I will review some of the challenges [email protected] in modelling a basin through its formation and filling and also touch on how this knowledge impacts our ability to use basins wisely. IP2 Louis Moresi Numerical Simulation of Fractured Reservoirs: Old School of Mathematical Sciences Challenges and New Ideas Monash University [email protected] Fractures are ubiquitous in geological formations and often control the successful exploitation of valuable resources such as hydrocarbons, water, and heat. Geoscientists, en- IP6 gineers, and mathematicians have struggled for decades to Locally Conservative Methods in Large Scale Sim- model and quantify the relevant physical and chemical pro- ulation cesses accurately. This presentation will review some of the key challenges and approaches, and introduce new model Efficient approximation methods for Stokes-type systems concepts and numerical techniques that could led to a step- are a crucial ingredient for many coupled multi-physics ap- change when simulating heat and mass transfer in fractured plications, e.g., in mantle-convection. The co-design of dis- geological formations. cretization concepts and solvers that satisfy local mass conservation, scale up to current peta-scale architectures and Sebastian Geiger result in a small time-to-solution is of special interest. Here Heriot-Watt University we discuss locally defined a posteriori flux corrections and Edinburgh a massively scalable hybrid matrix-free simulation frame- [email protected] work. This work is part of the DFG funded priority program SPPEXA.

IP3 Barbara Wohlmuth M2, Centre for Mathematical Sciences, Grimmond CANCELLED Technische Universit¨at M¨unchen, Germany [email protected] Talk is cancelled.

Sue Grimmond SP1 University of Reading SIAG/GS Career Prize Lecture: Title Not Avail- [email protected] able at Time of Publication

Abstract not available at time of publication. IP4 Jerome Jaffre A Multi-Scale Approach to Global Ocean Climate INRIA-Roquencourt Modeling 78153 Le Chesnay cedex France Jerome.Jaff[email protected] Two advances in the field of applied mathematics have enabled a new approach to global ocean climate modeling. First, the creation of optimal, smoothly-varying Voronoi CP1 meshes has enabled the specification of different resolu- Dynamics of a Compositional Flow on Porous Me- tions in different parts of the ocean. Second, a mimetic dia discretization of the rotating shallow-water equations in- sures that important conservation principles, such as en- The compositional flow in porous media involves phase cre- ergy and potential vorticity, are maintained on these multi- ation and subsequent fluid transport coupled with phase scale meshes. This talk will highlight how the combination equilibrium. A great challenge in this work is that gas of these advances might transform how we think about and phase appeared and vanished periodically. We present a use global ocean climate models. 2 × 2 dynamic system on a single pore to study these behaviors. Several tests were run with different injected flow Todd Ringler rate to investigate the condition that the system goes to Los Alamos National Laboratory steady state or the gas phase appeared and vanished peri- GS15 Abstracts 59

odically. Miller, Bill Gray, and Pam Birak.

Alex Chang Carl T. Kelley Nat’l Pingtung Teacher’s Coll North Carolina State University Department of Mathematics Mathematics Department [email protected] tim [email protected]

CP1 CP1 Nonlocal Continuum Description of Flow in Porous Mathematical Modeling for Geothermal System Media with Long Bypassing Connections Via Sub-Systems and Applications to Secure Hy- drocarbons Waste Disposal In porous media multiple pathways exist between different locations, and flow at a given position has contributions In this presentation we consider a geothermal system and from paths of different length. Considering pore network present a new mathematical model for the geothermal sys- representations of such media, there exist pores which get tem. We view the system in terms of its sub-systems. Lo- bypassed by long tubes. To capture the nonlocal effects cal and asymptotic stability of the model is discussed and due to long bypassing connections, a nonlocal continuum applications to secure hydrocarbons waste disposal. The model is proposed. The model is applied to different porous interesting case of propane is explored. media and the results are compared with Darcy and pore network simulations. Benard O. Nyaare JARAMOGI OGINGA ODINGA UNIVERSITY OF Amir Hossein Delgoshaie SCIENCE AND TECHNOLOGY Institute of Fluid Dynamics, ETH Zurich, Sonneggstrase STUDENT 3, [email protected] Zurich CH-8092, Switzerland [email protected] CP1 Daniel W. Meyer Modeling the Influence of Biosurfactant Adsorp- Institute of Fluid Dynamics tion on Rock Wettability in a Meor Process [email protected] A very general model is presented in the companion work in this congress (Daz-Viera, M., Ortiz-Tapia, A., Hernndez- Hamdi Tchelepi Prez, J., (2015). A flow and transport model in porous Stanford University media for microbial enhanced oil recovery studies. SIAM Energy Resources Engineering Department GS15). Here, is studied the effect of changed biosurfactant [email protected] concentration through adsorption in a rock core, on the residual oil saturation, modeled as a linear function of the Patrick Jenny trapping number, which is in turn an empirical function of Institute of Fluid Dynamics biosurfactant concentration. ETH Zurich [email protected] Arturo Ortiz-Tapia Mexican Petroleum Institute [email protected] CP1 Numerical Methods in Secondary Oil Recovery Martin A. Diaz-Viera INSTITUTO MEXICANO DEL PETROLEO In this talk we present a large time step overlapping grids [email protected] numerical method for hyperbolic conservation laws. The method is based on a finite volume method and has advantages that is relatively inexpensive and easy to imple- CP2 ment. We consider two systems of conservation laws used Duality Based Error Estimator for a Discontinuous in secondary oil recovery modeling multiphase flow of oil, Galerkin Discretization of Advection Problems gas and water, and we present numerical results using the above numerical method. We show that the dual weighted residual method provides an error estimator for a regularized 1D advection equa- Ilija Jegdic tion which converges to the error estimator of the purely Department of Mathematics, University of Houston advective problem under the condition that the primal so- i [email protected] lution in the weak formulation can be tested with the dual solution. Our counter example shows that the weak formulation is not defined if the primal and dual solution have CP1 coinciding discontinuities. Calibration of a Tcat Model for Salt Water Intru- sion Susanne Beckers,Jörn Behrens KlimaCampus, University of Hamburg In this talk we present a novel TCAT model for salt wa- [email protected], ter intrusion. The model is a partial differential algebraic [email protected] equation (PDAE). We discuss the numerical solution of the equations and the calibration of the model against experi- Winnifried Wollner mental data. This is joint work with Deena Giffen, Casey Univeristy of Hamburg 60 GS15 Abstracts

[email protected] medium.

Aboubacar Konate CP2 Phd Student at Institut Fran¸cais du Pétrole A High-Resolution Scheme for Advective-Diffusive [email protected] Transport Modeling on Arbitrary Polyhedral Grids Vivette Girault A high-resolution finite volume scheme for the discretiza- University of Paris VI tion of advection operatorator on arbitrary 3D polyhedral [email protected] grids is presented. The scheme features local linear reconstruction of concentration on mesh elements, which pro- Xavier Claeys vides second order accuracy in smooth regions and front Paris 6 - LJLL capturing. This reconstruction is accomplished using op- [email protected] timization methods, adapted to the problem. The scheme is compared to conventional methods within the existing Guillaume Enchery groundwater flow and transport modeling software. It’s ap- IFPEN plications to complex problems are shown, namely density- [email protected] driven flow and reactive transport modeling. Sylvain Desroziers Ivan Kapyrin IFP Energies Nouvelles Russian Academy of Sciences [email protected] [email protected]

CP2 CP2 Radial Basis Based Spectral Collocation Method Large-Scale 3D Geo-Electromagnetic Modeling for Orr-Sommerfeld Eigenvalue Problem in Fluid with Parallel Adaptive High-Order Finite Elements Dynamics

Electromagnetic methods of geophysics aim at studying the The Orr-Sommerfeld eigenvalue problem decides hydrody- subsurface electrical conductivity distribution, and typi- namic stability in the analysis of parallel fluid flow in an cally require the solution of a large number of problems idealized infinitely long domain. Spectral methods are re- derived from Maxwell’s equations. In this contribution, we ported to be viable tools for numerical solution of a dif- investigate the use of adaptive high-order finite elements ferential equation involving simple domain and smoothly (FEs) to discretize these problems in large-scale parallel defined problems. In this work, we present a spectral col- settings. We present a new scalable algorithm for solving location method on chebyshev grids using multiquadratic the resulting linear systems, based on block-diagonal and radial basis function to obtain derivative approximation for auxiliary-space preconditioning. A particular advantage the numerical solution of Orr-Sommerfeld eigenvalue prob- of our solver is that it can handle arbitrarily high-order lems. FEs on unstructured and non-conforming locally refined meshes. The meshes are refined by using highly efficient Pankaj K. Mishra goal-oriented error estimator. The solver is also algebraic Department of Geology and Geophysics in nature, so it is efficient for a wide range of frequencies, Indian Institute of Technology, Kharagpur boundary conditions, physical sources, and large conduc- [email protected] tivity contrasts. We use 3D magnetotelluric modeling to demonstrate that the adaptive high-order FE discretiza- Sankar K Nath, Amol D Sawant tion with the new solver is beneficial for many relevant Indian Institute of Techology, Kharagpur problems. West Bangal, India 721302 [email protected], [email protected] Tzanio V. Kolev Center for Applied Scientific Computing Lawrence Livermore National Laboratory CP2 [email protected] A High Order Finite Difference Method to Simu- late Wave Propagation in Fluid-Filled Fractures Alexander Grayver ETH Zurich Interface waves along fluid-filled fractures can carry in- [email protected] formation about fracture geometry, which is of interest to oil and gas industry, and volcanologists. To simulate these waves we use summation by parts finite differences CP2 on curvilinear, multiblock grids solving the linear elastic A Multiscale Discontinuous Galerkin Method for wave equation and a linearized approximation of the com- Transport Modeling pressible Navier-Stokes equations. We enforce coupling conditions weakly and investigate accuracy and stiffness We study in this work a multiscale method designed for using eigenspectra calculations. Coupling to quasi-one- convection-difusion problems and based on a Discontinuous dimensional conduits using transfer functions is also dis- Galerkin discretization. Using results of homogenization, cussed. we prove an a priori error estimate in the case where all parameters of the problem are assumed to be periodic. We Ossian Oreilly also present numerical results where the Darcy equation Department of scientific computing is first solved and the multiscale method is then applied uppsala to simulate the transport of a tracer within the porous [email protected] GS15 Abstracts 61

Eric M. Dunham unaccounted physical processes, have a significant influ- Department of Geophysics ence on model forecast accuracy. In this talk we present Stanford University a multi-model ensemble system coupled with an assimila- [email protected] tion algorithm to improve the forecast of the ionosphere- thermosphere environment. The main advantage of our Jan Nordstrom approach is that combining a number of models can help Department of Mathematics, Linköping University mitigate model errors suffered by any one model. A num- SE 581 83 Linköping, Sweden ber of numerical experiments are presented which compare [email protected] the forecast performance of assimilation with single-model and multi-model techniques.

CP3 Humberto C. Godinez Identification of Conductivity by Minimising a Los Alamos National Laboratory Gradient Co-Linearity Mismatch Norm Applied Mathematics and Plasma Physics [email protected] Behold, Let Ω ⊂ IR 2 be bounded by two heteroclinic orbits, Γ1,Γ2 of the ∇u-flow. Then ∇·(c∇u)=0in Sean Elvidge Ω implies c ≡ 0inΩ¯ [Chicone and Gerlach, 1987]. Space Environment and Radio Engineering Group 2 0 Let u ∈C(Ω) ∩C (Ω¯) be known. The (unique) con- University of Birmingham ductivitya ˆ, which complies with ∇·(â∇u)=f,canbe [email protected] identified by minimising with respect to b the norm of ∇a˜[b]×∇u−∇b×∇p under constraints, where ∇·(b∇p)=f anda ˜[b]∂j u := b∂j p, j =1or 2. This is an attempt at jus- CP3 Scarascia tifying the “comparison model’ algorithm [ and Bayesian Emulators in Spatial Inverse Problems Ponzini, 1972], which has seen successful practical applications to inverse hydrogeology ever since. We consider a Bayesian approach to nonlinear inverse prob- Giovani F. Crosta lems in which the unknown quantity (input) is a random Department of Earth- and Environmental Sciences spatial field. The Bayesian approach casts the inverse so- University of Milan Bicocca lution as a posterior probability distribution. The like- Giovanni [email protected] lihood term in the posterior distribution contains the forward simulator, which is complex and non-linear, therefore computationally expensive. We develop an emulator based CP3 approach where the Bayesian multivariate adaptive splines (BMARS) has been used to model unknown functions of Bayesian Inversion for Hydraulic Conductivity at the model inputs. The emulators run almost instanta- Wipp neously hence they are much computationally efficient as We cast the problem of inferring hydraulic conductivity compared to the forward simulators. Data from different from measurements of hydraulic head and transmissivity as sources and scales are also integrated using a Bayesian hier- a Bayesian inverse problem. Using a Metropolis-Hastings archical model. The estimation is carried out using trans- MCMC method to sample from the posterior distribution, dimensional Markov chain Monte Carlo method. Numeri- we construct the CDF of a quantity of interest, the travel cal results are presented by analyzing simulated as well as time of a particle released in the flow. We give numeri- real data from reservoir characterization. cal results for data from the Waste Isolation Pilot Plant (WIPP) in Carlsbad, NM. Anirban Mondal Case Western Reserve University Oliver G. Ernst,Björn Sprungk Department of Mathematics Applied Mathematics and TU Chemnitz Statistics Department of Mathematics [email protected] [email protected], [email protected] CP3 Daniel Rudolf Data Reduction Techniques Applied in Inverse Institute for Mathematics Modeling University of Jena [email protected] The Bayesian inverse modeling techniques uses the likelihood function as an engine for parameter estimation. This Hans-Jörg Starkloff likelihood function is affected by the data dimensionality of Fachgruppe Mathematik the inversion problem. We use a combination of different WSH Zwickau dimensionality reduction methods such as principal com- hans.joerg.starkloff@fh-zwickau.de ponents analysis (PCA), Fast Fourier Transformation and geometric methods for determining the intrinsic dimension for better characterization of spatial random fields applied CP3 in groundwater problems. Multi-Model Ensemble Assimilation for Enhance Model Prediction: Specification of Ionosphere- Carlos A. Osorio-Murillo Thermosphere Environment University California - Berkeley [email protected] The simulation of complex physical phenomena is common- place in many areas of science. A concern is that model Heather Savoy, Yoram Rubin errors and bias, resulting from uncertain parameters and University of California - Berkeley 62 GS15 Abstracts

[email protected], [email protected] Mazen Saad Ecole Centrale de Nantes [email protected] CP3 Constructing the Dynamic Tortuosity Functions from Dynamic Permeability Data at Distinct Fre- CP4 quencies Analysis and Numerical Approximation for Ad- sorption Models Dynamic tortuosity quantifies the effective interaction between solid and viscous fluid in poroelastic materials. It We focus on the structure of an adsorption model as sys- plays an important role in dissipation/dispersion in the tems of conservation laws (multicomponent case for ad- poroelastic wave equations, which have been used to model sorption), with equilibrium and non-equilibrium type non- waves in fluid saturated rocks. However, it is difficult to linearities, where the latter are associated with microscale measure. The recent results on using the dynamic perme- diffusion. We also work with an unusual type isotherm ability, which is easier to measure, at different frequencies called Ideal Adsorbate Solution, which is defined implicitly. to reconstruct the dynamic tortuosity function for materi- For the IAS adsorption system, we show sufficient condi- als with arbitrary pore space geometry will be presented. tions that render the system hyperbolic. We also construct numerical approximations for equilibrium and nonequilib- Miao-Jung Y. Ou rium models. University of Delaware, USA Department of Mathematical Sciences F. Patricia Medina [email protected] Department of Mathematics Oregon State University [email protected] CP4 Evaluate and Analysis of Experimental Data in As- Malgorzata Peszysnka sociated with a Sand Packed Model Using a Nu- Oregon State University merical Method at Polymer Flooding Process to [email protected] Enhanced Oil Recovery

Polymer Flooding as one of the Chemical Enhanced Oil CP4 Recovery (EOR ) plays an important role during EOR pro- Reactive Transport at the Pore-Scale: the Impact cess. Polymer solution with controlling mobility ratio of in- of Flow Field Heterogeneity jected water can recover further percent of Original Oil In Place (OOIP).This study concerns a numerical method to We present a Lagrangian pore-scale method to simulate evaluate obtained results of a sand packed model. Injection carbonate dissolution on 3D micro-CT images of rocks. rate and concentration as two major parameters are fund Particle advection employs a new semi-analytical stream- and better analysis of them can lead to the desired results. line tracing algorithm. Dissolution is controlled by the flux A numerical method in order to evaluate such parameters of particles through the pore-solid interface. Validation is was selected and utilized . Based on experimental data, done using dynamic imaging data. Using rocks of various related equation from numerical method are constructed degrees of heterogeneity, we show that dissolution is con- and after creating equations, resulted for reach to further trolled by the relative importance of advection, diffusion oil recovery polymer solution should be firstly injected at and reaction, and also by the flow field heterogeneity (e.g high rate and then be flooded with low rate of injection. hydraulic tortuosity). As well as, polymer solution should be injected with low concentration and then high concentration respectively. Joao P. Pereira Nunes Imperial College London Omid Arjmand [email protected] Department of Chemical Engineering, Islamic Azad University, Branko Bijeljic [email protected] Department of Earth Science and Engineering Imperial College London CP4 [email protected] Weak Solutions to a Nonlinear Degenerate Equa- tion Arising in Chemotaxis Or Porous Media Martin Blunt Dept. Earth Science and Engineering We are interested in the mathematical analysis of a general Imperial College London degenerate nonlinear parabolic equation modeling the sat- [email protected] uration of one phase in a multiphase ow in porous media. The equation presents degenerate terms of order 0 and of order 1 to handle with the pressure term. The degeneracy CP4 of the dissipative term occurs in the region where one of Numerical Aspects of Equilibrium Calculations in the phases is missing and the dissipative fonction vanishes Tight Oil Formations at two points, we obtain solutions in a weaker sense compared to the classical formulation. Therefore, a degenerate Despite the large potential of unconventional resources, weighted formulation is introduced taking into account the many unknowns still exist regarding the physics of mul- degeneracy of the dissipative term. tiphase flow in these settings. These include accurate representation of phase equilibrium in tight formations and ef- Moustafa Ibrahim fective implementation of these models in simulation tools. University of Nantes In this work, we analyze the numerical aspects of including [email protected] capillarity phenomena in VLE calculations in an effort to GS15 Abstracts 63

arrive at a robust and efficient algorithm for compositional Multiscale Simulation simulation of unconventional reservoirs. We consider multiscale methods in which microscale and Marjan Sherafati macroscale models are explicitly coupled in a single hy- PhD candidate at University of Southern California brid multiscale simulation. A limited number of hybrid [email protected] multiscale simulations of biogeochemical earth systems exist based on customized approaches for model coupling. Kristian Jessen We describe a generalized approach to hierarchical model University of Southern California coupling designed for high-performance computational sys- [email protected] tems and an example implementation based on coupling two models with different representations of physics and biogeochemistry at two distinct scales. CP4 Timothy D. Scheibe, Xiaofan Yang High-Dimensional Visualization of Flow Response Pacific Northwest National Laboratory from Ensemble of Exhaustively Sampled Reservoir [email protected], [email protected] Models

Ensemble-based reservoir simulation has become increas- CP5 ingly feasible in recent years due to the computational Model-Order Reduction for Subsurface Flow Using advancement. One of the criticisms is: how can we in- a Trajectory Piecewise Quadratic Approach terpret such numerous simulation results? Big data analytics is the key to solving the problem. We propose a A trajectory piecewise quadratic (TPWQ) representation new high-dimensional visualization method to rapidly in- of nonlinear effects is combined with proper orthogonal terpret flow response from large ensemble of reservoir mod- decomposition to provide a reduced-order subsurface flow els, which consists of more than thousands, exhaustively model. The method enables the fast computation of ap- sampled from high-dimensional space spanned by geologi- proximate pressure and saturation states for new well set- cal uncertainty parameters. tings in oil-water problems. Results demonstrate that TPWQ can be used as an error indicator for trajectory Satomi Suzuki,DaveStern piecewise linear (TPWL) models. The incorporation of ExxonMobil Upstream Research TPWQ into an efficient production optimization procedure [email protected], is also illustrated. [email protected] Sumeet Trehan Stanford University Tom Manzocchi Department of Energy Resources Engineering University College Dublin [email protected] [email protected] Louis Durlofsky CP5 Stanford University [email protected] Upscaling Interpretation of Nonlocal Fields, Gra- dients and Divergences CP5 In this talk, the interrelation between weight-function up- Upscaling Barrier Systems and Calculating Five- scaling (measurement) and the definition of various non- Spot and Line Drive Well Rates Using Theta Func- local operators will be explored. Let f = f ∗ g where tions and Elliptic Integrals f ∗ g is the convolution product which represents the effect of upscaling via an instrument (defined by g) on a Using theta functions and elliptic integrals we derive a field variable f and its localized counterpart. Nonlocal novel practical formula for the effective vertical absolute field variables are defined and employed for upscaling. It permeability for a general class of generic barrier systems. will be shown via Fourier transform, for judicious choice The results can also be applied for deriving explicit formu- of the arbitrary function ρ,thatGρf(x)=∇f(x)where las for single phase production rates in wells in five spot Gρf(x) is the nonlocal gradient of f and ∇f is the classical patterns and for line drive patterns. The analysis also in- gradient. Upscaled representations for the adjoint of Gρ volves the so-called nome which is related to modular func- and the nonlocal divergence are also obtained. A nonlocal tions and the monster group. self-diffusion equation is upscaled and written in terms of nonlocal operators. Dag Wessel-Berg SINTEF Petroleum Moongyu Park [email protected] Purdue University [email protected] CP6 John H. Cushman Optimal Compressive-Sampling Measurement Ma- Center for Applied Mathematics trices for Seismic Acquisition Purdue University We discuss and compare various applications of compres- [email protected] sive sampling in seismic data acquisition. The sampling scheme directly impacts the mutual coherence of the resulting dictionary, which is in turn crucial to a successful CP5 recovery of sparse signals. Based on a Fourier signal rep- A General Framework for Hierarchical Hybrid resentation, we show that the maximum mutual coherency 64 GS15 Abstracts

of the dictionary can be minimized by a smart design of cesses and show how to convert the continuous frequency the sampling scheme. This can be physically interpreted problem to a discrete frequency approximation that is com- as minimizing the maximum aliasing power. putationally tractable.

Xander Campman Yenming Lai Shell Global Solutions University of Texas [email protected] ICES [email protected] Zijian Tang, Boris Kuvshinov Shell Global Solutions International B.V. Radu Balan [email protected], [email protected] University of Maryland [email protected]

CP6 Estimation of Spatial Uncertainties of Geophysical CP6 Tomographic Models Constrained Optimization Framework for 1D Seis- mic Wave Propagation Problems Models derived from geophysical inversion (e.g., seismic tomography) often lack a clear indication of the associated We create a unified algorithmic framework that accommo- spatial uncertainties, which are as important for the in- dates several constrained optimization schemes for solving terpretation as the models themselves. This study inves- one-dimensional seismic wave propagation problems. We tigates how quantitative estimates of spatial uncertainties use a PDE-constrained optimization formulation where we (e.g., in meters) can be obtained by analysis of equivalent introduce inequality constraints over the inversion param- models using a posteriori covariance analysis. We focus on eter, e.g. the material properties. Our goals are to pro- efficiency and flexibility for deriving structure related un- vide a unified affine invariant approach, to improve a line- certainties that also account for the directionality of the search step computation, and ultimately to identify robust spatial uncertainties. schemes that incorporate inequality constraints for solving the inverse problem with interior-point, and active set Peder Eliasson methods. SINTEF, Norway [email protected] Anibal Sosa Universidad Icesi Michael Jordan [email protected] SINTEF Petroleum Research Norway Carsten Burstedde [email protected] Universität Bonn [email protected]

CP6 Aaron A. Velasco Optimal Experimental Design for Geophysical University of Texas at El Paso Imaging of Flow in Porous Media Geological Sciences [email protected] Designing experiments for imaging fluid flow requires both the integration of the dynamical system describing the flow and the geophysical imaging technique. In this talk we ex- CP6 plore optimal experimental design methods for such prob- Study of Torsional Wave in the Crustal Layer with lems, and demonstrate the applicability of the techniques Varying Inhomogeneity for the problem of imaging subsurface flow using seismic methods. The study deals with the propagation of torsional surface waves in a homogeneous crustal layer over a transversely Jennifer Fohring isotropic layer over a gravitating dry sandy Gibson half Faculty of Science space under the influence of initial stress. In the isotropic UBC layer the directional rigidity as well as the density varies [email protected] exponentially. In the homogeneous crustal layer rigidity and density remains constant. The dispersion equation has Eldad Haber been obtained in the closed form and the results have been Department of Mathematics shown graphically. The University of British Columbia [email protected] Sumit K. Vishwakarma Indian School of Mines, Dhanbad, Jharkhand, India-826004 CP6 [email protected] Optimal Space-Time-Frequency Design of Micro- phone Networks CP7 We use an array of microphones to extract a single source The Impact of Correlated Observational Errors in out of a multi-source, multi-path environment. Our convex High-Resolution Atmospheric Data Assimilation optimization technique not only chooses D microphones out of N possible choices but also designs the taps of the The fast-growing volume of high-resolution atmospheric multirate filterbanks that process each of the D outputs. measurements has prompted the need for modeling cor- We model our sources as random wide sense stationary pro- related observational errors in atmospheric data assimila- GS15 Abstracts 65

tion systems. An adjoint-based error covariance sensitivity [email protected] approach is formulated to identify high-impact error correlation structures and provide a priori estimates to forecast error reduction. Mathematical and computational aspects CP7 are presented in four-dimensional variational data assim- A Semi-Implicit, Semi-Lagrangian Dg Framework ilation. The forecast impact of spatial and inter-channel for Adaptive Numerical Weather Prediction error correlations is analyzed for hyperspectral satellite instruments assimilated in Navy’s NAVDAS-AR/NAVGEM. We present an adaptive discretization approach for NWP model equations, which combines the semi-Lagrangian technique with a TR-BDF2 semi-implicit time discretiza- Dacian N. Daescu tion and with a DG spatial discretization with (arbitrarily Portland State University high) variable and dynamically adaptive element degree. Department of Mathematics and Statistics The resulting method has full second order accuracy in [email protected] time, is unconditionally stable and can eﬀectively adapt at runtime the number of dof employed in each element, in Rolf Langland order to balance accuracy and computational cost. Naval Research Laboratory Monterey, CA Giovanni Tumolo [email protected] ICTP, Trieste, Italy [email protected]

CP7 Luca Bonaventura Improving Numerical Stability of the Non- Politecnico di Milano Hydrostatic Global Environmental Multiscale At- MOX, Dipartimento di Matematica F. Brioschi mospheric Model for High Resolution Forecasting [email protected]

Improving numerical stability of atmospheric models for CP8 high resolution forecasting applications, particularly over complex orography, may necessitate a combination of ad- Towards Improved Characterization of Geochemi- justments to the existing models. Several modifications cal Hot Moments: A Combined Wavelet-Entropy within the non-hydrostatic Global Environmental Multi- Approach scale model, ranging from adjustments in spatiotemporal discretizations to changes in the hybrid vertical coordinate A novel wavelet-entropy technique is used to investigate system, are currently being investigated at Environment hot moments of geochemical activity in groundwater and Canada to ascertain their implications on the overall nu- seeps in the Rifle field site, CO. Wavelet analysis was merical stability of the model. Pertinent results will be conducted along three different transects within the Rifle presented at the conference. floodplain and entropy analysis was based on site characteristics. Hot moments were associated with seasonal and Syed Zahid Husain, Claude Girard annual hydrologic variations along the contaminated and Meteorological Research Division seep transects, respectively. In contrast, a different fre- Environment Canada quency ( 3 months) constituted hot moments in a naturally [email protected], [email protected] reduced zone. Bhavna Arora, Dipankar Dwivedi, Susan Hubbard, Carl Steefel, Kenneth Williams CP7 Lawrence Berkeley National Laboratory Advancing the All-Scale Eulag Model Towards [email protected], [email protected], [email protected], cis- Energy-Efficient Exa-Scale Simulation of Atmo- [email protected], [email protected] spheric Flows.

We investigate complementary role and the relative com- CP8 putational performance on classical and modern super- An Eulerian Strategy for Disperse Phase Flows computer architectures of the consistent semi-implicit soundproof/compressible model formulation applied to A new method is introduced for the transport of a disperse the archetype weather problems using the all-scale non- phase (aerosol, particle-laden ﬂow and/or spray). It is ro- oscillatory forward-in-time EULAG model. The consistent bust and accurate and allows adaptive use of the many semi-implicit integrators of the compressible and sound- descriptions available for disperse phases (population bal- proof PDEs share the two algorithmic engines: the non- ance, Monte-Carlo sampling, moments, and sectional dis- oscillatory MPDATA advection schemes and the precon- cretization) as well as their full coupling together. A case is ditioned non-symmetric Generalized Conjugate Residual computed with agglomeration, as handled by a high-order- solver with newly developed parallel alternate direction im- in-size sectional approach. plicit preconditioners. Francois Doisneau Zbigniew P. Piotrowski, Andrzej Wyszogrodzki Combustion Research Facility Institute of Meteorology and Water Management Sandia National Laboratories [email protected], [email protected] [email protected]

Piotr Smolarkiewicz CP8 2European Centre for Medium-Range Weather Forecasts Unidirectional Flow with Temperature-Dependent, Reading, United Kingdom Shear Thinning Viscosity and Biases in Estimation 66 GS15 Abstracts

of Lower Crustal Viscosity of the most efficient and scalable preconditioners. This is achieved by either subtle aggregation heuristics that honor Crustal deformation is routinely used to infer the viscosity the physical properties of the problem or specialized multi- of the lower crust. Inferences using cumulative deforma- grid cycles, called either Krylov- or AMLI-cycle. In this tion over million year time scales are typically lower than talk we will present a CPR-like preconditioner using the those estimated from decadal scale deformation. Models of former AMG method for the pressure system, and show its lower crustal flow most often assume Newtonian viscosity scalability for reservoir simulations. in a homogeneous lower crustal channel. Using a solution for Poiseuille flow with temperature-dependent, non-linear Markus Blatt viscosity, appropriate for the the lower crust, we explore Interdisciplinary Center for Scientific Computing the biases in viscosity estimates using simplified models. University Heidelberg [email protected] Eric Hetland University of Michigan [email protected] CP9 Analysis of the Hybrid Upwinding for Fully- Semechah Lui Implicit Simulation of Multiphase Flow with Grav- California Institute of Technology ity [email protected] Accurate description of the dynamics in the subsurface requires solving the PDEs that represent the conservation CP8 laws of multiphase flow in porous media. In these PDEs, Prediction of Water Flow in Irrigation Network by the flow is coupled to the highly nonlinear transport of Using Numerical Techniques species. We present a numerical scheme honoring this coupling that combines the Fully-Implicit Method with a hy- Prediction of water flow in rivers and canals and sediment brid upwinding of the flux across an interface between two movement can be carried out with sufficient accuracy us- control volumes. We obtain a monotone and differentiable ing numerical models. In this work, we will use approxi- numerical flux resulting in fast convergence of Newton- mate techniques for water flow calculations and sediment based nonlinear solvers, which reduces the computational transportation for a full network of natural and constructed cost of a simulation. channels of Pakistan. Reference: Lee, S. H., Efendiev, Y., Tchelepi, H. A., [2015], Hybrid Upwind Discretization of Nonlinear Multi- Waseem A. Khan phase Flow with Gravity, submitted to Advances in Water Sukkur Institute of Business Administration Resources. [email protected] Francois P. Hamon Stanford University CP8 [email protected] On Various Kriging Predictors for Geoid Densifi- cation: a Comparison Hamdi Tchelepi Stanford University For geoid densification, traditionally the method of Least- Energy Resources Engineering Department Squares Collocation (LSC) has been heavily used which [email protected] requires the knowledge of a suitable covariance function. Interestingly, it could be shown that equivalent results can be achieved by means of Kriging, a method that is usually CP9 based on the semi-variogram or, perhaps, the homeogram. Componentwise Time-Stepping for Radially Sym- This equivalence, however, turns out to be perfect only as metric Pde long as the spatial ”coherency functions” are not estimated separately. In this study, the influence of such estimates on Time-dependent PDE with radially symmetric solutions a variety of empirical Kriging predictors (Simple Kriging, are of particular interest in reservoir simulation, where the Ordinary Kriging, Optimal Biased Kriging) is analyzed, center of the domain represents a well. This talk presents a and some conclusions will be drawn. new approach to such PDE, in which stiffness is overcome through individualized approximation of each component Tae-Suk Bae of the solution, in a basis of orthogonal polynomials. The Sejong University proposed method represents an extension of Krylov sub- The Ohio State University space spectral (KSS) methods, which overcome stiffness [email protected] for PDE on rectangular domains, to circular domains.

Burkhard Schaﬀrin James V. Lambers, Megan Richardson School of Earth Sciences University of Southern Mississippi The Ohio State University Department of Mathematics aschaﬀ[email protected] [email protected], [email protected]

CP9 A Parallel Cpr-Like Preconditioner Based on Non- CP9 Smoothed Aggregation Amg Modiﬁed Sequential Fully Implicit Scheme for Compositional Flow Simulation For ﬂow in porous media non-smoothed algebraic multigrid (AMG) based on aggregation has turned out to be one The Fully Implicit Method (FIM) is widely employed for GS15 Abstracts 67

reservoir simulation. However, in the Multi-Scale Finite- Friction Volume approach, sequential strategies are used to couple flow and transport. For problems with tightly coupled Section: 4. Lithosphere and pedosphere modeling Subsec- nonlinear interactions between flow and transport, these tion: d. Plate tectonics and earth dynamics We present approaches may require many more Newton iterations, here a novel algorithm for elastodynamic problems of rate- and/or smaller time steps compared with FIM. We ana- and-state friction, along with first results on existence lyzed the nonlinear coupling between flow and transport and uniqueness of solutions as well as convergence of the for multiphase, multi-component systems that involve sig- scheme. At its center lies a rate-and-state decoupling fixed- nificant compressibility effects and interphase mass transfer point iteration, the stability of which is demonstrated by and we propose a modified scheme. We show across a wide the example of a two-dimensional laboratory-scale subduc- parameter range that this new algorithm has convergence tion zone simulation, which is shown to be in good agree- properties consistently better than usual ones. Black-oil ment with laboratory measurements. As an outlook, we and compositional systems in depletion and compression present preliminary three-dimensional results. settings are presented and discussed. Elias Pipping Arthur Moncorge Free University of Berlin TOTAL Mathematical Institute [email protected] [email protected]

Patrick Jenny Ralf Kornhuber Institute of Fluid Dynamics FU Berlin ETH Zurich Fachbereich Mathematik und Informatik [email protected] [email protected]

Hamdi Tchelepi Matthias Rosenau, Onno Oncken Stanford University Helmholtz Centre Potsdam Energy Resources Engineering Department [email protected], onno.oncken@gfz- [email protected] potsdam.de

CP9 CP10 Time Stepping for Advection Dominated Methane Hydrate Models with Signiﬁcant Salinity Depen- Multiple Steady Solutions of a Model Subpolar dence Ocean Forced by Localized Wind

Comprehensive methane hydrate models account for A simple model of the subpolar North Atlantic can produce methane and salt concentration as well as for variable pres- closed, recirculating cells in the Irminger and Labrador sure and temperature, and their most difficult part is a ro- Seas, consistent with float data. But it can also produce bust phase behavior solver coupled to transport. If temper- an inertial solution with swift, open currents that do no ature is assumed known, one can consider several variants recirculate. We explore this transition in a periodic chan- of time-stepping for the resulting reduced phase behavior nel to isolate the dynamics at work. Weak forcing leads model. In the talk we discuss convergence and accuracy to the classic beta plume, while strong forcing causes the of the numerical scheme for the case when advection is circulation to strengthen and elongate. dominant; this is assessed using recently derived analytical solution as well as experimental data from Ulleung basin. Alexander Fuller, Thomas Haine Johns Hopkins University Malgorzata Peszynska [email protected], [email protected] Department of Mathematics Oregon State University [email protected] CP10 Offshore and Coastal Wind Resource Characteri- Wei-Li Hong sation for Mexican Waters Center of Arctic Gas Hydrate Arctic University of Norway Preliminary results for an offshore and coastal wind en- [email protected] ergy atlas for Mexico are presented, based on statistical wind energy computations using upscale climate data, and Ralph Showalter, F. Patricia Medina meteorological station wind data from coastal locations, Department of Mathematics both extrapolated to a height of 90m above ground level. Oregon State University Some study case scenarios, at particular locations in the [email protected], Gulf of California and the Mexican North-Eastern Pacific, [email protected] will also be discussed.

Marta Torres Vanesa Magar College of Earth, Ocean, and Atmospheric Sciences Centro de Investigaci´on en Ciencias y Educaci´on Superior Oregon State University de [email protected] Ensenada (CICESE) [email protected]

CP9 Markus Gross, Cuauhtemoc Turrent Subduction Zone Simulations with Rate-and-State CICESE 68 GS15 Abstracts

[email protected], [email protected] Helmut-Schmidt-University University of the Federal Armed Forces Hamburg [email protected] CP10 A New Well-Posed Vorticity Divergence Formula- tion of the Shallow Water Equations MS1 A completely new vorticity-divergence formulation of the A Multipoint Flux Mixed Finite Element Method two-dimensional shallow water equations including bound- with Non-Matching Hexahedral Grids ary conditions is derived. The new formulation is necessary since the conventional one does not lead to a well-posed We propose and analyze several methods for extending initial boundary value problem for limited area modelling. the multipoint flux mixed finite element method to al- The new vorticity-divergence formulation include four de- low efficient simulations on multiblock domains with non- pendent variables instead of three, and require more equa- matching distorted hexahedral grids. Numerical tech- tions and boundary conditions than the conventional for- niques are developed based on the enhanced velocity finite mulation. On the other hand, it forms a symmetrizable element method and the local flux mimetic finite difference hyperbolic set of equations with well defined boundary con- method. We develop a reasonable assumption on geometry, ditions that leads to a well-posed problem with a bounded discuss implementation issues, and give several interesting energy. numerical results.

Jan Nordstrom Benjamin Ganis Department of Mathematics, Link¨oping University The University of Texas at Austin SE 581 83 Link¨oping, Sweden Center for Subsurface Modeling [email protected] [email protected]

Sarmad Ghader Mary F. Wheeler Institute of Geophysics, University of Tehran Center for Subsurface Modeling, ICES Tehran, Iran University of Texas at Austin [email protected] [email protected]

CP10 Ivan Yotov Univeristy of Pittsburgh Simulation of Multiscale and Multiphysics Coastal Department of Mathematics Ocean Flows by Integration of Geophysical Fluid [email protected] Dynamics and Fully 3D Fluid Dynamics Models

Integration of geophysical fluid dynamics and fully 3D fluid dynamics models is proposed to predict multi- MS1 scale/multiphysics coastal ocean flows. This integration is Solving the Nonlinear and Nonstationary Richards able to simulate distinct flow phenomena at spatial scales Equation with Adaptive Domain Decomposition O (1) m – O (10,000) km with high fidelity. The method- and Subcycling ology is discussed, and its unprecedented capabilities are illustrated by applications to emerging problems such as Modeling the transport processes in a vadose zone plays impact of storm surge on coastal infrastructure that are an important role for a wide range of environmental issues. beyond the reach of other existing models. Water flow is governed by Richards equation. Certain ma- Hansong Tang,KeQu terials with dominantly uniform pore sizes (e.g. coarse- Dept. of Civil Eng., City College of NewYork, CUNY grained materials) can exhibit steep gradients of constitu- [email protected], [email protected] tive functions. Numerical approximation of the Richards equation requires sequential solutions of systems of linear equations arising from discretization and linearization of Anil Kumar Agrawal the problem. Typically, one has to solve huge systems of Dept. of Civil Eng., City College, City Univ. of NewYork linear equations to obtain only a few updates of solution. [email protected] Then the local updates typically represent local disturbances (e.g. moving wetting front). A method for adaptive MS1 subdomain split, that enables sequential solutions of subdomains covering the local disturbances only is currently Variational Space-Time Approximation of Trans- under an intense development. The method was already port Processes and Iterative Solver labeled as dd-adaptivity. Our recent presentation will focus on multi-time-step improvement of our dd-adaptivity Numerical simulation of time dependent transport is desir- algorithm. able in several fields of technology. While the discretization in space involves significant challenges, temporal approximations have received little interest and have often been Michal Kuraz limited to low order methods. We present two families of Czech University of Life Sciences Prague continuous and discontinuous variational time discretiza- Department of Water Resources and Environmental tion schemes that are combined with mixed finite element Modeling approximations in space. Error estimates and numerical [email protected] studies are presented. The solver technology for the arising systems is addressed further. Petr Mayer Czech Technical University in Prague Markus Bause Department of Mathematics GS15 Abstracts 69

[email protected] based on the equilibrated flux reconstruction which can distinguish the different error components. Our estimate gives a guaranteed upper bound on the overall error as well as MS1 a polynomial-degree-robust local efficiency. Some numer- Fully-Implicit Nonlinear Flux Approximation for ical examples showcase the performance of our adaptive Two-Phase Flow in Porous Media strategy.

Classical linear Finite Volume methods do not fulfill prop- Martin Cermák erties like monotonicity or extremum principles for general VSB-Technical University of Ostrava meshes or anisotropic behavior. Therefore, during the last [email protected] decade different authors developed nonlinear Finite Vol- ume methods satisfying discrete extremum principles. We Frédéric Hecht will give a detailed comparison between linear and non- University Pierre et Marie Curie linear methods combined with different solution strategies, [email protected] such as the fully-implicit or the adaptive-implicit. A special focus is set to the applicability for complex flow processes in porous media. Zuqi Tang INRIA, Paris, France Martin Schneider [email protected] University of Stuttgart, Germany [email protected] Martin Vohral´ık INRIA Paris-Rocquencourt Rainer Helmig [email protected] IWS, University of Stuttgart, Germany Dept. of Hydromechanics [email protected] MS2 Full Waveform Inversion Without Source Estima- Bernd Flemisch tion University of Stuttgart, Germany bernd.fl[email protected] Full waveform inversion attempts to estimate elastic parameters of the subsurface by fitting synthetic data to real seismic data. Usually the source time signature is unknown MS1 and is estimated by the inversion scheme. We use a simple Adaptive Multistep Time Discretization and Lin- finite-difference modeling scheme to compute the downgo- earization Based on a Posteriori Estimates for the ing source wavefield directly from two-component streamer Richards Equation. dataandemploythiswavefieldinthefullwaveformfor- ward modeling. This removes the need for simultaneous We derive a posteriori error estimates based on the dual estimation of elastic parameters and source signature. norm of the residual of the Richards equation. The error is decomposed into space, time, and linearization terms. Borge Arntsen Error estimators are computed with reconstructions espe- Norwegian University of Science and Technology cially designed for a multistep Discrete Duality Finite Vol- [email protected] ume scheme. We stop the fixed-point iterations when the linearization error becomes negligible, and we choose the Uno B. Vaaland time step to balance the time and space errors. Results are Norwegian University of Science and Technology, Norway presented to several test cases. [email protected] Pierre Sochala BRGM Espen Raknes, Wiktor Weibull [email protected] Norwegian University of Science and technology [email protected], [email protected] Vincent Baron UniversitédeNantes Laboratoire de Mathématiques Jean Leray MS2 [email protected] Block-Diagonal Approximation of the Hessian for Multi-Parameter FWI Yves Coudière INRIA Bordeaux Sud-Ouest, équipe CARMEN In multi-parameter waveform the trade-off between pa- 200, avenue de la vieille tour, 33405 Talence, France rameters is sub-surface point dependent due to the lim- [email protected] ited acquisition aperture. The estimation of the radiation patterns of each model parameter is challenging in wave- equation approach because it requires the knowledge of the MS1 diffraction angles. We propose to extend the diagonal ap- An Adaptive Inexact Uzawa Algorithm Based on proximation of the Hessian of the least-square misfit by a Polynomial-Degree-Robust a Posteriori Estimates block-diagonal approximation. We shall discuss an efficient for the Stokes Problem implementation with random pulse excitations to compute simultaneously the receiver wavefields. We are interested in designing an adaptive inexact Uzawa algorithm applied to the linear Stokes problem solved by Albert Deuzeman all standard conforming and conforming stabilized finite Shell Global Solutions element method. We present an a posteriori error estimate [email protected] 70 GS15 Abstracts

Ren´e-douard Plessix [email protected] Shell Global Solutions International [email protected] MS2

MS2 Data Conditioning and Model Conditioning to Ad- dress Factors of 10x with FWI Multi-Scale Inversion of Subsurface Velocity Mod- els Using Cartoon-Texture Decomposition Although data conditioning and model conditioning are conceptually mundane aspects of inversion, they can in- We propose a multiscale formulation of full-waveform influence inversion efficiency and effectiveness by a factor of version (FWI) that is similar to image decomposition into 10x. They are hard to do well, they often involve craft and a cartoon and texture used in Image Processing. The experience, and they often need to be customized to each inversion problem is formulated as unconstrained multi- individual data application. It is probably appropriate to norm optimization and solved using Bregman iterations consider this conditioning on the experimental side of geo- and gradient-projection methods. We demonstrate the pro- physics. There is industry need for academia to investigate posed model decomposition approach by recovering low this mundane, experimental side of applied geophysics. and high-wavenumber subsurface velocity model components from noisy data, and discuss the effect of noise on the feasibility and accuracy of multiscale inversion. Christof Stork ION Geophysical Musa Maharramov [email protected] Stanford University [email protected] Andreas Rueger Landmark Biondo Biondi [email protected] Geophysics Department Stanford University [email protected] MS3 Consider Parsimony in Fault and Fissure Modeling for Land Subsidence Investigations MS2 Land Elastic Waveform Inversion for Seismic Ve- Parsimony should be a key consideration when develop- locity Model Building ing numerical models to simulate fault behavior in coupled poroelastic and fluid flow aquifer systems. Parsimony Surface waves in land seismic data complicate the retrieval is dictated by three important factors: (1) objective, (2) of the (compressional) velocity long-wavelengths. With scale, and (3) observations. In the investigation we con- acoustic waveform tomography we remove them in the in- sider a fault-zone case in which both parsimony is used verse problem. With large elastic parameters, the low- (traditional continuum poromechanics) along with more frequency first event is not always a pure acoustic one due complex cohesive zone fault modeling and compare three- to tuning effects. In this waveform tomography context, we dimensional surface displacements and water levels in both then propose an elastic waveform inversion with a modi- modeling approaches. fied surface boundary condition to avoid generating surface waves in the modeling. In this presentation, we will discuss Thomas Burbey the relevance and limitations of this approach. Virginia Tech [email protected] Rene-Edouard Plessix, Carlos Perez Solano Shell Global Solutions International [email protected], [email protected] MS3 Accuracy and Robustness of the Lagrangian Ap- MS2 proach for the Numerical Simulation of Faults Waveform Inversion of Seismic Data Stress variations induced by gas/oil production may ac- The earth physics of seismic waves is modeled with acous- tivate pre-existing regional faults. To predict seismicity tic and elastic equations. A new method is called IDWI, consequences, it is important to simulate fault mechanics for iterative direct waveform inversion is proposed. The in the actual geological setting. Faults yield discontinuity current full wave form methods have limitations; in the in the displacement field that finite elements cannot ad- use low frequency data, the non-linearity of the objective dress. Interface finite elements are used to simulate the functions, and computational expense. Demonstrations of fault behaviour. A Lagrangian approach has been devel- synthetic velocity models data results and real field data oped to enforce contact condition. It is proved that the examples are presented illustrating the usefulness of this Lagrangian approach is more robust than the Penalty ap- new method. proach.

Changsoo Shin Andrea Franceschini Seoul National University University of Padova [email protected] [email protected]

Ralph P. Bording Carlo Janna, Massimiliano Ferronato Alabama A&M University Dept. ICEA - University of Padova GS15 Abstracts 71

[email protected], [email protected] tial for induced seismicity from reservoir ﬂuid injection and production.

MS3 Ruben Juanes, Birendra Jha Computational Framework for Unstructured Dis- MIT crete Fracture Models with Application to Oil Re- Civil and Environmental Engineering covery [email protected], [email protected]

This work focuses on a numerical method for solving the coupled flow and geomechanics for large scale fractured MS3 subsurface formations. We present a formulation that ex- A 3-Dimensional Model for the Simulation of Hy- tends the Discrete Fracture Model typically used for flow draulic Fracturing and transport problems. A mixed formulation combining continuous Galerkin Finite Elements and Finite Volumes is Optimizing the hydraulic fracturing process requires under- developed. The set of coupled nonlinear equations is solved standing on the fracture process in relation with the poro- by a fully coupled method. The framework is fully inte- mechanical properties of the rock formation. In this con- grated within the multi-phase flow simulator AD-GPRS. tribution we will present a 3 dimensional partition-of-unity based model for hydraulic fracturing in saturated porous rocks. The position of the fracture surface is represented Timur T. Garipov by two evolving level set functions. The performance of the Department of Energy Resources Engineering, model will be demonstrated by the analysis of the propa- Stanford University gation of hydraulic fracture planes. [email protected] Ernst Remij,JorisRemmers,JacquesHuyghe,David Mohammad Karimi-Fard Smeulders Stanford Eindhoven University of Technology [email protected] [email protected], [email protected], [email protected], [email protected] Hamdi Tchelepi Stanford University MS3 Energy Resources Engineering Department [email protected] Coupled Reservoir and Geomechanical Numerical Modeling of Water Injection into a Fractured For- mation MS3 Computational Modeling of Coupled Multiphase Optimization of fracturing operations in well completion Flow and Geomechanics to Study Fault Slip and for oil and gas, geothermal and other operations requires Induced Seismicity modeling of the complex mechanics of the dynamic shear- induced fracture network and the resulting enhanced per- The coupling between subsurface flow and geomechanical meability region. We discuss and contrast several ap- deformation is critical in the assessment of the environmen- proaches to model the problem. Rigorous methods, based tal impacts of groundwater use, underground liquid waste on theory of joints and equivalent media are described for disposal, geologic storage of carbon dioxide, and exploita- both static and dynamic fracture systems, and compared tion of shale gas reserves. In particular, seismicity induced with a simple approach using empirical functions for mod- by fluid injection and withdrawal has emerged as a central ifying both mechanical and flow properties of the failed element of the scientific discussion around subsurface tech- media. nologies that tap into water and energy resources. Here we present a new computational approach to model cou- A . (Tony) Settari pled multiphase flow and geomechanics of faulted reser- University of Calgary voirs. We represent faults as surfaces embedded in a three- [email protected] dimensional medium by using zero-thickness interface elements to accurately model fault slip under dynamically Mohammad Nassir evolving fluid pressure and fault strength. We incorporate Taurus Reservoir Solution the effect of fluid pressures from multiphase flow in the me- [email protected] chanical stability of faults and employ a rigorous formulation of nonlinear multiphase geomechanics that is capable of handling strong capillary effects. We develop a numeri- MS4 cal simulation tool by coupling a multiphase flow simulator General Curvilinear Ocean Model Application: with a mechanics simulator, using the unconditionally sta- Completely Three-Dimensional Modeling of San ble fixed-stress scheme for the sequential solution of two- Diego Bay Hydrodynamics way coupling between flow and geomechanics. We validate our modeling approach using several synthetic, but real- The General Curvilinear Ocean Model (GCOM) is unique istic, test cases that illustrate the onset and evolution of in its ability to solve non-hydrostatic momentum equations earthquakes from fluid injection and withdrawal. We also utilizing completely three-dimensional curvilinear grids. present the application of the coupled flow-geomechanics GCOM is designed to work at super-high resolutions (tens simulation technology to the post mortem analysis of two of meters) on problems resolving strong current forces act- earthquake sequences: (1) the Mw=5.1, May 2011 Lorca ing on complex bathymetry near the coastline. These prob- earthquake in south-east Spain, to investigate the possibil- lems include turbulence from flow through channels and ity that the earthquake was induced by groundwater ex- curved boundaries, river and estuary flows, and how bot- traction; and (2) the Mw=5.8, May 2012 earthquake in tom surface rugosity affects current flow. The model has the Cavone oilfield in northern Italy, to assess the poten- shown successful results in idealized simulations, this pre- 72 GS15 Abstracts

sentation details model application in studying the hydro- [email protected] dynamics of San Diego Bay, California. The entrance channel to San Diego Bay is unique in its use as a conduit for Isabel Ramirez naval submarines, this lends itself well to application for Centro de Investigacion y Educacion Superior de the GCOM fully three-dimensional curvilinear approach. Ensenada Speciﬁcally, estimates of tidal ﬂow, temperature, salinity, [email protected] and current velocity at small scales within the bay are nested with Regional Ocean Model System output. Martin Verlaan Randy Bucciarelli Deltares, Marine and Coastal Systems. Delft, The Computational Science Research Center Netherlands San Diego State University [email protected] [email protected] Jose Castillo Computational Science Research Center MS4 San Diego State University Nesting Nonhydrostatic UCOAM within Hydro- [email protected] static ROMS

The Regional Ocean Modeling System (ROMS) is a hy- MS4 drostatic free-surface ocean model ideally suited to simu- Merging Tsunamis and Resulting Impact on late mesoscale to basin-scale ocean processes. The Uni- Coastal Regions fied Curvilinear Ocean Atmosphere Model (UCOAM) is a nonhydrostatic large eddy simulation (LES) model de- Tsunamis often severely devastate some coastal areas while signed specifically for high-resolution simulations. In this leaving others with little damage. This unpredictable sit- research, a hybrid model is developed that nests a fine-grid uation has been a major challenge for accurate and timely UCOAM model within a coarser-grid ROMS. The hybrid tsunami forecasting for evacuating coastal communities. model is tested in idealized flow over a seamount. Here we show evidence from satellite observations of the 2011 Tohoku-Oki earthquake-induced tsunami that sheds Paul Choboter light on this issue. Three satellites observed the same Dept of Mathematics tsunami front, and for the first time, one of them recorded Cal Poly San Luis Obispo a tsunami height about twice as high as that of the other [email protected] two. Model simulations confirm that the amplified tsunami is one of several jets formed through topographic refraction Mary P. Thomas when tsunamis travel across ocean ridges and seamount San Diego State University chains. This process causes the tsunami front to merge [email protected] as it propagates, resulting in doubling its wave height and destructive potential in certain directions before reaching Jose Castillo shore. We conclude that the potential of tsunami merg- Computational Science Research Center ing jets should be taken into consideration for designing San Diego State University coastal tsunami hazard maps and assessing risk levels at [email protected] coastal oil refineries and nuclear power facilities. Y. Tony Song MS4 Jet Propulsion Laboratory Ensemble Filters to Reduce Uncertainties in San California Institute of Technology Quintin Bay Hydrodynamic Forecast System [email protected]

Uncertainties in the hydrodynamics model parameters have been accurately estimated though automated calibra- MS4 tion and validation process in previous studies. However, Parallelization of a 3D Curvilinear Non-hydrostatic uncertainties propagated over time are still largely un- Coastal Ocean Model known, and have yet to be tested in San Quintin Bay. For our research, we implemented a Delft3D Model to study DRAFT: The UCOAM model, developed by Abouali and the hydrodynamics of San Quintin Bay, in which Data As- Castillo, is a high-resolution (sub-km) Large Eddie Simula- similation (DA) techniques have played an important role. tion (LES) CFD model capable of running ocean and atmo- The mathematical methods of DA describe algorithms for spheric simulations. It is the only environmental model in combining the observations of a dynamical system (a com- existence today that uses a full, 3D curvilinear coordinate putational model that describes its evolution), with other system, which results in increased accuracy, resolution, and reduced times to solution. UCOAM is a petascale model: relevant information. The aim of this study is to find the 2 10 optimal ensemble size for the EnsKF to evaluate the long- it requires significant memory (10 arrays with 10 ele- term predictive capability of the Delft3D Model by us- ments) ; communication along all 3 dimensions; and simu- ing water level, current, and temperature measurements lations generate TBytes of data. To facilitate simulations, from different locations within the bay. OpenDA is con- we have developed a computational environment (CE) that sidered an effective tool for delivering real-time forecasting includes a parallel, MPI framework for the model, and via the introduction of the Ensemble Kalman Filter algo- cyberinfrastructure-based services. For the parallel model, rithm; therefore, the automatic procedure is expected to we have designed a modular, parallel framework (PFW), result in an improved model forecast. written in F95, that supports staggered grid, CFD applications. The framework includes modules that allow each Mariangel Garcia processing element (PE) to track the execution environ- CSRC-San Diego State University ment including: communicator groups; local and global GS15 Abstracts 73

scope data decomposition; ghost and halo communication Complexity and Enabling Rapid Development in cells; the location and distribution of the staggered grid Ecosystem Hydrology. variables; and utility tools (ﬁle I/O, timing, plotting, analysis). In this talk we discuss our experiences in developing The growing role of simulation in Earth systems science and testing the parallel framework. The parallel frame- has led to a signiﬁcant increase in the number and com- work has been used to develop several applications, includ- plexity of processes in modern simulators. This increase ing nesting the model within the global Regional Ocean has created a need for multiphysics simulation frameworks Model System. We also present results that demonstrate that facilitate dynamic selection of processes, component scaling of the parallel and application frameworks to nearly testing, and numerical experimentation with model repre- 2000 nodes, and show that the applications scale similarly sentation and coupling strategies. We present the ideas to other comparable coastal ocean models. behind Arcos, a strategy built on a dependency graph and process tree, and its use for managing this complexity. Mary P. Thomas San Diego State University Ethan T. Coon [email protected] Los Alamos National Laboratory [email protected]

MS4 David Moulton The Impact of Vegetation and Culverts on Sedi- Los Alamos National Laboratory ment Transport in a San Francisco Bay Salt Marsh Applied Mathematics and Plasma Physics [email protected] We study sediment transport pathways in a San Fran- cisco Bay salt marsh using observations and the three- dimensional, unstructured-grid SUNTANS model. Two Painter Scott field deployments were conducted to measure currents, wa- Oak Ridge National Laboratory ter levels, salinity, and suspended sediment for three weeks [email protected] during a rainy winter period and a dry summer period in 2014. These data are used to obtain a general under- Markus Berndt standing of the hydrodynamics and sediment transport in Los Alamos National Laboratory the marsh, paying particular attention to the differences [email protected] between the dynamics of the wet- and dry-period deployments. A majority of the marsh is covered by dense vegetation that is submerged only during spring tides, and MS5 hence most of the sediment transport dynamics are gov- Three-Dimensional Estuarine Model Based on erned by flow through the marsh channels with intermit- Hardware-Agnostic Finite Element Solver tent transport to and from the marshes. The observations are used to validate the three-dimensional model that is Modeling of coastal and estuarine flows poses several nu- used to compute sediment fluxes throughout the marsh. merical challenges. Key features of coastal models are vari- Results show that tidal flows consistently drive landward able mesh resolution, strict mass conservation, low numer- fluxes of sediment from San Francisco Bay into the marsh, ical diffusion, and computational efficiency. We present while intermittent river inflow events induce seaward sedi- first results of a 3D baroclinic model, implemented on a ment fluxes, flux patterns that are expected in shallow es- flexible finite element solver framework that utilizes auto- tuarine systems composed of mudflats and vegetation. By matic code generation. The flexible solver framework al- running the model with and without marsh drag effects, lows rapid model development, generation of adjoint mod- we demonstrate that, as expected, the vegetation acts to els, and produces code optimized for current and emerging prevent erosion in the shallow mudflats. However, a more HPC architectures. important effect of the vegetation is to channelize the flows in the main channels and induce erosion of sediments that Tuomas Karna are transported landward and onto the vegetated mudflats. Center for Coastal Margin Observation & Prediction We also study the impact of culverts in the system on sed- Oregon Health & Science University iment transport pathways. Running the model with and [email protected] without the culverts shows that they act to limit seaward sediment transport. Antonio Baptista Oregon Health & Science University Yun Zhang [email protected] Stanford University [email protected] David Ham Department of Mathematics and Department of Oliver Fringer Computing Environmental Fluid Mechanics Laboratory Imperial College London Stanford University [email protected] [email protected]

Ivy Huang, Derek Fong, Stephen Moismith MS5 Stanford University Pushing Integrated Hydrologic Modeling Towards [email protected], [email protected], moni- the Exascale: Case Studies in Residence Time and [email protected] Scaling Using Hyperresolution Simulations over the Continental Us and the Colorado Headwaters

MS5 Regional or watershed, scale simulations have been eﬀec- Arcos: a Coupling Framework for Managing tive tools in understanding hydrologic processes. However, 74 GS15 Abstracts

there are still many questions, such as the adaptation of wa- Joseph Beisman ter resources to anthropogenic stressors and climate vari- Colorado School of Mines ability, that need to be answered across large spatial ex- [email protected] tents at high resolution. Understanding and simulating the residence time distributions of water from land sur- Reed M. Maxwell face to stream outlet is a fundamental open question in Department of Geology and Geologic Engineering hydrology often considered a grand-challenge. The resi- Colorado School of Mines dence time of water plays a critical role in understanding [email protected] important topics including weathering and land formation, and anthropogenic impacts on water quality such as nitrate benjamin Andre from agricultural sources. In response to these grand chal- NCAR Earth System Laboratory lenges in hydrology, we present the results of a parallel, [email protected] integrated hydrologic model simulating surface and subsurface flow at high spatial resolution (1 km) over much of continental North America (6.3 million square km). These Jeff Johnson, Marcus Day simulations provide predictions of hydrologic states and Lawrence Berkeley National Laboratory fluxes, namely water table depth and streamflow, at un- [email protected], [email protected] precedented scale and resolution. The physically-based modeling approach used here requires limited parameteri- Glenn Hammond zations and relies only on more fundamental inputs, such as Sandia National Laboratories topography, hydrogeologic properties and climate forcing. [email protected] Such large scale simulations necessitate massively parallel recourses and good computational efficiency. We further Carl Steefel demonstrate complex residence time distributions derived Lawrence Berkeley National Laboratory from these first-principles flow and transport simulation [email protected] over this same flow domain. Results show that while major North American river basins have median ages from 2-20 years, all stream waters may be composed of a wide MS5 range of residence timesfrom 0.1 to 10,000 yearsindicating Interoperable Design of Extreme-Scale Application a strong memory filter on streamwater chemistry. Software (ideas): A Community Approach to Soft- ware Productivity Reed M. Maxwell Department of Geology and Geologic Engineering The IDEAS project is leveraging an interdisciplinary com- Colorado School of Mines munity to address the productivity challenges that sci- [email protected] entists face on extreme-scale architectures. We will discuss the potential of this approach to enhance productivity Laura Condon through a combination of modern development workflows Colorado School of Mines and design abstractions that support a collection of inter- [email protected] operable components from new and existing codes, within a lightweight open framework. This approach is motivated and tested through process-rich Use Cases in hydrologic Stefan Kollet and biogeochemical modeling of terrestrial systems. Meteorological Institute University of Bonn David Moulton [email protected] Los Alamos National Laboratory Applied Mathematics and Plasma Physics Mary Michael Forrester [email protected] Hydrologic Science and Engineering Program Colorado School of Mines Carl Steefel [email protected] Lawrence Berkeley National Laboratory [email protected] MS5 Scott Painter Interfacing the Geochemical Code CrunchFlow Oak Ridge National Laboratory with HPC Transport Codes at Different Spatial Environmental Sciences Division Scales: Lessons and Outlook. [email protected]

Implementation of new geochemical capabilities into ﬂow Ethan T. Coon and transport codes is often circumvented by coupling Los Alamos National Laboratory them to existing reaction codes. We used this approach [email protected] to make CrunchFlow’s geochemistry available to HPC ﬂow and transport codes applicable across a range of spatial scales, from the pore scale (Chombo) to the watershed Sergi Molins (ParFlow). Recently, a new generic, interoperable coupling Lawrence Berkeley National Laboratory approach through Alquimia, a biogeochemistry API and [email protected] wrapper library, has been used to couple CrunchFlow to Amanzi. Glenn Hammond Sandia National Laboratories Sergi Molins, David Trebotich [email protected] Lawrence Berkeley National Laboratory [email protected], [email protected] Reed M. Maxwell GS15 Abstracts 75

Department of Geology and Geologic Engineering framework, which is shown to enhance the performance of Colorado School of Mines the dual filtering approach without significant increase in [email protected] the computational cost. Numerical results comparing the performance and robustness of the proposed scheme with Tim Scheibe, Xiaofan Yang the standard joint and dual EnKFs will be presented. Pacific Northwest National Laboratory [email protected], [email protected] Boujemaa Al-Fquih King Abdullah University of Science and Technology (KAUST) MS5 [email protected] Experience and Lessons on Modular Ecosystem Model Development Mohamad Gharamti Nansen Environmental and Remote Sensing Center As environmental models became more complicated, we Bergen, Norway need new tools to analyze and validate models and fa- [email protected] cilitate collaboration. Modular design and function test have gained attention recently. In this talk, we present our Ibrahim Hoteit methods and software tools to analyze environmental soft- King Abdullah University of Science and Technology ware and to generate scientific function testing models for (KAUST) the Community Land Model using three typical scenarios: [email protected] 1) individual function testing, 2) compiler-assisted module generation, and 3) a virtual tree model generation for root research. MS6 Gradient Quality in Ensemble Optimization Dali Wang Oak Ridge National Laboratory With an increase in the number of applications of ensem- [email protected] ble optimization (EnOpt) for production optimization, the theoretical understanding of the gradient quality has received little attention. An important factor that influ- MS6 ences the quality of the gradient estimate is the number Stochastic Optimization of Enhanced Oil Recovery of samples. In this study we use principles from statisti- Implementation Using Approximate Dynamic Pro- cal hypothesis testing to quantify the number of samples gramming needed to estimate an ensemble gradient that is comparable in quality to an accurate adjoint gradient. We develop Successful field implementation of enhanced oil recovery a methodology to estimate the necessary ensemble size to processes is dependent on finding the optimal policy in the obtain an approximate gradient that is within a predefined presence of numerous uncertainties, both reservoir related angle compared to the adjoint gradient, with a predefined and economic. This presentation will focus on the use of statistical confidence. Our results provide insight into the a stochastic approximate dynamic programming approach necessary number of samples required for EnOpt, in par- in producing optimal implementation policy for enhanced ticular for robust optimization, to achieve a gradient com- oil recovery. The method used was inspired by real options parable to an adjoint gradient. theory and was enhanced by incorporating the probabilistic collocation method. This was applied to a number of Jan Dirk Jansen examples. Delft University of Technology Department of Geotechnology Ali M. AlKhatib [email protected] Reservoir Engineering Technology Division, EXPEC Advanced Re Rahul Fonseca [email protected] TU Delft, The Netherlands [email protected] MS6 Olwijn Leeuwenburgh A New Dual Ensemble Kalman Filter for State Pa- TNO rameter Estimation in Subsurface Hydrology [email protected] The ensemble Kalman filter (EnKF) is a popular method for estimating the state and parameters in large scale appli- MS6 cations. The usual filtering procedure for state-parameters Bayesian Nonlinear Smoothing estimation is based on either joint or dual strategies, in which, at each assimilation cycle, a forecast step by the New schemes are presented for optimal Bayesian nonlinear model is followed by an update step with incoming ob- state estimation of nonlinear fluid and ocean dynamical servations. The joint approach directly updates the state systems, both forward and backward in time. The Bayesian and parameters as one single vector, while the dual ap- nonlinear smoothing combines reduced-order Dynamically- proach makes use of two separate filters; one to estimate Orthogonal (DO) equations with Gaussian Mixture Models the parameters and the other to estimate the state based (GMMs), extending linearized backward pass updates to a on the updated parameters. In this work, we propose a new Bayesian nonlinear setting. Examples are provided for fluid dual EnKF algorithm in which we reverse the order of the and ocean flows. This is joint work with our MSEAS group forecast-update steps following the one-step-ahead (OSA) at MIT. smoothing formulation of the Bayesian filtering problem. Compared to the standard dual EnKF, this introduces a Pierre Lermusiaux, Tapovan Lolla new update step to the state in a fully consistent Bayesian MIT 76 GS15 Abstracts

[email protected], [email protected] the imaging of multiphase flow at temperatures and pressures representative of subsurface flow. We use this technique to look at capillary trapping, contact angle measure- MS6 ment and the dynamics of multiphase flow. Viscous and Optimization Under Uncertainty: A Unified gravitational displacement of trapped CO2 is examined by Framework for a Class of Ensemble Data Assim- comparing pore-by-pore capillary pressure measurements ilation Algorithms to modelled pressure fields and pore parameterisations to reformulate the capillary and bond number based on the We present an expectation-maximization type framework pore-scale physics of remobilization. that can be employed to describe a class of ensemble data assimilation algorithms which may be iterative or non- Matthew Andrew iterative, and are derived from either a Bayesian or non- Imperial College London Bayesian perspective. Example algorithms include the con- [email protected] ventional ensemble Kalman filter with perturbed observations, the ensemble smoother and the ensemble Kalman Branko Bijeljic smoother that are suitable for linear or weakly nonlinear Department of Earth Science and Engineering systems, and their iterative counterparts that are imple- Imperial College London mented in situations with stronger nonlinearity. Some im- [email protected] plications of the proposed framework are explained, and potential future algorithm developments are discussed. Martin Blunt Xiaodong Luo Dept. Earth Science and Engineering International Research Institute Of Stavanger (IRIS) Imperial College London Bergen 5008, Norway [email protected] [email protected] MS7 MS6 Characteristic Length and Time Scales in Pore Adaptive Spectral High-Dimensional Model Repre- Scale Displacement Regimes sentation Techniques for Optimisation of Injection Strategy of CO2 Sequestration Recent advances in fast X-ray computed micro-tomography have made it possible to image pore scale displacement in Successful operation of CO2 storage sites relies on design- multiphase flow in porous rock at time intervals of 1-40 ing optimal control strategies of the injection wells under s. That enables us to study the immiscible displacement operational constrains. Solving this high-dimensional op- under dynamic flow conditions, i.e. keeping the visco- timisation problems is computationally demanding. We capillary balance. That allows us to study pore-scale dis- propose an efficient surrogate assisted algorithm to solve placement processes that occur in drainage and imbibition. this challenging problem. The utilised surrogate has three In drainage we find that Haines jumps often extend over novel aspects: (i) it relies on an ANOVA like decomposi- more than one pore and are cooperative, non-local phenom- tion termed High Dimensional Model Representation, (ii) ena which are conceptually different and also have a differ- component-wise interactions are approximated with adap- ent event size statistics than simple percolation models pre- tive sparse grid interpolation using polynomial basis func- dict. In imbibition we find a complex interaction between tions, (iii) the surrogate is adaptively partitioned closer to film swelling and corner film flow and the breakup of clus- the optimal solution within the optimisation iteration. ters. When following the transition from a connected phase flow to individual clusters, at the onset of oil mobilization Kurt Rachares Petvipusit which occurs at relatively large oil saturation, the main Dept. of Earth Science and Engineering mechanism is snap-off leading to a breakup of clusters. The Imperial College London large meniscus oscillations initiated by the snap-off, on the [email protected] other hand, also leads to coalescence events, which again points to the cooperative dynamics in the ganglion dynam- Ahmed H. ElSheikh ics regime. During forced imbibition, the visco-capillary Institute of Petroleum Engineering scaling group points to the cluster length being the char- Heriot-Watt University, Edinburgh, UK acteristic length scale for displacement, i.e. at which the [email protected] flow regime changes from a capillary-dominated to a viscous flow regime. By inspecting the individual radiographs Peter King from the tomography experiment, which are recorded at 40 Imperial College London ms time intervals, we get one to two orders of magnitude Department of Earth Science & Engineering better time resolution to study the detailed dynamics of [email protected] displacement dynamics, finding characteristic decay times after individual events of 1-2 seconds.

Martin Blunt Steﬀen Berg Dept. Earth Science and Engineering Shell Imperial College London steﬀ[email protected] [email protected] Ryan Armstrong MS7 School of Petroleum Engineering The Reservoir Condition Imaging of Pore-Scale University of New South Wales Flow: Trapping, Wettability and Dynamics [email protected]

Recent developments in x-ray micro-CT have allowed for Rucker Maja GS15 Abstracts 77

Johannes Gutenberg University of Mainz Houston, Texas, USA [email protected] [email protected]

Holger Ott, Apostolos Georgiadis, Leon Leu Faruk O. Alpak Shell Global Solutions International B.V. , Shell International Exploration & Production Inc., USA [email protected], [email protected], [email protected] [email protected]

Frieder Enzmann, Michael Kersten MS7 Geosciences Institute, Johannes-Gutenberg University, Control of Viscous Fingering Patterns in Porous 55099 Media Flow [email protected], [email protected] We study numerically and experimentally the dynamics and control of viscous fingering patterns in a circular Hele- MS7 Shaw cell as a model for porous media flow. The non- Numerical Analysis of ”Real” Pore-scale Flow locality and nonlinearity of the system, especially interactions among developing fingers, make the emergent pattern The fast and continuous development of technical basis for difficult to predict and control. By controlling the injec- computations and pore-scale (PS) measurement and visu- tion rate of the less viscous fluid, we can precisely suppress alization give rise to problem formulations which seemed the evolving interfacial instabilities. There exist denumer- inappropriate in the recent past. Based on pore-scale de- able attractive, self-similarly evolving symmetric, universal scription the direct numerical simulations (DNS) approach shapes. Experiments confirm the feasibility of the control is rapidly gaining in popularity despite the numerous tech- strategy, which is summarized in a morphology diagram. nical problems in its implementation. The short critical review of the methods used currently for the DNS (diffuse John Lowengrub interface, volume-of-fluid, level-set, DHD) is first presented Department of Mathematics in our work. The numerical methodology under consider- University of California at Irvine ation includes the geometrical description of flow regions [email protected] (which may be based on CT imaging), the grid generation (complex problem for real, i.e. as close as possible to reality, pore volumes) and application of efficient numeri- MS7 cal models for PS flow calculations. To test and validate Modeling Experiments and Gaining Insight by the relevant DNS model of PS flow in real media under Means of Pore-scale Simulations natural flow conditions the comparison to available analytical solutions, simulation and experimental results are We discuss the ability of pore-scale modeling to contribute provided. Among numerous possible oil recovery applica- to advancing our understanding of the relevant pore-scale tions within the relatively simple physical framework of the mechanisms and their impact at the Darcy scale. We fo- single and two-phase PS flow the medium transport prop- cus on models that resolve the dynamics of the fluids with erties determination, the investigation of fluids entrapment sub-pore resolution, such as the Volume Of Fluid method. and mobilization, the analysis of viscous fingering dynam- We demonstrate the ability of the method to model exper- ics in oil-water systems and the stationary configurations iments in micromodels and to provide insight into the role of two-phase flow at different viscosity ratios, transport of inertial effects due to rapid, irreversible fluid reconfigu- and capillary conditions, the imbibition and drainage flow ration. regime are addressed. The discussion on the challenges and limits of the DNS-based PSM using diffuse interface Ivan Lunati approach is provided. University of Lausanne [email protected] Igor Bogdanov,IlyaPeshkov University of Pau [email protected], [email protected] MS8 New Mixed Finite Elements on Quadrilaterals of Minimal Dimension MS7 Numerical Simulations of the Cahn-Hilliard Equa- We present two new families of mixed finite elements on tion in Porous Domains quadrilaterals. The new families are inf-sup stable, and they approximate optimally the velocity, pressure, and di- The Cahn–Hilliard equation is well-known for modeling vergence of the velocity. The spaces are of minimal di- phase reordering in binary fluid systems. Our goal is to mension subject to the approximation properties and fi- find a suitable discontinuous Galerkin method that is com- nite element conformity (i.e., they lie in H(div) and are putationally efficient on fine voxel-set-type grids arising constructed locally). The two families gives full and re- from CT imaging. We give a brief overview of possible duced H(div) approximation, like Raviart-Thomas and discretizations and propose a specific one. Optimal conver- BDM spaces. gence against prescribed solutions is shown and robustness is demonstrated by various numerical scenarios. Todd Arbogast Dept of Math; C1200 Florian Frank University of Texas, Austin Rice University [email protected] fl[email protected] Maicon R. Correa Beatrice Riviere National Laboratory of Scientific Computing Rice University LNCC, Brazil 78 GS15 Abstracts

[email protected] [email protected]

MS8 MS8 Enhanced Coarsening Strategy for the Multiscale Mimetic Finite Difference Method for the Richards Finite Volume Method Equation The MultiScale Finite Volume (MSFV) leads to non- Nonlinear diffusion equations (such as the Richards equa- monotone solutions if the fine-scale operator has high con- tion) are used to model geophysical flows in variably satu- trast in the coefficients. We enhance the MSFV coarse rated media. They require numerical schemes that remain grid by adapting the grid geometry to the heterogeneity robust and accurate under extreme conditions where the and anisotropy in the fine-scale system in order to improve diffusion coefficient is not only discontinuous but may also monotonicity and accuracy of the solution. In addition, we become very small or even degenerate. We present a new investigate the effects of the enhanced coarsening strategy family of mimetic finite difference schemes for these equa- on the convergence rate when MSFV is used as a precon- tions. These schemes incorporate upwind algorithms into ditioner in an iterative process. the conventional mimetic framework. Yixuan Wang Konstantin Lipnikov, Gianmarco Manzini Stanford University Los Alamos National Laboratory [email protected] [email protected], [email protected] Hadi Hajibeygi David Moulton TU Delft Los Alamos National Laboratory [email protected] Applied Mathematics and Plasma Physics [email protected] Hamdi Tchelepi Stanford University Mikhail Shashkov Energy Resources Engineering Department Los Alamos National Laboratory [email protected] [email protected]

MS8 MS8 Multipoint Flux and Stress Mixed Finite Element Methods for Flow and Mechanics on Quadrilaterals Discretizations of the Diffusion Equation with Multi-material Cells We discuss a new multipoint stress mixed finite element method for elasticity on quadrilaterals. It is based on the Multi-material (MM) cells appear when base mesh does not lowest order mixed elasticity space introduced by Arnold, conforms to material interfaces. The interfaces are recon- Awanou, and Qiu. A trapezoidal-type quadrature rule al- structed inside this MM cell and materials are represented lows for local stress elimination and reduces the method by pure material polygons, which form cell mini-mesh. To to a cell-centered scheme for displacements and rotations. solve diffusion equation we construct homogenized mate- The method is combined with the multipoint flux mixed rial properties for MM cells; then solve equations on base finite element method for flow to obtain a cell-centered mesh; and finally, to obtain solution in each material in the scheme for the Biot system of poroelasticity. MM cell, we solve equations on mini-mesh, using boundary conditions obtained from global solve. Ivan Yotov Univeristy of Pittsburgh Mikhail Shashkov, Konstantin Lipnikov Department of Mathematics Los Alamos National Laboratory [email protected] [email protected], [email protected]

Gianmarco Manzini MS9 LANL Beating Fwi Convergence Problems by Tomo- [email protected] graphic Fwi Convergence of full waveform inversion (FWI) can be im- MS8 proved by extending the velocity model along the time-lag axis. This extension enables us to linearly model large Locally Conservative Eulerian-Lagrangian Local- time shifts caused by velocity perturbations. This linear ized Adjoint Methods for Multiphase Flow modeling is based on a new linearization of the scalar wave equation. The resulting tomographic FWI method achieves The Eulerian-Lagrangian localized adjoint method (EL- convergence even when the starting model is far from being LAM), when formulated with indicator (piecewise con- accurate. stant, finite volume) space-time test functions, conserves mass locally in a Lagrangian sense (on subdomains that Biondo Biondi move with the flow). Recent developments in applying Geophysics Department these concepts to multiphase flows will be summarized. Stanford University [email protected] Thomas F. Russell National Science Foundation Ali Almomin Ofc. of Integrative Activities Stanford University GS15 Abstracts 79

[email protected] approaches, both recently suggested an more mature, and describe their relation to travel-time tomography.

MS9 Guanghui Huang Stereo-wave Tomography: A New Strategy for Computational and Applied Mathematics Seismic Imaging Rice University, Houston TX 77005 [email protected] Seismic shot gathers usually exhibit local coherency at least over a few records corresponding to adjacent stations. Full William Symes waveform inversion (FWI) is a generic method to determine Rice University the Earth’s properties from seismic measurements but does [email protected] not explicitly exploit this local coherency. We design a new method called stereo-wave tomography to precisely fill this gap. It consists of computing local radon transforms of the MS9 signal and of extracting information from these panels. Robust Adaptive Waveform Inversion Herve Chauris Full-waveform seismic inversion suffers from the effects of Ecole des Mines Paris cycle skipping, leading it to become trapped at a local [email protected] minimum in the objective function, if the starting model is not accurate. Adaptive waveform inversion overcomes MS9 this problem by designing a suite of filters that match the predicted data to the observed data; it formulates the in- Relaxation Methods for Inverse Wave Scattering version problem to find the earth model that turns these Inversion of kinematic parameters from scattered waves can matching filters into trivial filters that do nothing to input lead to hard optimization problems, e.g., when the mea- data. surements are interferometric, or when a background velocity needs to be estimated. I will explain how and when Mike Warner the semidefinite relaxation framework can be used to miti- Imperial College London gate some of the nonconvexity inherent in these problems. [email protected] Joint work with Augustin Cosse and Laurent Seppecher. Laurent Demanet MS10 Department of Mathematics, MIT Element-Based Algebraic Multigrid Upscaling for [email protected] Reservoir Simulation We present a dimension reduction approach for reser- MS9 voir simulations exploiting a finite element based algebraic Pros and Cons of Full- and Reduced-space Methods multigrid (or AMGe) technique which provides coarse mod- for Wavefield Reconstruction Inversion els with guaranteed accuracy. Coarse basis functions are determined by solving local eigenvalue problems, which en- By insisting on fitting observed data, Wavefield Recon- sures that high contrast coefficients can be represented on struction Inversion (WRI) is no longer cycle skipped and a coarse grid. Our reservoir simulation exploits a conser- therefore less reliant on the accuracy of starting mod- vative finite volume formulation of the Darcy equations of els. While extending the search space mitigates local min- porous media flow. ima, there are challenges scaling to 3D seismic when using reduced-space methods that require accurate solves. Con- Andrew T. Barker versely, full-space methods allow for inaccurate solves but Center for Applied Scientific Computing require storage of all wavefields. We weigh pros and cons Lawrence Livermore National Laboratory of these two approaches in the seismic context. [email protected]

Felix J. Herrmann Delyan Kalchev Seismic Laboratory for Imaging and Modeling University of Colorado The University of British Columbia [email protected] [email protected] Ilya D. Mishev Bas Peters ExxonMobil Upstream Research Company UBC Department Technical Software Development [email protected] [email protected]

MS9 Panayot Vassilevski Lawrence Livermore National Laboratory Analysis of Extended Waveform Inversion [email protected] Extended modeling permits a reformulation of waveform inversion, in some cases avoiding multiple physically- Yahan Yang irrelevant local solutions that plague the standard formu- ExxonMobil lation. Addition of (non-physical) degrees of freedom to [email protected]. the model-data relation permits precise ﬁt to data even in the absence of precise model information, thus avoiding the ”cycle-skipping” phenomenon that leads to multi- MS10 ple local solutions. We review several extended modeling Element-Based Algebraic Multigrid Leads to Ac- 80 GS15 Abstracts

curate Numerical Reservoir Simulation tions.

We will present scalable multilevel solution techniques Daniel Osei-Kuffuor,LuWang for a Mixed Finite Element discretization of the two- Lawrence Livermore National Laboratory phase porous medium flow equations. The results will oseikuff[email protected], [email protected] be presented for a numerical upscaling scheme based on an operator-dependent element-based Algebraic Multigrid Robert Falgout (AMGe) method recently developed at LLNL. To simu- Center for Applied Scientific Computing late at different spatial resolutions, with optimal compu- Lawrence Livermore National Laboratory tational cost and high accuracy, benefits applications such [email protected] as uncertainty quantification (Multilevel Monte Carlo) and optimization which is also investigated. Ilya D. Mishev ExxonMobil Upstream Research Company Max la Cour Christensen Department Technical Software Development Technical University of Denmark [email protected] [email protected]

MS10 MS10 Unified Framework for Block-Partitioned Solution Effective Solvers for Reservoir Simulation Methods for Coupled Poromechanics The most time-consuming part of modern reservoir simulation, which uses computational tools to predict the multi- This work focuses on solution strategies for coupled phase flow in porous media, is solving a sequence of large- poromechanical problems. Recently, several fully implicit scale and ill-conditioned Jacobian systems. In this work, and sequential implicit schemes have been proposed that we develop new effective preconditioners which are based exhibit stable and rapid convergence to the coupled solu- on the algebraic multigrid methods. Proper subspace split- tion. While superficially different, these schemes can be in- tings are developed according to some important properties terpreted as subtle variations of a block-preconditioned it- of the underlying physical systems and used to design the erative method. Rapid convergence results from the choice preconditioners. Field-scale reservoir simulation validates of sparse Schur complement approximation. Further, these the effectiveness and robustness of the solvers. partitioned approaches lead to sub-problems that are well addressed by algebraic multigrid methods. Xiaozhe Hu Tufts University Joshua A. White [email protected] Lawrence Livermore National Laboratory [email protected]

MS10 Nicola Castelletto Dept. ICEA Experience with AMG Solvers in Production University of Padova Reservoir Simulation [email protected] AMG (Algebraic Multi-Grid) is one of the most efficient solvers for linear systems from discretization of the pres- Hamdi Tchelepi sure equation in IMPES or Sequential Implicit formula- Stanford University tions. Classical AMG (Ruge-Stuben) works very well for Energy Resources Engineering Department monotone matrices from finite volume discretizations, but [email protected] cannot solve efficiently linear systems with the facility unknowns included because of the different nature of these equations. We share our experience how this problem can MS11 be overcome and discuss further extensions. Pushing an Estuarine Circulation Model to the Brink: Lessons Learned and Next Steps Ilya D. Mishev ExxonMobil Upstream Research Company SELFE, a low-order unstructured-grid circulation code, Department Technical Software Development has both succeeded and been severely challenged in mod- [email protected] eling the dynamics of a river-dominated multi-regime estuary. The modeling process, which is informed by a comprehensive set of long-term and high-resolution observations, MS10 is described. Results for SELFE are used to reflect on the An Algebraic Multigrid Solver for Fully-Implicit limitations of this and other leading-edge contemporary es- Solution Methods in Reservoir Simulation tuarine models. In addition, the modeling process is used to envision the requirements for a next-generation estuar- The linearized equations of oil reservoir simulations often ine and coastal model. yield a complex Jacobian linear system that is challenging to solve by iterative methods. We present our efforts to de- Antonio Baptista velop an AMG-preconditioned Krylov method for directly Oregon Health and Sciences University solving the original discretized system. The preconditioner [email protected] is designed to represent the coupling between the physical variables and account for the underlying physics of the Tuomas Karna system. We present performance results for the solver on Oregon Health & science University challenging applications emerging from reservoir simula- [email protected] GS15 Abstracts 81

Jesse Lopez mixing. Oregon Health & Science University [email protected] Matthew D. Rayson,EdwardGross Stanford University Yvette Spitz [email protected], [email protected] Oregon State University [email protected] Oliver Fringer Environmental Fluid Mechanics Laboratory Stanford University MS11 [email protected] A Revival of Semi-Lagrangian Advection Methods for Adaptively Refined Meshes? MS11 Semi-Lagrangian methods have long been used as advec- Aspects of Higher Order Discontinuous Galerkin tion schemes due to their unconditional stability property. Solutions to the Shallow Water Equations Their lack of formal conservation, and the somewhat ob- scure parallelization potential has lead many researchers Second order accurate Finite Volume and Continuous to abandon this type of methods. Reviewing the method Galerkin Finite Element solutions to the shallow water in light of its seamless integration into a posteriori adap- equations are widely used in coastal ocean hydrodynamics. tive mesh methods yields a new perspective. Recently However existing models are quite expensive to implement developed efficient (quasi-) conservative semi-Lagrangian for unstructured meshes. We examine aspects of using p=1 schemes with flux formulation of the governing equations through p=3 order Discontinuous Galerkin solutions to the yields an elegant ocean modeling method. shallow water equations including cost efficiency for triangular and quadrilateral elements as well as flow through Jörn Behrens channels. The later problem requires special handling of KlimaCampus, University of Hamburg the boundary conditions. [email protected] Joannes Westerink Department of Civil Engineering and Geological Sciences MS11 University of Notre Dame Simulating and Optimizing the Extraction of Tidal [email protected] Energy Using Multi-Scale Numerical Methods Steven Brus, Dam Wirasaet The acceleration of tidal current in coastal regions repre- Dept. of Civil and Environmental Eng. and Earth sents an attractive source of renewable energy. However, Sciences economic and environmental barriers must be overcome to University of Notre Dame allow the exploitation of this resource. This necessitates [email protected], [email protected] the development of numerical models that are able to predict impacts and returns of tidal turbine arrays, and cru- Clint Dawson cially that are also able to reliably contribute to their opti- Institute for Computational Engineering and Sciences mal design. This presentation will describe the approaches University of Texas at Austin we have taken to achieve these goals. [email protected] Matthew Piggott Dept. Earth Science and Engineering MS12 Imperial College [email protected] Uncertain Prediction of Marine Ice Sheet Dynam- ics and Volume Loss

MS11 Marine ice streams, most notably those in West Antarc- tica, may have begun rapidly retreating due to the marine Challenges in Three-Dimensional Hydrodynamic ice instability. However, uncertain ice dynamics and ex- Modelling of the Shallow Bays and Estuaries Along pensive computational models make predicting retreat rate the Gulf of Mexico Coast and volume loss difficult. Ice stream/shelf models that relate retreat rate and rate of volume loss to grounding line The Gulf of Mexico coast is characterized by wide, shal- thickness and ice shelf buttressing are used within Bayesian low (< 3 m deep) bays and estuaries with narrow openings inference methods to predict ice stream/shelf behavior. to the Gulf and geometrically complex shorelines. Tidal forcing is small (< 0.5 m range) yet strong tidal currents −1 Andrew Davis (>1.0 m s ) with large spatial variability exist at narrow MIT constrictions and shipping channels. We present hydro- [email protected] dynamic modeling results from Galveston Bay, Texas, using the three-dimensional, finite-volume SUNTANS model. We demonstrate the effectiveness of employing hybrid Patrick Heimbach, Youssef M. Marzouk quadrilateral/triangular grids in which the main chan- Massachusetts Institute of Technology nels are resolved with quadrilateral grids. Using results [email protected], [email protected] from the hybrid grid, we show that accurately predicting the low-frequency circulation and salinity distributions requires resolving the small-scale topographic features, im- MS12 plementing a host of different processes into the boundary Scalable Parameterized Surrogates Based on Low conditions, and correctly parameterizing the sub-grid scale Rank Tensor Approximations for Large-scale 82 GS15 Abstracts

Bayesian Inverse Problems large-scale Hydraulic Tomography and joint inversion using MRI imaging data. Hessian operators (of the negative log posterior) have played an important role in high-(infinite-) dimensional Jonghyun Lee Bayesian geophysical inverse problems, from characteriz- Stanford University ing the (inverse of the) posterior covariance under the [email protected] Gaussian approximation, to accelerating MCMC sampling methods by providing information on the local curvature Hongkyu Yoon in parameter space. The key to making computations Geoscience Research and Applications with them tractable is a low rank approximation of the Sandia National Laboratories (prior-preconditioned) data misfit component of the Hes- [email protected] sian. Here we consider the role of higher derivative operators in Bayesian inverse problems and whether scalable low Peter K Kitanidis rank approximations can be constructed. Stanford University Nick Alger [email protected] The University of Texas at Austin Center for Computational Geosciences and Optimization MS12 [email protected] From Data-to-Predictions under Uncertainty for Tan Bui Antarctic Ice Sheet Flow University of Texas at Austin We present efficient and scalable algorithms for a data-to- [email protected] prediction process under the Gaussian approximation and in the context of modeling the flow of the Antarctic ice Omar Ghattas sheet and its effect on sea level. The ice is modeled as The University of Texas at Austin a viscous, incompressible, creeping, shear-thinning fluid. [email protected] The observational data come from InSAR satellite measurements of surface ice flow velocity, and the uncertain parameter field to be inferred is the basal sliding param- MS12 eter. We show that the work required for executing this Dealing with Uncertainties in Decadal Global data-to-prediction process is independent of the state di- Ocean State Estimation mension, parameter dimension, and data dimension.

Over the last 1.5 decades the consortium ”Estimating the Noemi Petra Circulation and Climate of the Ocean” (ECCO) has devel- University of California, Merced oped a framework for ﬁtting a state-of-the-art global ocean [email protected] (and sea ice) general circulation model (GCM) to much of the available diverse streams of satellite and in situ ob- Toby Isaac servations via a deterministic least-squares approach. A ICES key ingredient is the availability of an adjoint model of The University of Texas at Austin the time-evolving GCM to invert for uncertain initial and [email protected] surface boundary conditions, as well as internal model parameters. With increasing maturity of the framework and the decadal global state estimates so produced, increased Georg Stadler attention is warranted to assess the ﬁdelity of prior errors Courant Institute for Mathematical Sciences assigned to the observations and the inversion (control) New York University variables, as well as a rigorous assessments of posterior un- [email protected] certainties. The latter is a key open question, both for the provision of realistic uncertainties in climate reconstruc- Omar Ghattas tions, as well as implications for forecasting. Ongoing work The University of Texas at Austin to tackle these problems in the context of ECCO will be [email protected] described.

Patrick Heimbach MS12 Massachusetts Institute of Technology Inference of Parameters in Mantle Flow Stokes [email protected] Models

The ﬂow in earth’s mantle and the associated tectonic plate MS12 motion is often modeled using nonlinear Stokes equations Fast Large-Scale and Joint Subsurface Inversion with temperature- and strain rate-dependent viscosity. To Using Principal Component Geostatistical Ap- describe poorly known/understood phenomena such as the proach plate coupling strength or the relation between strain rate and stress, parameters are introduced in the constitutive Geostatistical approaches, widely used for inverse problems relation. Using a Bayesian inference approach, we study in geosciences, require the computation of the Jacobian ma- the prospects and limitations of inverting these parameters trix from min(m,n) forward runs for m unknowns and n ob- from surface observations. servations. Jacobian computation can be prohibitive when m and n become large. The Principal Component Geosta- Georg Stadler tistical Approach (PCGA) using low-rank approximation Courant Institute for Mathematical Sciences of the prior covariance is an eﬃcient implementation with New York University controlled accuracy. Our PCGA method is illustrated with [email protected] GS15 Abstracts 83

Michael Gurnis these facies models pose significant difficulty in using clas- California Institute of Technology sical inverse modeling techniques, which are typically de- [email protected] signed for continuous, linear, and multi-Gaussian systems. In this talk, two alternative methods are presented for pre- Vishagan Ratnaswamy serving the geologic complexity of the facies models during California Institute of Technology data assimilation. Seismological Laboratory [email protected] Benham Jafarpour Viterbi School of Engineering University of Southern California Johann Rudi [email protected] ICES The University of Texas at Austin [email protected] MS13 Adaptive ES-MDA for Data Assimilation Omar Ghattas The University of Texas at Austin The ensemble smoother with multiple data assimilation has [email protected] proved to be a robust ensemble-based data assimilation method provided inflation factors are chosen correctly. We provide a procedure based on the theory of regularizing MS13 Levenberg-Marquardt to choose the inflation factors adap- Preserving Geological Realism of Channelized Fa- tively during the data assimilation process. Examples indi- cies in Complex Reservoir cate the adaptive procedure further improves the reliability of the original ES-MDA algorithm. Ensemble-based data assimilation methods have been successfully applied for parameter estimation in reservoir mod- Albert C. Reynolds, Duc Le els. However, when complex reservoir geology exists, cer- University of Tulsa tain reservoir structures may lose the plausibility during [email protected], [email protected] data assimilation. This work will address these issues on a real field with a newly extended facies parameterization ap- MS13 proach coupled with Iterative Adaptive Gaussian Mixture (IAGM) Filter. We investigate the interaction between fa- Sequential Assimilation, Multiple Assimilation and cies and nonfacies layers and the preservation of geological Iteration channel continuity during data assimilation. Four non-iterative parameter estimation methods, apply- Yuqing Chang ing four different ways to assimilate data, are compared to an iterative method on problems with weakly non-linear, International Research Institute of Stavanger (IRIS), simplistic forward models. Asymptotic calculations in an Norway idealized setting reveal interesting relations between the [email protected] methods. Numerical calculations with randomized model settings are performed to verify the asymptotic results. MS13 Numerical results where random effects are averaged out strongly support the asymptotic results, while numerical Seismic History Matching Combining Ensemble results for a single model setting are significantly blurred. Kalman Filter and Model Order Reduction Tech- niques Trond Mannseth Centre for Integrated Petroleum Research We present a methodology to update the reservoir model of University of Bergen, Norway porosity and permeability by simultaneously matching pro- [email protected] duction and seismic data. The inversion scheme is based on the Ensemble Kalman Filter method, combined with model order reduction techniques such as Proper Orthogo- MS13 nal Decomposition. In the proposed workflow, seismic data Ensemble Based Reservoir Characterization Using are matched by introducing a reduced parameterization of Seismic and Production Data time-lapse seismic-inverted results. The methodology is illustrated using a 2D synthetic example. Reduced and full During the last decade ensemble based methods has shown parameterization results are compared. great success in history matching using production data. Applying repeated seismic data has shown to be more chal- Dario Grana lenging. Part of the challenge is the error quantification of Department of Geology and Geophysics, University the seismic data. By including the seismic inversion in the ofWyoming, workflow, we can have a better error quantification of the [email protected] inverted seismic data (acoustic velocities). The workflow is illustrated on a synthetic 2-D case.

MS13 Geir Naevdal Nonlinear Flow Data Assimilation into Training- International Research Institute of Stavanger Image-Based Facies Models & Centre of Integrated Petroleum Research, UoB [email protected] Assimilating nonlinear ﬂow data into complex geologic facies models that are simulated from a training image (a Kjersti Eikrem conceptual geologic model) has proven to be challenging. International Research Institute of Stavanger In particular, the categorical and non-Gaussian nature of [email protected] 84 GS15 Abstracts

Morten Jakobsen tency and stability conditions. The consistency condition, Department of Earth Science which ensures the well-posedness, is an exactness property, University of Bergen i.e., all the schemes of the family are exact when the solu- [email protected] tion is a polynomial of an assigned degree. The degrees of freedom are the solution moments on mesh faces and inside Yan Chen mesh cells, thus resulting in a non-conforming discretiza- International Research Institute of Stavanger tion. Higher order schemes are built using higher order mo- [email protected] ments. The developed schemes are verified numerically on convection-diffusion-reaction problems with constant and spatially variable (possibly, discontinuous) tensorial coeffi- MS14 cients for the diffusive term. Convective and Elliptic CVD-MPFA Darcy Fluxes Gianmarco Manzini Convective and elliptic CVD-MPFA (control-volume dis- Los Alamos National Laboratory tributed multi-point) Darcy flux approximations will be [email protected] presented. A range of aspects including grid effects and gravity flux approximation will be discussed. [Lamine S. MS14 and Edwards M. G., Multidimensional Upwind Schemes and Higher Resolution Methods for Three-component Two- Hybrid Finite Element - Finite Volume Scheme for phase Systems Including Gravity Driven Flow in Porous Multiphase Flow in Geologic Media with Full Ten- Media on Unstructured Grids to appear Comp. Meth. sor Flow Properties App. Mech Eng.] [Edwards M G, Zheng H., Quasi M- Today, most reservoir simulators only handle grid-aligned Matrix Multi-Family Continuous Darcy-Flux Approxima- permeability components. This serious limitation can be tions with Full Pressure Support on Structured and Un- overcome with hybrid simulation methods: We combine structured Grids in 3-D SIAM J. Sci. Comput 33 (2) pp. finite element- with finite volume- discretization methods 455-487 2011] [Edwards M G., Global and Local Central using operator splitting: the pressure equation is solved ac- Non-Upwind Finite Volume Schemes for Hyperbolic Con- cumulating full tensor finite-element mobility integrals; the servation Laws in Porous Media Int. J. Numer Meth, Flu- transport equation is solved, reconstructing the required ids Vol 64, Issue 7, 10 November 2010, Pages: 793811] multidimensional finite-volume facet flux, using projections MG Edwards of the permeability tensor and the saturation functions that Swansea U. can also be of tensorial nature. mgedwards15gmail.com Stephan Matthaei, The University of Melbourne MS14 [email protected] A High Resolution Finite Volume Method for the Simulation of Oil-Water Displacements in Roman Manasipov Anisotropic and Heterogeneous Petroleum Reser- Montan University of Leoben, Austria voirs Using a Multidimensional Limiting Process Montanuniversität Leoben [email protected] In the present work, we use a robust Multidimensional Limiting Process (MLP) together with a high order finite Lukas Mosser volume method to discretize the saturation equation for Leoben U. the oil-water displacement problem producing accurate and Austria monotone solutions. For the solution of the pressure equa- [email protected] tion, we use a non-orthodox Multipoint Flux Approxima- tion Method based on a Diamond type stencil (MPFA-D). In order to assess the accuracy of the proposed methodol- MS14 ogy, we solve some benchmark problems found in literature. High Order Moving Mesh Finite Volume for Two Phase Flow Problems. Márcio Souza Federal University of Paraba We present here a High order moving mesh finite volume [email protected] method for the simulation of two phase flow in porous media. The method consist of transforming the equa- Fernando Contreras, Paulo Lyra, Darlan Carvalho tion of the flow stated on a fixed domain into a problem Federal University of Pernambuco on a moving domain. Then one combine an optimization Brazil mesh procedure, an O-method finite volume strategy and [email protected], [email protected], a constraint minimization strategy to build a finite-volume [email protected] where the user choose the order of convergence in advance. The algorithm is highly parallelisable and resolve steep fronts properly. MS14 Simplice Firmin Nemadjieu Virtual Element Methods for Flows and Transport { } in Porous Media Institut f u¨ r Numerische Simulation Endenicher Allee 60. D-53115 Bonn. Room: 2.049. We present a family of schemes for solving elliptic partial [email protected] differential equations on unstructured polygonal and polyhedral meshes. These discretizations can be interpreted in Sorin Pop the framework of mimetic finite difference methods and vir- CASA tual element methods. These methods satisfy local consis- Eindhoven University of Technology GS15 Abstracts 85

[email protected] Schlumberger-Doll Research [email protected] Paul A. Zegeling Dept. of Mathematics Utrecht University MS15 [email protected] Optimal Compressive Sampling Measurement Ma- trices for Seismic Acquisition

MS14 Abstract not available at time of publication. Nonlinear Finite Volume Discretization Methods for Anisotropic Diffusion Equation Zijian Tang Shell Global Solutions International B.V. In this work several nonlinear finite volume methods for [email protected] anisotropic diffusion equation are being derived. These methods either preserve nonnegativity of the solution or Xander Campman discrete maximum principle. Methods are compared with Shell Global Solutions well-known classical multipoint flux approximations on [email protected] benchmark problems and problems of practical interest.

MS15 Kirill Terekhov A Linear Sampling Method for Reconstructing Stanford University Fluctuations in an Elastic Wave Field [email protected] A method for reconstructing fluctuations of an elastic wave Denis Voskov field based on observed scattered waves is presented in this Energy Resources Engineering Department paper. The concept of the solvability index is for the in- Stanford Univeristy version equation is newly developed here in order to have [email protected] the spatial distribution of the solvability index describe the spatial spreads of the fluctuations of the wave field. Several Hamdi Tchelepi numerical results are shown to verify the accuracy of the Stanford University present method. Energy Resources Engineering Department [email protected] Terumi Touhei Department of Civil Engineering Tokyo University of Science MS15 [email protected] What Makes Full Waveform Inversion Difficult?

The earth computer generates the recorded seismic data. MS15 The digital computer generates the model data from hu- A Stable Data-Constrained Formulation of Full- man generated parameter fields: density, P-wave and Waveform Inversion with Wavefield Reconstruc- Shear-wave velocities, attenuation, anisotropy, topography, tion for Few Principle Sources numerical approximations, partial differential equations, and other questionable activities. To the first order we We avoid local minima related to cycle skipping by consid- try to estimate the uncertainty of each phenomenon, and ering a modified data-constrained FWI formulation where illustrate the effects on the FWI objective functions. observed data is fitted exactly. This formulation is a well- conditioned limit of the Lagrangian dual of Wavefield Re- Ralph P. Bording construction Inversion. To mitigate instabilities, we use a Alabama A&M University source encoding strategy based on singular vectors of the [email protected] wavefields. In addition, we propose a frugal SVD that efficiently computes the principle components of the wave- Changsoo Shin fields directly from the data. Seoul National University [email protected] Rongrong Wang University of British Columbia [email protected] MS15 Recent Advances in Optimal Experimental Design Felix J. Herrmann for Imaging Seismic Laboratory for Imaging and Modeling The University of British Columbia Given geophysical observed data, full waveform inversion [email protected] aims at quantitatively characterizing the subsurface model parameters. These data are collected, given a design, using a set of control parameters including acquisition geometries Ozgur Yilmaz and tool settings. However, a successful data acquisition, Mathematics processing and inversion also depends on many uncertain University of British Columbia variables. In this talk, I will review recent advances in [email protected] experimental design for obtaining cost-effective acquisition surveys while enhancing full waveform inversion results. MS16 Hugues Djikpesse A Physics-Based Block-Triangular Preconditioner 86 GS15 Abstracts

for Coupled Flow and Geomechanics Institute of Fluid Dynamics [email protected] We present a block-triangular preconditioner for the solution of Biot’s equations of coupled consolidation obtained Patrick Jenny by mixed displacement/pressure formulations based on fi- Institute of Fluid Dynamics nite element and finite volume discretization schemes. The ETH Zurich preconditioner is constructed from a block LU decomposi- [email protected] tion of the coefficient matrix. Crucial for the competitive performance of the preconditioner is the sparse approximation of the Schur complement by a scaled pressure mass MS16 matrix, that depends element-wise on the inverse of a suit- Numerical Issues in the Simulation of Coupled able bulk modulus. Poromechanics by Mixed Finite Elements Nicola Castelletto The numerical solution to coupled poromechanics is still a Dept. ICEA challenging task because of several issues: (1) pore pres- University of Padova sure instability, (2) large number of unknowns, and (3) ill- [email protected] conditioning of the discretized system. The use of Mixed Finite Elements can alleviate the numerical oscillations in Jihoon Kim the pressure solution, but give rise to very large and ill- Texas A&M University conditioned systems of algebraic equations. The use of ef- Department of Petroleum Engineering ficient block preconditioners is presented and discussed to [email protected] accelerate convergence in complex real-world applications.

Joshua A. White Massimiliano Ferronato Lawrence Livermore National Laboratory Dept. ICEA - University of Padova [email protected] [email protected]

Hamdi Tchelepi Stanford University MS16 Energy Resources Engineering Department Stable Discretizations for the Biot Equations [email protected] We consider three important limits for stable discretizations of Biot’s equations: Incompressible fluid, incompress- MS16 ible solid, and small timesteps. Robust discretizations Stabilized Mixed Finite Elements for Twofold Sad- should be able to handle any combination of these lim- dle Point Problems in Deformable Double Porosity its, however, due to the saddle-point structure of Biot’s Media equations, this can be elusive. As a novel result, we show that the hybridized variational finite volume framework High-fidelity descriptions of double porosity media such as (which includes the multi-point flux (MPFA) and multi- fissured rocks require an explicit treatment of two-scale point stress (MPSA) approximations) allows the construc- pore pressures. Three-field mixed finite elements for cou- tion of a naturally stable cell-centered finite volume dis- pled deformation and flow in double porosity media en- cretization for Biot’s equations. We give an overview of counter a so-called twofold saddle point problem in the the proof, including explicit bounds on the stability con- limit of undrained deformation/incompressible flow. We stants,andnumericalexamples. present an extension of the pressure projection stabilization technique, which has proven to be robust for various Jan M. Nordbotten single saddle point problems, to circumvent the twofold Department of Mathematics saddle point problems arising in deformable double poros- University of Bergen ity media. [email protected]

Jinhyun Choo, Ronaldo I. Borja Stanford University MS16 [email protected], [email protected] Coupled Flow and Geomechanics for Fractured Poroelastic Reservoirs

MS16 An accurate hydrocarbon recovery prediction from frac- Numerical Modeling of Flow-Mechanics Coupling tured (hydraulic and discrete) shale reservoirs requires ade- in Fractured Reservoirs with Porous Matrix quate modeling of underlying physical processes and robust solution schemes. A coupled reservoir-fracture flow model A finite volume solver for flow induced slip failure was is presented which accounts for complex reservoir geome- developed. For the stress-strain relations, linear poro- try including non-planar fractures. Different flow models elasticity approximations are used. A semi-implicit method for fractures and reservoir are used to capture flow physics is employed to couple stress and pressure calculations. accurately. The geomechanical effects are included using Shear failure along prescribed fractures depend on both multiphase Biot’s equations. A solution scheme is pre- local stress and pressure solutions. To obtain the displace- sented followed by numerical results to demonstrate model ments, a new equilibrium based on the dynamic friction capabilities. law relating fluid pressure, shear and compressive traction forces along the fracture manifold, is solved. Gurpreet Singh The University of Texas at Austin Rajdeep Deb Center for Subsurface Modeling ETH Zurich [email protected] GS15 Abstracts 87

Mary F. Wheeler, Gergina Pencheva Maria Lukacova-Medvidova Center for Subsurface Modeling, ICES University of Mainz University of Texas at Austin [email protected] [email protected], [email protected]

Kundan Kumar MS17 Department of Mathematics Adaptive Measure-Theoretic Parameter Estima- University of Bergen, Bergen, Norway tion for Coastal Ocean Modeling [email protected] High-resolution computational meshes for coastal ocean Thomas Wick modeling often require high-resolution parameter fields. Johann Radon Institute for Computational and Applied Unfortunately, using field measurements to determine Math these parameters can be prohibitively expensive. Regard- Austrian Academy of Sciences less, complex hydrological models require some represen- [email protected] tation of parameters fields such as those used to represent momentum loss due to a combination of bottom friction, vegetation, and other structures. We explore the applica- MS17 tion of adaptive measure-theoretic parameter estimation to estimate spatially varying bottom friction parameters for Wetting/Drying in the 3D Discontinuous Galerkin coastal ocean models. Model Lindley C. Graham We present anisotropic slope limiting algorithm for a 3D University of Austin at Texas coastal ocean model based on the discontinuous Galerkin Institute for Computational Engineering and Sciences method. The method works by separating vertical and hor- (ICES) izontal limiting post-processors. The purpose of this sepa- [email protected] ration is to reduce numerical diffusion caused by the limiting procedure. Several academic and realistic test cases demonstrate the performance of the scheme. Clint Dawson Institute for Computational Engineering and Sciences Vadym Aizinger University of Texas at Austin University of Erlangen-Nürnberg [email protected] [email protected] Troy Butler University of Colorado Denver MS17 [email protected] Well-Balanced Schemes for the Shallow Water Equations with Coriolis Forces Joannes Westerink Department of Civil Engineering and Geological Sciences In this talk, we consider shallow water equations with the University of Notre Dame bottom topography and Coriolis forces. These equations [email protected] play an important role in modeling large scale phenomena in geophysical flows, in which oceanic and atmospheric circulations are often perturbations of the geostrophic MS17 equilibrium. For oceanographic applications, it is essen- Stabilization in Runge-Kutta Methods for Nonlin- tial to develop a well-balanced numerical method – the ear Geophysics method, which exactly preserves a discrete version of the geostrophic equilibrium states. Otherwise if numerical spu- Stabilizing explicit-in-time solvers is important when try- rious waves are created, they may quickly become higher ing to recovering accurate and robust solutions. Even so, than the physical ones. We design a special piecewise linear much of the present work in the area has been aimed at reconstruction, which is combined with the well-balanced linear test problems, that ignore the delicate interplay be- update in time and implement it in the context of the finite- tween the different subsystems that naturally couple in the volume framework. Theoretical proofs and numerical ex- more common nonlinear systems setting. In this talk we periments clearly demonstrate that the resulting numeri- discuss some of the nuances of these systems, present a cal scheme preserves geostrophic equilibria exactly. Our method for stabilizing nonlinear systems, and discuss the construction is general and can be used for a variety of virtues of different types of Runge-Kutta methods in these numerical method. contexts.

Alina Chertock Craig Michoski North Carolina State University UT Austin Department of Mathematics [email protected] [email protected] Clint Dawson Michael Dudzinski Institute for Computational Engineering and Sciences Helmut Schmidt University of the Federal Armed Forces University of Texas at Austin Hamburg [email protected] [email protected] Ethan Kubatko Alexander Kurganov Department of Civil, Environmental and Geodetic Tulane University Engineering [email protected] The Ohio State University 88 GS15 Abstracts

[email protected] are taken in account.

Alen Alexanderian Martin A. Diaz-Viera University of Texas at Austin INSTITUTO MEXICANO DEL PETROLEO [email protected] [email protected]

Charles Paillet Arturo Ortiz-Tapia The Ecole normale sup´erieure de Cachan (ENS Cachan) Mexican Petroleum Institute [email protected] [email protected]

Joaquin Hernandez-Perez MS17 INSTITUTO MEXICANO DEL PETROLEO [email protected] Local 3D Ocean Waves Model for Aquatories with Complex Boundaries MS18 We present an approach for the multi-model coupling of global ocean and local 3D flows in aquatories with complex Fast Solvers for Coupled Problems and Applica- boundaries. The examples of such flows are wetting of tions to Geomechanics a shore line, waves approaching a pier or flow around an offshore platform. The local model is based on the solution Many problems in geophysics comprise interactions of proof the 3D Navier-Stokes equations with free surface and cesses, and are typically formulated as a system of coupled boundary conditions from the global ocean. PDEs. In most cases this systems are transient and often also non-linear. Hence, developing efficient solvers is Kirill Nikitin, Yuri Vassilevski often a delicate task and must include combining suitable Institute of Numerical Mathematics schemes for (i) time integration, (ii) linearization, and (iii) Russian Academy of Sciences geometric and algebraic multigrid solvers. In this presen- [email protected], [email protected] tation, we take an application oriented approach, and focus on the problem classes of poroelasticity problems and density-driven-flow. For these two examples, we comment MS17 on similarities and differences, and then provide details on the solution strategy. An Ocean Oil Spill Model Arne Naegel Challenges of and recent progress in the development of an Goethe University Frankfurt oil model for the fate of surface and subsurface oil spills will [email protected] be summarized. We are building a computational platform for ocean/oil dynamics by tackling modeling and computation together. The goal is to produce a model with variable MS18 resolution and concomitant physics. For specificity we will Modeling of Chemical Enhanced Oil Recovery on summarize how this plays out in the context of modeling General Hexahedral Grids oil spills near the shore. Accurate numerical simulations are required for design and Juan M. Restrepo evaluation of enhanced oil recovery strategies such as ASP Oregon State University (Alkaline Surfactant Polymer) and foam flooding. We dis- Department of Mathematics cuss the significance of accurate fluxes for non-Newtonian [email protected] viscosity calculations. A multipoint flux mixed finite element method is used for discretization. This improves con- Clint Dawson centration and saturation front predictions owing to better Institute for Computational Engineering and Sciences calculation of advection, diffusion and dispersion terms. University of Texas at Austin The numerical results show the effect of accurate fluxes on [email protected] recovery predictions.

Shankar C. Venkataramani Gergina Pencheva University of Arizona Center for Subsurface Modeling, ICES Department of Mathematics University of Texas at Austin [email protected] [email protected]

Gurpreet Singh MS18 The University of Texas at Austin A Flow And Transport Model In Porous Media For Center for Subsurface Modeling Microbial Enhanced Oil Recovery Studies [email protected]

In this work, a flow and transport model which was imple- Kundan Kumar mented using a finite element method to simulate, analyze Department of Mathematics and interpret MEOR processes at core scale under labo- University of Bergen, Bergen, Norway ratory conditions is presented. The flow model is based [email protected] on the oil phase pressure and total velocity formulation, in which the capillary pressure, relative permeabilities, the Changli Yuan effects of gravity and the dynamic porosity and permeabil- Center for Subsurface Modeling, ICES ity modification due to the clogging-declogging phenomena University of Texas at Austin GS15 Abstracts 89

[email protected] Department of Geosciences and Engineering Delft University of Technology Xin Yang [email protected] The University of Texas at Austin [email protected] Matthias Möller Department of Applied Mathematics Mary F. Wheeler Delft University of Technology Center for Subsurface Modeling, ICES [email protected] University of Texas at Austin [email protected] Hans Kraaijevanger, Johan Romate, Hans Groot Shell Global Solutions International Rijswijk MS18 [email protected], [email protected], Robust Mass-Conservative Schemes for Two-Phase [email protected] Flow in Porous Media Jan Dirk Jansen We will present a robust, mass conservative numerical TU Delft, The Netherlands scheme for two-phase flow in porous media. The fluids are ’[email protected]’ assumed immiscible and incompressible. The solid matrix is also assumed non-deformable. The formulation adopted here uses the global pressure and a complementary pres- MS18 sure (obtained by using the Kirchhoff transformation) as Simulating CO2 Foam Sequestration in Porous Me- primary unknowns. The system to be solved includes two dia coupled nonlinear partial differential equations, one degenerate elliptic - parabolic and one elliptic. The discretization CO2 sequestration in saline aquifers usually suffers from in space is based on mixed finite element method (lowest low volumetric sweep efficiency. CO2 foam injection can order Raviart-Thomas elements) and in time on backward lower gas mobility and therefore suppresses the channel- Euler. A robust iterative method is proposed for lineariza- ing caused by heterogenous permeability and the overrid- tion. The convergence of the scheme is rigorously shown, ing caused by gravity and thus increases the storage vol- order of convergence estimates being obtained. The con- ume. We simulate the problem using the reservoir simula- vergence of the linearization scheme does not depend on tor IPARS. The foam model we use considers the change the mesh diameter or on the number of spatial dimensions. of the gas mobility based on the factors of surfactant con- Finally, relevant numerical examples will be presented. centration, gas velocity and limiting water saturation. Florin A. Radu Institute of Mathematics Xin Yang University of Bergen The University of Texas at Austin fl[email protected] [email protected]

Kundan Kumar Mojdeh Delshad, Mary Wheeler Department of Mathematics University of Texas at Austin University of Bergen, Bergen, Norway [email protected], [email protected] [email protected] MS19 Iuliu Sorin Pop Dept of Mathematics and Computer Sciences Frequency Scalable Hessian Preconditioners for TU Eindhoven Seismic Full Waveform Inversion [email protected] Hessian solves are the primary computational bottleneck in Newton’s method for frequency domain full waveform in- Jan M. Nordbotten version. Using traditional preconditioners, the number of University of Bergen Krylov iterations per solve scales poorly with frequency. [email protected] Moreover, each Krylov iteration is expensive, requiring one forward and one adjoint wave solve per frequency per MS18 source. We present a new Hessian preconditioner for frequency domain seismic full waveform inversion that ex- Non-Physical Oscillations in Foam Enhanced Oil hibits better scalability with respect to increasing wave Recovery frequency. If hydrocarbon recovery methods fail because of viscous Nick Alger ﬁngering and gravity override one can turn to enhanced The University of Texas at Austin oil recovery methods, like foam injection. Foam generation Center for Computational Geosciences and Optimization can be described by a set of strongly nonlinear PDEs. For- [email protected] ward simulation methods lead to temporal oscillations, due to discretization artifacts. The heat equation with discontinuous thermal diﬀusivity shows similar oscillations. By Omar Ghattas applying a new discretization scheme we solve this prob- The University of Texas at Austin lem. We propose a similar technique for the foam model. [email protected]

Tan Bui Jakolien M. Van Der Meer University of Texas at Austin 90 GS15 Abstracts

[email protected] fractures and an inhomogeneous rock matrix in the vicinity of the geotechnical openings.

MS19 Klaus-Peter Kr¨ohn Universal Optimization Framework for Robust, Gesellschaft f¨ur Anlagen- und Reaktorsicherheit (GRS) Regularized and Constrained Full Waveform Inver- mbH sion [email protected]

In this talk, we shall describe a scalable universal optimization framework that allows for seamless incorporation of a MS20 broad range of noise models, forward models, regularizers and reparametrization transforms. The formulation covers Fault Leakage Analysis for Geological Co2 Seques- robust noise models (as Huber and students t), as well as tration Using a Coupled Multiphase Flow / Ge- sparse regularizers, projected constraints, and Total Vari- omechanics Model with Embedded Discontinuities ation regularization. The framework is also expandable - we explain the adjustments that are required for any new CO2 injection into saline aquifers bears the risk of fault formulation to be included. leakage or even reactivation. The injected volume that can be contained by a sealing fault is estimated with a coupled Lior Horesh multiphase flow- and geomechanics model where the fault Mathematical Sciences & Analytics is represented as a frictional interface that becomes leaky IBM Research upon failure. The model is discretized with an extended hy- [email protected] brid finite element - finite volume method with split-node discontinuity. Results are contrasted with similar studies Stephen Becker from the literature. University of Colorado at Boulder [email protected] Stephan K. Matthai The University of Melbourne [email protected] Aleksandr Aravkin IBM T.J. Watson Research Center [email protected] Roman Manasipov Montan University of Leoben, Austria Montanuniversität Leoben Ewout van Den Berg [email protected] IBM [email protected] MS20 Sergiy Zhuk IBM Research - Ireland Grid Generation for Simulations of Groundwater [email protected] Flow in Fractured Porous Media In the presented approach we consider the full dimensional MS20 bulk medium and contained fracture networks that we ap- The Peclet Number of Poroelasticity and Its Role proximate by low dimensional manifolds. In order to re- in the Convergence of Multigrid Solvers solve arising jumps in the flow variables, those manifolds are surrounded by a zero-thickness layer of so called ’de- In several geomechanical applications (e.g. simulation of generated elements’ which help to associate additional un- soils), the finite element discretization of poroelasticity sys- knowns with the different fracture sides during discretiza- tems may present unstable solutions. For these situations tion. We describe the required meshing steps and necessary we define a novel Peclet number. It allows to introduce a adjustments in the involved discretization techniques. lower bound on the time step-size that guarantees accuracy of the solution in the n-dimensional case. We discuss the Sebastian Reiter importance of this bound for the convergence of a multigrid Goethe-Center for Scientific Computing solver in a biomechanical application, i.e. the simulation Goethe-Universität Frankfurt of the periodontal ligament. [email protected]

Rolf Krause,MarcoFavino Dmitry Logashenko Institute of Computational Science Goethe Center for Scientiﬁc Computing University of Lugano Goethe University Frankfurt a.M. [email protected], [email protected] [email protected]

MS20 Andreas Vogel University of Frankfurt, Germany Application of an Advanced Fracture Flow Model [email protected] to Field-scale Problems The code d3f (distributed density-driven flow) for simu- Alfio Grillo lations in highly complex ground-water flow systems has Polythecnic of Turin, Italy been advanced by a sophisticated discretization scheme to alfi[email protected] cope with fracture flow. A short sketch of this scheme will be presented as well as simulations of the underground flow Gabriel Wittum system in the granitic rock around the Hard Rock Labora- Goethe Center for Scientific Computing tory at sp, Sweden. The models include tunnels, boreholes, Goethe University Frankfurt GS15 Abstracts 91

[email protected] Dmitry Logashenko, Sabine Stichel Goethe Center for Scientiﬁc Computing Goethe University Frankfurt a.M. MS20 [email protected], Massively Parallel Solvers for Density Driven Flow [email protected]

Multigrid methods for the solution of large sparse matrices Andreas Vogel arising from grid-based discretizations of partial differen- University of Frankfurt, Germany tial equations are well known for their optimal complex- [email protected] ity, i.e., the computation effort only increases linearly with the problem size. This makes them a promising algorithm Gabriel Wittum when focusing on the weak scaling properties of such a Goethe Center for Scientific Computing matrix solver. However, while reducing the problem size Goethe University Frankfurt within a multigrid algorithm on coarser grid levels is its [email protected] strength, this gives rise to a potential performance bottleneck when parallelization is taken into account. Indeed, on coarser grid levels the inner to boundary ratio of the grid MS21 parts assigned to a process become unpleasant and a paral- Representation of the Arctic Ocean in Ocean/sea- lel smoother on those coarse levels will suffer from the fact Ice Components of Current Climate Models that mostly communication at the boundary takes place and only little computation on the inner part is performed. The representation of Arctic Ocean hydrography and cir- In order to overcome this bottleneck we present an algo- culation in 15 coupled global ocean/sea-ice models has rithm that avoids this situation by gathering coarser levels been investigated. All models used the CORE-II atmo- to fewer processors leaving the remaining processors idle. spheric and runoff forcing as specified by the CLIVAR To this end we introduce vertical interface connections that Ocean Model Development Panel. Most models are com- allow this gathering process and adapt the transfer opera- ponents of climate models with a resolution similar to what tors of the multigrid algorithm to respect these interfaces. used in CMIP5. An effort will be made to group model bi- Arriving at a single process on the coarsest level a serial ases based on resolution and choice of vertical coordinate, base solver, e.g., LU factorization, can be used. We show horizontal discretization, and parameterizations. that this approach leads to nice weak scaling behavior for an exemplary application: Discretizing a pde system for Mats Bentsen density driven flow using a vertex-centered finite volume Bjerknes Centre for Climate Research scheme and implicit Euler time stepping we analyze the ef- Bergen, Norway ficiency of the geometric multigrid solver in the first New- [email protected] ton linearization of the first time step. It turns out that up to 130,000 processors the weak scaling efficiency is still Mehmet Ilicak above 80%. Uni Research Climate [email protected] Sebastian Reiter Goethe-Center for Scientific Computing Helge Drange Goethe-Universität Frankfurt University of Bergen [email protected] helge.drange@gfi.uib.no Andreas Vogel University of Frankfurt, Germany MS21 [email protected] Adaptive Refinement Strategies and a Lagrangian Particle Method for Geophysical Flow Gabriel Wittum G-CSC, University of Frankfurt A Lagrangian Particle Method (LPM) for geophysical flow [email protected] on the sphere is introduced for applications related to weather and climate modeling. LPM is characterized by the Lagrangian formulation of the equations of motion, the MS20 use of singular Green’s functions to solve PDEs, and an Modelling and Computation of Thermohaline adaptively refined remeshing procedure that minimizes er- Groundwater Flows in Fractured Porous Media ror due to Lagrangian mesh distortion. Standardized test cases for the tracer transport equation and the barotropic Density driven and thermohaline flows can show convec- vorticity equation are used to demonstrate the convergence tion rolls, i.e. a kind of simplified vortex formation. This properties of the scheme and to compare its error to meth- plays a role in the computation of these flows in fractured ods employed by current dynamical cores. Several adaptive porous media. We simulate the flows using an adaptive fi- refinement strategies are discussed to improve both the ef- nite volume algorithm. For the representation of fractures, ficiency and accuracy of the method as flows evolve in time. two approaches are used, a full-dimensional and one with Ongoing work to extend the method to the shallow water reduced dimension. We derive a criterion for the validity equations is discussed. of the simplified representation and present an algorithm using adaptive dimensional representation. Peter A. Bosler University of Michigan Alfio Grillo Applied and Interdisciplinary Mathematics Dept. of Mathematical Sciences [email protected] Polythecnic of Turin, Italy alfi[email protected] Mark A. Taylor 92 GS15 Abstracts

Sandia National Laboratories, Albuquerque, NM Models [email protected] As atmospheric models are pushed towards higher and higher resolutions, there is an increasing need to re- MS21 evaluate the numerical methods that have traditionally Cloud Simulations with the Nonhydrostatic Unified been used for simulating atmospheric flows. This talk will Model of the Atmosphere (NUMA) discuss some of the outstanding issues that still remain for global atmospheric modeling at high resolutions, and This talk will describe our recent work on cloud simula- current efforts to address these issues in next-generation tions using the Nonhydrostatic Unified Model of the At- modeling systems. mosphere (NUMA). NUMA is a scalable 3D compressible Navier-Stokes solver designed for weather prediction. Paul Ullrich NUMA is unified in using both continuous and discontin- University of California, Davis uous element-based Galerkin methods. We will present [email protected] results for 3D thunderstorm simulations and will describe all of the necessary algorithms required for such simulations including the scalability of the model, stabilization, Jorge E. Guerra and visualization. Department of Land, Air and Water Resources University of California, Davis Andreas Mueller, Daniel Abdi, Simone Marras, Michal A. [email protected] Kopera, Francis X. Giraldo Naval Postgraduate School [email protected], [email protected], [email protected], MS22 [email protected], [email protected] Interactive Processing of Geophysical Data

MS21 Almost all geophysical software is written as a series of batch processing steps, sometimes with a GUI tacked on. Multiple Time Scales and Pressure Forcing in Dis- To process a dataset the user sets some parameters, runs continuous Galerkin Approximations to Layered the data through a single step, evaluates the results, then Ocean Models reruns or moves to the next processing step. The ap- Barotropic-baroclinic time splitting is widely used in ocean proach can be thought of pushing data through a process- circulation modeling to separate the fast and slow motions ing pipeline, storing intermediate datasets on disk. Twenty into distinct subsystems. This talk addresses two aspects of years ago this was an optimal approach given the relative this usage in the context of DG methods. (1) For purposes speed of compute vs. IO and limited RAM. Today, rela- of computing pressure at cell edges, a splitting of variables tively, IO is much more expensive than compute and RAM makes it possible to reduce the associated Riemann prob- is several orders of magnitude larger. An alternate ap- lem to a much simpler system of lower dimension. (2) proach is to think of processing as an interactive process. The numerical solutions of the layer equations and the fast When you view a given portion of your dataset, data is vertically-integrated barotropic equations must continually pulled from disk, or some intermediate memory level, run be made consistent. The method discussed here has the un- through the various processing steps and displayed. When expected eﬀect of introducing a type of time ﬁltering into you move to a new location the process is repeated. As the forcing for the layer equations, so that those equations you add additional processing steps to your chain, you get canbesolvedstablywithalongtimestep. instant feedback.

Robert L. Higdon Robert Clapp Oregon State University SEP, Stanford University [email protected] [email protected]

MS21 MS22 A Global Ocean Circulation Model Based on a Madagascar Opens-source Software Package: In- Mimetic Discretization Approach terface to Reproducible Research A new global ocean general circulation model, ICON-O, is introduced. ICON-O solves the ocean primitive equa- Madagascar is an active open-source project, which pro- tions on a triangular icosahedral grid. The models dy- vides tools for large-scale multidimensional data analysis namical core and its subgridscale closures coherently uses of geophysical data, as well as reproducible documents a novel mimetic discretization approach. The discretiza- with workflow examples. Since its public release in 2006, tion is described and numerical experiments are shown to more than 80 people have contributed to the project. The demonstrate the models capabilities. ICON-O is the ocean main data object in Madagascar is a multidimensional ar- component of the new coupled atmosphere-ocean model ray stored as a file on disk. Following the Unix philosophy, ICON that the Max Planck Institute for Meteorology and Madagascar programs are filters that process files and can the German Weather Service jointly develop. be combined with Unix pipes or scripts. This allows for a great flexibility in mixing languages and programming in- Peter Korn terfaces. While the majority of Madagascar programs are Max Planck Institute for Meteorology written in C, there are programming interfaces to other lan- [email protected] guages: Fortran-77, Fortran-90, C++, Java, Matlab, and Python. I will discuss the importance of reproducible research (as pioneered by Jon Claerbout and his students at MS21 Stanford) and will describe examples of designing parallel Towards Robust Multi-Scale Global Atmospheric computational algorithms by taking advantage of Mada- GS15 Abstracts 93

gascar’s Unix-style encapsulation. Modeling algorithms involve physical fields, the laws coupling them, and numerical realizations (grids, finite ele- Sergey Fomel ment meshes); optimization algorithms are built on math- University of Texas at Austin ematical abstractions such as vectors, linear operators, and [email protected] differentiable functions. Bridging these disparate levels of abstraction to construct inversion applications poses a software design problem. The author will review the strengths MS22 and weaknesses of a libary-based solution. Pysit: Seismic Imaging Toolbox for Python William Symes The Python Seismic Imaging Toolbox (PySIT) is research- Rice University scale platform for prototyping numerical algorithms for full [email protected] waveform inversion (FWI). PySIT is a common platform which implements standard methods from the literature and from which researchers can quickly develop and repro- MS23 ducibly compare or benchmark new methods against the state-of-the-art. This talk will outline PySIT’s structure in A Global-Local Optimization Template for Multi- the context of the mathematical framework for FWI, with ple History-Matched Reservoir Parameters an emphasis on the accessibility enabled by the Python programming language. Parameterization of petroleum reservoirs is an important component of reservoir management. However, the process Russell Hewett of reservoir parameterization is fraught with nonunique- Total ness of estimated parameters. Such nonuniqueness leads [email protected] to large uncertainty and risks in reservoir management. One way to reduce and quantify the uncertainty in parameter estimation is to generate multiple equiprobable realiza- MS22 tions of the parameters. We introduce an algorithm called Canopy Geo GLOCAL that generates multiple realizations of reservoir parameters by performing global optimization at a coarse- Abstract not available at time of publication. scale and local optimization at a finer scale.

Eric Jones Abeeb Awotunde Enthought King Fahd University of Petroleum & Minerals [email protected] [email protected]

MS22 MS23 The MRST Open-source Toolbox for Reservoir Multi-Scale Assimilation with Scale Dependent Simulation Discrepancy in Model and Observation The MATLAB Reservoir Simulation Toolbox (MRST) is a We present a method of using classical wavelet based multi- free, open-source framework for rapid prototyping of new resolution analysis to separate scales in model and ob- computational methods and workflow tools for reservoir servations during the application of an ensemble Kalman engineering. In the talk, we outline how MRST to can be filter. When forecasts are performed using modern data used to quickly implement simulators that are efficient and assimilation methods observation and model error can be robust, easy to extend with new models and functionality, scale dependent. The dependence on scale in observational and applicable to models of industry-standard complexity. error can be caused by properties of the observation mech- In particular, we discuss two of the key numerical technolo- anism. Scale dependent model error can be due to biases gies implemented in the software: in the model when poorly understood physical processes • discrete differentiation and averaging operators, which are excluded. During data assimilation the blending of er- enable you to write codes in a compact and readable ror across scales can result in model divergence since large form that is close to the mathematical formulation of errors at one scale can be propagated across scales dur- the discretized flow equations, ing the analysis step. Applying the multi-scale decomposi- • automatic differentiation, which enables you to evalu- tion causes little computational increase over standard en- ate the values of gradients, Jacobians, and adjoint- semble Kalman filtering. Our methods are demonstrated based sensitivities to machine-precision accuracy on a one dimensional Kuramoto-Sivashinsky (K-S) model without having to analytically compute the necessary and an application involving the forecasting of solar pho- partial derivatives. tospheric flux. Kyle S. Hickmann Knut-Andreas Lie Tulane University SINTEF ICT, Dept. Applied Mathematics [email protected] [email protected] Humberto C. Godinez MS22 Los Alamos National Laboratory Applied Mathematics and Plasma Physics Coupling High-Performance Modeling with Opti- [email protected] mization: a Library Approach to Building Inver- sion

Inversion via data-ﬁtting combines modeling (of wave phe- MS23 nomena, for the seismic incarnation) with optimization. Identiﬁability of Location and Magnitude of Model 94 GS15 Abstracts

Anomalies from Production Data similation of production data. Computational examples show that using these estimates in INSIM results in rea- Classic identifiability analysis of flow barriers in incom- sonable future performance predictions. pressible flow reveals that it is not possible to identify the location and permeability of low-permeable barriers from Albert C. Reynolds, Zhenyu Guo, Hui Zhao production data, and that only averaged reservoir proper- University of Tulsa ties in-between wells can be identified. We extended the [email protected], [email protected], zhao- classic analysis by including compressibility effects. Nu- [email protected] merical and semi-analytical results show that it is possible to identify the location and the magnitude of the permeability in the barrier from noise-free data. By introducing MS23 increasingly higher noise levels the identifiability gradually deteriorates, but the location of the barrier remains iden- Data Assimilation for Complex Geological Models tifiable for much higher noise levels than the permeability. Using Optimization-Based Pca Parameterizations A parameterization procedure based on principal compo- Siavash Kahrobaei nent analysis (PCA), referred to as optimization-based Delft University of Technology PCA or O-PCA, is described. The method enables the rep- [email protected] resentation of non-Gaussian geological models in terms of relatively few uncorrelated parameters. The O-PCA repre- Gerard Joosten sentation is incorporated into a randomized maximum like- Shell lihood (RML) method, which entails gradient-based min- [email protected] imization, to enable data assimilation and uncertainty assessment. Results demonstrate the efficacy of the subspace RML method for history matching two-, three-facies, and Paul Van den Hof bimodal geomodels. TU Eindhoven and TU Delft [email protected] Hai X. Vo Stanford University Jan Dirk Jansen [email protected] Delft University of Technology Department of Geotechnology Lou J. Durlofsky [email protected] Stanford University Dept of Petroleum Engineering MS23 [email protected] Probabilistic Particle Swarm Optimization (Pro- Pso) for Using Prior Information and Hierachichal MS24 Parameters Multiscale Modeling of Spatially Heterogeneous In this research, the equations in general Particle Swarm Cellular Processes Including Metabolic Channeling Optimization (PSO) are reformulated from a probabilistic point of view. The mathematics of PSO algorithm is We make a rigorous derivation of an upscaled model converted from the behavior of stochastic particle motion of a system of microscopic non-linear reaction diffusion to the equivalent sampling from the distribution (PDF) of equations in a porous medium consisting of three com- particle positions. The equations for the probability dis- ponents separated by interfaces. The differential equa- tribution function of the particles position are derived. By tions in the different domains are coupled by non-linear doing so, this probabilistic PSO (Pro-PSO) provides the flux-transmission conditions. Additionally we consider means of incorporating any probabilistic form of prior in- a reaction-diffusion process on the microscopic surface. formation into PSO framework and utilizing parameters These models can be applied e.g. to metabolic processes hierarchically to improve computational performance. in (plant) cells, especially under consideration of metabolic channeling at mitochondrial membranes. Jaehoon Lee Stanford University Markus Gahn [email protected] University of Erlangen-Nuermberg Mathematics Department Tapan Mukerji [email protected] Department of Geophysics Stanford University Peter Knabner [email protected] Department of Mathematics University of Erlangen [email protected] MS23 Calibration and Prediction with a Data-Driven Maria Neuss-Radu Model University of Erlangen-Nuremberg We derive and implement an interwell reservoir simulation Mathematics Department model (INSIM) for model calibration and future perfor- [email protected] mance prediction. After defining a connection list between nodes in a network model, pressures are solved as in IMPES and saturations are calculated by a front tracking proce- MS24 dure. Parameters along connections are estimated by as- Multiscale Modelling and Simulation of Processes GS15 Abstracts 95

in Membranes and Tissues [email protected], [email protected]

We are concerned with processes in membranes and tissue. Using multi-scale homogenization methods it is possible to MS24 derive reduced systems. In many applications processes Methane Transport in the Hydrate Zone have to be modelled on the molecular scale. We consider a population of ions penetrating a membrane through chan- A two-phase two-component model is formulated for the nels. A stochastic model for the dynamics is developed and advective-diﬀusive transport of methane in liquid phase simulated in case of nano- and micro-channels. This report through sediment with the accompanying formation and is based on joint research with Neuss-Radu (Erlangen) and dissolution of methane hydrate. This free-boundary prob- 1 Capasso, Morale and Zanella (Milano). lem has a unique generalized solution in L ; the proof combines analysis of the stationary semilinear elliptic Dirichlet Willi J¨ager problem with the nonlinear semigroup theory in Banach IWR, University of Heidelberberg space for an m-accretive multi-valued operator. [email protected] Ralph Showalter, Malgorzata Peszynska Department of Mathematics MS24 Oregon State University [email protected], A Multi-Scale Approach to Modeling of Gas Trans- [email protected] port in Shales

We consider gas transport in shales, consisting of MS24 nanoporous organic material, microporous inorganic ma- Numerical Simulation of Plaque Formation in Ves- trix, and a system of secondary fractions. The model sels incorporates free gas diffusion and filtration as well as the effect of gas adsorption and diffusion of desorbed gas. In this talk, we formulate a model to describe plaque Macroscopic equations for free gas amount in-place are ob- formation. This model includes the interaction between tained through two successive steps: homogenization over blood flow and vessel wall, and the penetration of chemical nanoporous level leads to a microscopic description which is species in vessels. Numerical simulations are performed to further homogenized to lead to description of macroscopic investigate the mechanisms, that lead to the formation and flow. growth of plaques. We verify the numerical approach by convergence analysis of numerical solutions and describe Viktoria Savatorova effective methods to maintain the mesh quality under a University of Nevada Las Vegas, USA/ NRNU ”MEPhI”, large deformation. Russia [email protected] Yifan Yang Interdisciplinary Center for Scientific Computing(IWR) Elena L. Kossovich University of Heidelberg National University of Science and Technology MISIS [email protected] Moscow, Russia [email protected] Thomas Richter Institute for Applied Mathematics Alexey Talonov Heidelberg University National Research Nuclear University [email protected] Moscow, Russia [email protected] Willi Jäger IWR Heidelberg University MS24 [email protected] Analysis of Hemodynamic Factors in the Simula- tions of Atherosclerotic Plaque Growth Maria Neuss-Radu University of Erlangen-Nuremberg Atherosclerosis, the major cause of cardiovascular disease, Mathematics Department is a chronic inflammation that starts when LDL cholesterol [email protected] enter the intima of the blood vessel to be oxidized. This complex process leads to the formation of an atherosclerotic plaque and possibly to its rupture. This talk is de- MS25 voted to the study of simplified mathematical models cap- Almost Parallel Flows in Porous Media turing essential features of the early stage of atherosclerosis and to the influence of hemodynamic factors in the simu- We consider a reduced two-phase flow model for mostly lations of atherosclerotic plaque growth. unidirectional porous media flows. It is a nonlinear transport equation, in which velocity depends nonlocally on sat- Adelia Sequeira uration [Yortsos, 1995]. However, solutions of this model Department of Mathematics cannot be defined in the distributional sense, as a direct Instituto Superior Tecnico consequence of the reduced regularity of the two-phase flow [email protected] model. Therefore, we consider a Brinkman two-phase flow model, where existence of weak solutions is proved [Co- Telma Silva, Jorge Tiago clite et al., 2014]. Following [Yortsos, 1995], we derive CEMAT, Depart. of Mathematics, IST, Universidade de an extended model similar to the model proposed by Has- Lisboa sanizadeh and Gray [Hassanizadeh and Gray, 1993], but in 96 GS15 Abstracts

a completely different context. Assuming a medium of lay- dimensional multi-phase flow code using the HPC numeri- ers, the extended model is a system of 1D equations coupled cal framework Arcane. We first show results obtained with due to vertical mixing. We study the effect of the higher- this code applied to numerically challenging test cases in order terms in the extended model and the mediumsnum- reactive transport modelling such as precipitation and dis- ber of layers on the fluids spreading speed, which is usually solution of minerals or gas-water equilibrium. We then test overestimated [Menon and Otto, 2006,Yortsos and Salin, the code for validation against more realistic benchmark 2006]. studies and discuss the results.

Alaa Armiti-Juber Thibault Faney University of Stuttgart IFPEN, Applied mathematics department [email protected] 1-4 avenue du bois préau, 92500 Rueil-Malmaison, France [email protected] Christian Rohde University of Stuttgart Anthony Michel Institut für Angewandte Analysis und Numerische IFP Simulation [email protected] [email protected] Quang Long Nguyen IFPEN MS25 [email protected] A Numerical Model for Reactive Twophase Multi- component Flow MS25 We present a numerical framework for efficiently simulat- Volume Averaging for Dispersion and Heteroge- ing partially miscible two-phase flow with multicomponent neous Nonlinear Reaction in Porous Media reactive transport in porous media. The system of coupled PDEs, ODEs and AEs is treated by a model preserving In this study we conduct upscaling for mass transport in reformulation technique and the use of a nonlinear, im- porous medium with heterogeneous nonlinear reaction at plicitly defined resolution function. By choosing persistent the fluid-solid interface in a multi-scale dissolution prob- primary variables and using a complementarity approach, lem, using the method of volume averaging. We investi- interphase mass exchange and the local appearance and gate the impact of flow properties, chemical features and disappearance of the gas phase can be handled. nonlinear reaction orders on the effective parameters in the Fabian Brunner macro-scale model, which can be obtained by solving the University of Erlangen corresponding closure problems. The importance of two [email protected] non-traditional effective parameters is studied in an application.

MS25 Jianwei Guo,MichelQuintard Institut de Mécanique des Fluides de Toulouse A Mathematical Formulation for Reactive Trans- [email protected], [email protected] port in Porous Media Adapted to Co2 Sequestra- tion Farid Laouafa Carbon capture and storage (CCS) is currently one of the INERIS major options to reduce greenhouse gas emissions from [email protected] power plants. However, the implementation of CCS has been slowed down by uncertainties about the long term evolution of injected carbon into deep saline aquifers. Re- MS25 active transport numerical models [Steefel, C. I. et al., Re- Numerical Simulation of Two-Phase Multi- active transport modeling: An essential tool and a new Component Flow with Reactive Transport in research approach for the Earth sciences, Earth and Plan- Porous Media etary Science Letters, 240, 53955, 2005] are used to predict temperature and pressure variations, brine and gas phases Two-phase multicomponent flow with chemical reactions displacement, and chemical effects of gas-water-rock interplay a significant role for the long term simulation of CO2 actions. One of the main challenges of these models is to geological storage. We propose a decoupling algorithm accurately represent the coupling between transport phe- based on the separation of the system between water and nomena and mass transfer occurring in sub-surface porous gas components (with the most influence on the flow sub- media. system), and the dissolved components (undergoing reac- In this work, we present a new mathematical formulation tive transport). We show numerically that the mass con- for reactive transport in porous media. This fully implicit servation error introduced is negligible. The method is multi-component, multi-phase flow formulation is able to validated on test cases from the literature, using a code deal with phase appearance and disappearance combined based on DuMuX. with stoichiometric mass transfer. The novelty of our work consists in the extension of concepts used so far to deal Michel Kern only with phase equilibrium [Coats, K. H., An Equation of INRIA State Compositional Model, SPE-8284-PA, 1980] [Eymard, [email protected] R. et al, Vertex-centred discretization of multiphase compositional Darcy flows on general meshes, Computational Etienne Ahusborde Geosciences, 16, 987-1005, 2012] to both homogeneous and Université de Pau et des Pays de l’Adour heterogeneous equilibrium reactions. Pau, France We implement our mathematical formulation in a three- [email protected] GS15 Abstracts 97

Viatcheslav Vostrikov large-scale numerical models. Université de Pau et des Pays de l’Adour & Maison de la Simulation, France Dany Dumont [email protected] UniversitéduQuébec àRimouski dany [email protected]

MS25 High Order Discretization for Simulating Miscible MS26 Displacement Process in Porous Media Ocean Waves Drive a Turbulent Ocean

We present a high order method for miscible displace- The oceans are the major reservoir of heat and carbon on ment simulation in porous media. The method is based short timescales, and the circulation of the oceans results on discontinuous Galerkin discretization with weighted av- from the wind and buoyancy changes that flow through the erage stabilization technique and flux reconstruction post- surface. All of this action for the climate system must pass processing. The mathematical model is decoupled and through the ocean surface layer and its dynamics, which solved sequentially. We apply domain decomposition and are interesting in their own right. I will discuss some of algebraic multigrid preconditioner for the linear system re- the most important processes in the surface layer, relate sulting from the high order discretization. The accuracy new results involving the roles of surface waves and sub- and robustness of the method are demonstrated in the con- mesoscale fronts and instabilities, and quantify the signifi- vergence study with analytical solutions and heterogeneous cance of these phenomena in the functioning and sensitivity porous media respectively. We also investigate the effect of the climate system. of grid orientation and anisotropic permeability using high order discontinuous Galerkin method in contrast with cell- Baylor Fox-Kemper centered finite volume method. The study of the parallel Brown University implementation shows the scalability and efficiency of the [email protected] method on parallel architecture. We also verify the simulation result on highly heterogeneous permeability field from MS26 the SPE10 model. Propagation of Torsional Surface Wave in Jizhou Li An Anisotropic Porous Layer over a Non- Rice University Homogeneous Substance Department of Computational and Applied Mathematics [email protected] The present paper studies the propagation of torsional surface waves in an anisotropic porous medium over a non-homogeneous substance. Two types of inhomogene- MS26 ity namely quadratic and hyperbolic have been considered Microseismicity, Seismic Velocity, and Observa- in the lower substance. The dispersion equation has been tions That Reveal Crustal Response to Dynamic obtained for each case in a closed form by means of variable Stress separable method. In a particular case, when upper layer is isotropic with non porous and lower half-space is ho- Stress state and elastic properties of the Earths crust are mogeneous the dispersion equation coincides with classical important to seismic hazards, earthquake physics, and re- result of Love wave. Dispersion curves are plotted for dif- source extraction and can be observed indirectly through ferent variation in poroelastic constant and inhomogeneity seismicity, seismic velocities, and strain. Dynamic stresses parameters. The effects of the medium characteristics on produced by the 2012 M8.6 Indian Ocean earthquake trig- the propagation of torsional surface waves are discussed. gered bursts of shallow normal faulting events offshore Japan which are associated with an increase in seismic ve- Santimoy Kundu locities onshore. Increased seismic velocities are associated Indian School of Mines, Dhanbad with changes in the strain field produced by normal fault- kundu [email protected] ing earthquakes. Shishir Gupta Andrew A. Delorey Indian School of Mines, Dhanbad, Jharkhand, Los Alamos National Laboratory India-826004 [email protected] shishir [email protected]

Paul Johnson Anup Saha, Santanu Manna Los Alamos National Laboratory, USA Indian Schoo of Mines, Dhanbad [email protected] [email protected], [email protected]

MS26 MS26 On Modeling Wave-Induced Sea Ice Motion and Use of the Effective Wavefield in the Prediction Break-Up at the Large Scale of Ocean-Wave Interactions with Rough Extended Obstacles Granular properties of sea ice in the marginal ice zone (MIZ) are strongly affected by surface gravity waves. They Ocean waves attenuate with distance travelled into the sea- cause floes to break, move back and forth, drift and col- ice covered ocean. This is reminiscent of the wave localisa- lide, which in turn influence the large-scale behavior of the tion phenomenon. In certain situations, the effective wave- ice cover. In this perspective, the floe size distribution is field, which is amenable to multiple-scale methods, can be central for modeling MIZ dynamics. This talk will discuss used to predict attenuation, but in others it is highly in- ways to model wave-ice interactions and their effects in accurate, e.g. attenuation due to a rough seabed in inter- 98 GS15 Abstracts

mediate water depth. We report recent progress on this [email protected] phenomenon, with a focus on attenuation due to sea ice.

Sebastian Rupprecht, Malte A. Peter MS27 University of Augsburg Dynamic X-ray Microtomography: Displacement [email protected], Processes and Relaxation Dynamics in Multiphase [email protected] Flow With recent advances at X-ray micro-computed tomogra- Luke Bennetts phy synchrotron beam lines, it is now possible to study University of Adelaide pore-scale flow in porous rock under dynamic flow condi- [email protected] tions. The collection of 4 dimensional data allows for the direct 3D visualization of fluid-fluid displacement in porous Hyuck Chung rock as a function of time. With this data we are able to Auckland University of Technology identify individual imbibition and drainage events, predict [email protected] oil blob mobilization, measure interfacial curvature, and monitor relaxation dynamics during multiphase flow.

MS26 Ryan Armstrong School of Petroleum Engineering Wave-Mean Flow Interactions in the Ocean University of New South Wales [email protected] Inertia-gravity waves and mean flows associated with lateral density gradients are ubiquitous in the ocean. Clas- Holger Ott sical theory predicts that the interaction between the fast Shell Global Solutions International B.V. waves and the slow mean flows should be weak. New the- [email protected] ories suggest, however, that this interaction can be strong at ocean fronts, regions where lateral density gradients are Apostolos Georgiadis, Maja Rücker especially intense. An overview of these theories will be Shell Global Solutions International BV presented and the implications for the energetics of the [email protected], [email protected] ocean circulation will be discussed. Steffen Berg Leif Thomas Shell Stanford University steff[email protected] [email protected]

MS27 MS27 Kinematics of Multiphase Flow in Porous Media: Imaging Multiphase Dynamics with Fast Micro- Insights from Micro-Models Tomography Microfluidic experiments are used to validate a two-fluid- phase flow model for porous medium systems that includes We present recent work using dynamic synchrotron based components based upon both conservation equations and microtomography to image dynamic drainage and im- kinematics. Laboratory experiments were performed in bibition at a resolution of 4 microns. Three drainage which the external fluid pressures were varied and the sys- events were analysed, showing equilibrium capillary pres- tem was observed as it dynamically relaxed to an equi- sure changes and both local and distal snap-off. Capillary librium state. Experimental observations showed varying pressure measurements of disconnected and connected gan- time scales for changes in boundary pressures, fluid satu- glia show that snap-off must be caused by dynamic (rather rations, and interfacial curvatures, corresponding with the than quasi-static) forces. Snap-off during imbibition, how- mechanisms formulated in the theoretical model. ever, appears to be an equilibrium process where quasi- static assumptions apply. Amanda Dye University of North Carolina Matthew Andrew [email protected] Imperial College London [email protected] James E. McClure Advanced Research Computing Hannah Menke, Kamal Singh Virginia Tech Department of Earth Science and Engineering [email protected] Imperial College London [email protected], [email protected] Laura J. Pyrak-Nolte Department of Physics Martin J. Blunt Purdue University Department of Earth Science and Engineering [email protected] Imperial College [email protected] William Gray University of North Carolina Branko Bijeljic [email protected] Department of Earth Science and Engineering Imperial College London Cass T. Miller GS15 Abstracts 99

University of North Carolina tems. Free flow and porous medium models are coupled Chapel Hill with the transition region model via appropriate interface casey [email protected] conditions. The transition region model is an alternative to the sharp interface model. The two modeling approaches will be compared for single-phase and two-fluid-phase sys- MS27 tems, and numerical simulation results will be presented. Physics-based Models of Multiphase Flow in Porous Media Iryna Rybak Formulation of models of multiphase flow in porous me- Universität Stuttgart dia is complicated by the need to formulate equations at [email protected] the macroscale, to account for processes occurring at interfaces between phases, and to ensure that smaller scale Cass Miller processes are properly accounted for. These complications Environmental Sciences and Engineering Department have caused some ill-posed models to be proposed and im- University of North Carolina plemented. Here, we point out some inconsistencies, pro- casey [email protected] pose a proper model, and demonstrate some of the existent processes that impact system behavior. MS28 William G. Gray Issues with Coupling Macrophysics and Micro- University of North Carolina - Chapel Hill physics in the ACME Climate Model [email protected] Because the equations governing cloud parameterizations Amanda Dye are uncertain, relatively little effort has been put into their University of North Carolina numerical implementation. We show here, however, that [email protected] numerics errors in the implementation of and coupling between macrophysics and microphysics parameterizations in James E. McClure the ACME model have a first-order impact on global cli- Advanced Research Computing mate. Substepping or using more sophisticated numerical Virginia Tech schemes for macrophysics and microphysics are shown to [email protected] reduce this error. Peter Caldwell Cass T. Miller Lawrence Livermore Nat’l Lab University of North Carolina [email protected] Chapel Hill casey [email protected] MS28 MS27 Numerical Errors in Coupling Micro and Macro- physics in the Community Atmosphere Model Digital Rocks Portal for Fast Storage and Retrieval of Porous Microstructure Images We investigate numerical errors in version 2 of the Morrison-Gettelman microphysics scheme and its coupling The recent imaging advances (such as X-ray microtomog- to a development version of the macrophysics scheme in raphy) have provided datasets that reveal the pore-space version 5 of the Community Atmosphere Model (CAM5). microstructure (nanometer to centimeter scale) and allow Our analysis utilizes the Kinematic Driver framework, investigation of flow and mechanical phenomena from first which combines CAM5 macro- and microphysics schemes principles using numerical approaches. However, images with idealizations of all other model components making it are large, from diverse sources and not easily accessible. easier to diagnose problems. Initial results suggest that nu- We are developing an open repository that organizes im- merical convergence requires time steps much shorter than ages and related measurements of different porous materi- those typically used in CAM5. als, jumpstarts productivity and enables scientific inquiry and engineering decisions founded on data-driven basis David J. Gardner (https://pep.tacc.utexas.edu/). Lawrence Livermore National Laboratory [email protected] Joyce Rigelo University of Wyoming [email protected] Peter Caldwell Lawrence Livermore Nat’l Lab [email protected] Masa Prodanovic University of Texas at Austin Department of Petroleum and Geosystems Engineering Jean Sexton [email protected] Southern Methodist University [email protected]

MS27 Carol S. Woodward Modeling Coupled Porous Medium and Free Flow Lawrence Livermore Nat’l Lab Systems using TCAT Approach [email protected] Thermodynamically constrained averaging theory (TCAT) is applied to formulate a solvable closed model for the tran- MS28 sition region between porous medium and free ﬂow sys- A Finite-Diﬀerence Algorithm with Characteristic- 100 GS15 Abstracts

Based Semi-Implicit Time-Integration for the Euler Indiana University Equations with Gravitational Forcing [email protected]

We propose a high-order finite-difference algorithm for at- Mickael Checkroun mospheric flows with semi-implicit time-integration. A University of California, Los Angeles characteristic-based flux-splitting is introduced to separate [email protected] the slow (convective) and fast (acoustic) modes. Additive Runge-Kutta methods are used to integrate in time; the Arthur Bousquet fast modes are solved implicitly while the slow modes are Indiana University solved explicitly. We verify our approach for benchmark at- [email protected] mospheric flow problems, and show that the semi-implicit approach allows significantly higher time-step sizes without compromising accuracy and resolution. Joe Tribbia National Center for Atmospheric Research Debojyoti Ghosh [email protected] Mathematics and Computer Science Division Argonne National Laboratory [email protected] MS28 A Simple But Effective Method for Quantifying Emil M. Constantinescu and Attributing Time-Stepping Errors in Climate Argonne National Laboratory Models Mathematics and Computer Science Division [email protected] We present a test strategy that evaluates the time-step convergence properties of atmospheric general circulation MS28 models, with special attention to the representation of sub- Physics Dynamics Coupling in Atmospheric Mod- grid scale processes. The method provides a quantitative els: Review and Outlook assessment of the overall time-stepping error in a model. It can also help identify which processes and assumptions Physics dynamics coupling (PDC) in atmospheric models are responsible for poor numerical convergence. is a multidisciplinary problem. It has recently found a platform in the PDC workshop series. Summarizing the Hui Wan, Philip J. Rasch results of the first workshop in this series, held recently Pacific Northwest Nat’l Lab in Ensenada, Mexico, this talk will outline the core prob- [email protected], [email protected] lem and current and future issues. Following a review of the literature the impact of physics dynamics coupling on Mark A. Taylor model performance, analysis to support design strategies Sandia National Laboratories, Albuquerque, NM and idealized testing will be discussed. [email protected] Markus Gross Christiane Jablonowski CICESE University of Michigan [email protected] Ann Arbor MI 48109-2143 [email protected] MS28 Numerical Simulations of the Humid Atmosphere above Mountain MS29 On the Role of Constrained Linear Optimization to We aim to study a finite volume scheme to solve the two Construct Higher-order Mimetic Divergence Oper- dimensional inviscid primitive equations of the atmosphere ators with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions. In that respect, a version of a projection method is introduced We develop a general algorithm implementing a variant to enforce the compatibility condition on the horizontal of the Castillo-Grone Method (CGM) called the Castillo- velocity field, which comes from the boundary conditions. Runyan Method (CRM) to construct k-th order mimetic The resulting scheme allows for a significant reduction of divergence operators (k even). This algorithm is then mod- the errors near the topography when compared to more ified to study the restrictions of the CRM, when it comes to standard finite volume schemes. We then report on nu- the construction of uniformly eight-order accurate mimetic merical experiments using realistic parameters. Finally, divergence operators. This modification consists of repos- the effects of a random small-scale forcing on the velocity ing the problem of constructing an eight-order divergence equation is numerically investigated. The numerical results as a constrained linear optimization (CLO) problem, thus show that such a forcing is responsible for recurrent large- yielding a new variant of the CGM implemented by means scale patterns to emerge in the temperature and velocity of a CLO-based algorithm. fields. Peter Blomgren, Jose Castillo YoungJoon Hong San Diego State University Indiana University [email protected], [email protected] [email protected] Eduardo J. Sanchez Roger M. Temam Computational Science Research Center Inst. for Scientific Comput. and Appl. Math. San Diego State University GS15 Abstracts 101

[email protected] ing the Castillo-Grone method, satisfy the conservation laws of their continuous counterparts. To demonstrate the efficacy of the mimetic discretization scheme, different vari- MS29 ations of the RTM algorithm are solved and compared. Mimetic Discretization Operators Trevor Hawkins Mimetic discretizations or compatible discretizations have San Diego State University been a recurrent search in the history of numerical meth- Department of Mathematics and Statistics ods for solving partial differential equations with variable [email protected] degree of success. There are many researches currently active in this area pursuing different approaches to achieve Peter Blomgren this goal and many algorithms have been developed along San Diego State University these lines. Loosely speaking, ”mimetic” or ”compatible” [email protected] algebraic methods have discrete structures that mimic vector calculus identities and theorems. Specific approaches to discretization have achieved this compatibility follow- MS29 ing different paths, and with diverse degree of generality in Well-Posed Boundary Conditions for the Incom- relation to the problems solved and the order of accuracy pressible Vorticity Equation Using a New High obtainable. Here, we present theoretical aspects a mimetic Order Mimetic Arakawa-Like Jacobian Differential method based on the extended Gauss Divergence Theo- Operator rem as well as examples using this methods to solve partial differential equations using the Mimetic Library Toolkit Mimetic schemes are widely used in long-time computa- (MTK). tions of geophysical flows. A high order mimetic expression for the celebrated Arakawas Jacobian for the two- Jose Castillo dimensional incompressible vorticity equation is developed. Computational Science Research Center Mimetic properties such as skew-symmetry, energy and en- San Diego State University strophy conservation for the semi-discretization are proved [email protected] using summation-by-parts operators. A new form of well- posed boundary conditions is derived on a general two- MS29 dimensional domain. The discrete version of the boundary conditions are weakly imposed. Numerical experiments Roofline-based Optimization of Elastic Wave Prop- corroborate the results. agation with Mimetic Free Surface Cristina La Cognata Elastic full wave propagation is an expensive process in Linköping University terms of both computational resources and development of [email protected] the software needed to perform it. Therefore, it is desirable to optimize the performance of the code while minimizing the development costs. We present the roofline-directed Chiara Sorgentone methodology to determine the impact of the optimization La Sapienza University of Rome process and as a guideline to know when to stop it. An [email protected] isotropic problem with mimetic free surface is shown as example. Jan Nordstrom Department of Mathematics, Linköping University Miguel Ferrer SE 581 83 Linköping, Sweden Barcelona Supercomputing Center [email protected] [email protected]

Mauricio Hanzich MS29 Barcelona Supercomputing Center (BSC) Numerical Methods in Geophysical Exploration: [email protected] An HPC Approach

Albert Farrés The field of geophysical exploration is aiming at closing the Barcelona Supercomputing Center gaps between physics, algorithmics and supercomputing. [email protected] We show current development, compromises and break- throughs in both forward and inverse modelling of large 3D Josep de La Puente datasets. We will put a particular focus on highly efficient Barcelona Supercomputing Center and versatile numerical schemes for wave propagation, re- Spain silient workflows and architecture-aware optimizations. [email protected] Josep de La Puente Barcelona Supercomputing Center MS29 Spain [email protected] Mimetic Finite Differerence Methods for 2D Re- verse Time Migration Miguel Ferrer We introduce the use of mimetic methods for Reverse Time Barcelona Supercomputing Center Migration (RTM) subsurface imaging. In this paper, both [email protected] the forward and reverse seismic waves are modeled with mimetic differential operators over the standard staggered Mauricio Hanzich grid. These discrete differential operators, constructed us- Barcelona Supercomputing Center (BSC) 102 GS15 Abstracts

[email protected] and monitoring of CO2 sequestration projects.

Jean Kormann Nikita Chugunov, T.S. Ramakrishnan Barcelona Supercomputing Center Schlumberger-Doll Research [email protected] [email protected], [email protected]

MS30 MS30 Simultaneous Optimization of Mining Complexes Closed-Loop Approaches for Real-Time Mining and Mineral Value Chains with Uncertain Metal and Petroleum Extraction A Comparison Supply and Market Demand Advanced data acquisition and process modelling technol- A mining complex and related mineral value chain is an ogy provides online data about different aspects of the re- integrated business extracting materials from mines, treat- source extraction process. Closed-loop approaches have ing extracted materials through connected processing facil- recently been applied to utilize the value of this infor- ities and generating mineral products sold to customers or mation for improved production control in mineral re- spot market. Materials extracted (supply) and commodity source extraction. Similar techniques have been developed prices (demand) are uncertain. Simultaneous optimization in the petroleum industry combining computer-assisted of a mining complex is approached through stochastic inte- model updating with model-based production optimiza- ger programming; metaheuristics are developed to provide tion. This contribution reviews methods applied, high- efficient solutions to applications entailing millions of vari- lights differences and assesses the potential value added ables. Examples show major improvement in production for both application domains. and net-present-value.

Joerg Benndorf Roussos Dimitrakopoulos Department of Geoscience & Engineering Department of Mining and Materials Engineering Delft University of Technology McGill University [email protected] [email protected]

Jan Dirk Jansen Ryan Goodfellow TU Delft, The Netherlands COSMO Lab, McGill University ’[email protected]’ [email protected]

MS30 MS30 Uncertainty-Based Mine Development and Pro- Multiobjective Optimization with Nonlinear Con- duction Optimization with a Hybrid Genetic - Pat- straints with Application to Optimal Well Control tern Search Algorithm: Example from An Iron Ore under Geological Uncertainty Mine We develop methodology based on the normalized bound- A hybrid method using genetic algorithms (GAs) and pat- ary intersection method for the solution of multiobjective tern search (PS) is proposed for solving large-scale mine optimization problems with nonlinear constraints where production optimization under geological uncertainty from the solution is represented by the Pareto front. Each opti- an Indian iron mine. The solution of the production op- mization sub-problem is solved by an augmented-Lagrange timization problem is obtained by solving a sequence of algorithm. The overall procedure is applied for optimiza- sub-problems and each sub-problem is solved using the pro- tion of water flooding under geological uncertainty where posed method. In this hybrid method, GAs help to identify the objectives include maximization of net-present value, approximate areas of the search space and PS helps to im- minimization of risk and minimization of variance. prove approximations to the maxima. Xin Liu, Al Reynolds Snehamoy Chatterjee Tulsa University Department of Geological and Mining Engineering and [email protected], [email protected] Sciences Michigan Technological University MS30 [email protected] An Efficient Robust Production Optimization Method for Closed-loop Reservoir Management MS30 A methodology for production optimization under geolog- On Applications of Global Sensitivity Analysis ical uncertainty is presented. Efficiency is achieved by to Performance Optimization and Monitoring of performing the optimization over a reduced set of rep- Reservoirs under Uncertainty resentative realizations, where the number of representative realizations is determined through a systematic multi- We present an overview of various applications of Global level optimization-with-validation procedure. An efficient Sensitivity Analysis (GSA) to relevant oilfield challenges gradient-based method is used as the core optimizer. This including well test design and interpretation, reservoir per- treatment, together with gradient-based history matching, formance evaluation and design of monitoring programs is incorporated into a closed-loop reservoir management under reservoir uncertainty. We also discuss an adap- workflow, which is then applied to challenging problems. tive optimization workflow combining mean-variance approach with GSA. Illustrative examples will include opti- Mehrdad Shirangi mization of enhanced oil recovery, characterization of frac- Dept of Energy Resources Engineering tured reservoirs, and uncertainty analysis for performance Stanford University GS15 Abstracts 103

[email protected] the only source of moisture to drive microbial activity and nutrient diffusion. The results of this modeling study sug- Louis Durlofsky gest that hydraulic lift is an actively controlled adaptation Stanford University mechanism that allows plants to remain active during long [email protected] dry spells by acquiring nutrients from the dry near surface soils while relying on deep soil moisture reserves for transpiration. MS31 Temrat A. Ghezzehei Pore Scale Model for Non-Isothermal Flow with Univercity of California Mineral Precipitation and Dissolution [email protected] Motivated by rock-fluid interactions occurring in a geothermal reservoir, we consider a pore scale model describing Ammar Albalasmeh fluid flow and solute transport through the void space and Jordan University of Science and Technology mineral precipitation and dissolution at the interface be- [email protected] tween fluid and grains. The precipitation and dissolution affect the porosity. We also include heat transport through Nathaniel Bogie both fluid and grains and take into account thermal effects University of California, Merced on fluid properties and chemical reactions. We apply for- [email protected] mal homogenization to derive upscaled effective models.

Carina Bringedal MS31 University of Bergen Homogenization of Freezing and Thawing Pro- Realfagbygget, Allégt. 41 5020 Bergen, Norway cesses in Porous Media [email protected] We show well-posedness of a pore-scale model for freezing Inga Berre and thawing processes in porous media, based on phase- Department of Mathematics field equations. We prove the existence of new extension University of Bergen operators for non-Dirichlet boundary conditions on peri- [email protected] odic domains, which allow us to gain scale-independent estimates of the solutions. Using two-scale homogeniza- Florin A. Radu tion, we derive macroscopic equations which contain the Institute of Mathematics microscopic effects and are effectively treatable by numeri- University of Bergen cal methods. Applications of the model include the release fl[email protected] of climate gases from thawing permafrost soil. Martin Höpker Iuliu Sorin Pop University of Bremen Dept of Mathematics and Computer Sciences Postfach 33 04 40, 28334 Bremen, Germany TU Eindhoven [email protected] [email protected]

MS31 MS31 Mechanistic Modeling of the Formation and Con- Hydrodynamics of the Rhizosphere: How Roots solidation of Soil Microaggregates Modulate Flow and Transport Properties in their Immediate Environment We want to discuss the mathematical, mechanistic modeling and numerical treatment of processes leading to the Plants roots inhabit in the soil environment, where their formation, stability, and turnover of soil micro-aggregates. mobility is severely restricted and resources such as water, This includes a review of compartment models, but aims at nutrients and air, are frequently scarce and patchy. To sur- deterministic aggregation models including detailed mech- vive in this restrictive environment plants modify their im- anistic pore-scale descriptions to account for the interplay mediate environment to their benefit, particularly the rhi- of geochemistry and microbiology, or the link to soil func- zospherea small volume of soil that surrounds each individ- tions. Multiscale techniques resulting in complex, coupled ual root. One mechanism that plants use for this purpose is models including nonlinearities of the processes and spatial exudation of complex organic molecules and thereby mod- heterogeneity are considered. ify the soil characteristics. Here, we present a mathematical model of alteration of soil hydrodynamic properties. In Alexander Prechtel particular, we focus on the water retention potential of the Mathematics Department hydrogels formed when the exudates are hydrated. Here University of Erlangen-Nuremberg, Germany we will present results from two related simulation stud- [email protected] ies. First, we demonstrate that exudates play important role in facilitating water flow by providing built-in water Nadja Ray potential gradient within the rhizosphere. This results in University of Erlangen-Nuremberg fairly wet environment near the roots, which is important [email protected] for nutrient diffusion, microbial activity, and nutrient cy- cling. Secondly, we show that exudates facilitate the release of water from roots to the rhizosphere at night, when MS31 transpiration is shut down. This is a widely documented Flow and Transport in Evolving Porous Media phenomenon, known as hydraulic lift, in many dry regions. In most dry areas, the hydraulic lift water is likely to be In recent research, upscaling flow and transport in porous 104 GS15 Abstracts

media has been undertaken for models integrating elec- [email protected] trostatics or deformations of the porous matrix. In our talk, we first introduce a pore-scale model in terms of coupled, nonlinear partial differential equations describing MS32 these processes. To capture changes in the pore-scale geom- Thermal Modeling on the Bravo Dome etry induced by heterogeneous reactions, we use a level-set framework. Finally, a computationally reasonable model Thermochronological measurements suggest initial injec- is obtained applying two-scale asymptotics, and simulation tion of hot, magmatic CO2 into the Bravo Dome aquifer results are presented. 1.2-1.5 My ago. We investigate this hypothesis by carry- ing out numerical simulations of the original CO2 injection, Nadja Ray taking into account thermal effects (density and viscosity University of Erlangen-Nuremberg changes, energy flow) and impact of aquifer heterogeneity. [email protected] We examine the transport of heat carried by the CO2 towards the regions for which thermochronological samples are available, to further constrain the parameters involved. MS31 Analytical Solutions for Cation Exchange Reac- Odd A. Andersen tions in Porous Medium Applied Mathematics SINTEF ICT Hyperbolic theory of conservation laws are used to obtain [email protected] analytical solutions for 1D flow with cation exchange reactions. Riemann solution in composition (phase) space comprises constant concentrations separated by waves. A MS32 comparison with laboratory and field data is presented for three cations. Challenges to extend for more components Simulation of the Emplacement Process for a Nat- are highlighted. ural CO2 Reservoir

Ashwin Venkatraman Due to their low solubility, noble gases can be used as re- The University of Texas at Austin liable tracers for monitoring CO2 dissolution at geological [email protected] time scale, as it has been done in the case of the Bravo dome, a natural CO2 reservoir, by measuring the concentration of Helium. We have implemented a compositional solver for C02, Helium, Neon and water, based on simple MS32 PVT laws. Simulating the CO2 emplacement process then Causes of Sub Hydrostatic Pressure at Bravo Dome enables us to interpret in a more accurate way the spatial distribution of the components concentrations. The Bravo dome field in northeast New Mexico is one of the largest gas accumulations worldwide and the largest Xavier Raynaud natural CO2 accumulation in North America. The field is SINTEF ICT only 580-900 m deep and Sathaye et al. (2014) estimated [email protected] that 1.3 Gt of CO2 is stored in the reservoir. The reservoir is divided in to several compartments with near gas-static pressure. The pre-production gas pressures in the two main MS32 compartments that account for 46% and 18% of the mass Interpretation of Noble Gases in Natural CO2 of CO2 stored at bravo dome are 5.5 MPa and 4.5 MPa Fields below hydrostatic pressure, respectively. Common expla- nations for sub-hydrostatic pressures include erosional un- Noble gas isotopes can be used to distinguish contributions loading (Neuzil and Pollock 1983), regional groundwater of atmospheric, crustal, and mantle gases in subsurface gas circulation through low permeability beds (Senger et al. accumulations. Despite being chemically unreactive, the 1987), and cooling (Barker 1972). Here we introduce the low solubility of noble gases in brine relative to CO2 causes dissolution of CO2 into the brine as a new process that these components to become enriched at the front of CO2 can reduce gas pressure in a compartmentalized reservoir. migration processes. We present analytical models, com- This research suggests that erosional unloading, thermal bined with field and experimental data that can inform effects, and dissolution of CO2 into brine can only explain future studies of natural CO2 migration using noble gas 12% ± 3%, 30% ± 15%, and 20% ± 5% of the total pres- isotope distributions. sure drop, respectively. This suggests that CO2 dissolution may contribute significantly to reduce the initial pressure Kiran J. Sathaye build-up due to injection. Our results also imply that the The University Of Texas Austin formation was already significantly below hydrostatic pres- Kiran Sathaye ([email protected]) sure before the CO2 was emplaced and that underpressured formations should be primary targets for geological CO2 storage. MS33 Upscale and Multiscale Methods in Electromagnet- Daria Ahkbari ics The University Of Texas Austin [email protected] Abstract not available at time of publication.

Marc A. Hesse Luz Angelica A. Caudillo Mata University of Texas Earth, Ocean and Atmospherical Sciences Department Department of Geological Sciences University of British Columbia GS15 Abstracts 105

[email protected] [email protected]

MS33 MS33 Optimization Through Multiscale Methods Krylov Model-Order Reduction of Transient Seis- mic Wave Propagation in Unbounded Domains Multiscale finite element (MS-FEM) methods can significantly reduce the computational costs associated with The efficient and accurate modeling of transient acoustic solving quasi-static Maxwells equations in electromagnetic wave propagation inside the subsurface of the Earth is imaging. The main idea is to project the discretized PDE of paramount importance in seismic exploration. In this onto a low-dimensional subspace whose basis depends on talk, we present a new Krylov subspace reduction method the, in practice unknown, electric conductivity. This de- that computes these wave fields in a very effective manner. pendency renders the use of MS-FEM methods for geo- The extension to infinity is modeled using an optimized physical inversions very challenging. This talk presents a complex-scaling method (a variant of the well-known Per- new optimization approach that updates the conductivity fectly Matched Layer technique) and transient wave fields estimate as well as the multiscale basis. are computed by constructing Krylov subspace field approximations of a so-called stability-corrected wave func- Lars Ruthotto tion. In addition, we show that our approach allows us to Department of Mathematics and Computer Science directly identify which scattering poles are dominant and Emory University contribute the most to a received time-domain signal. Nu- [email protected] merical experiments that illustrate the performance of the method are presented as well. Eldad Haber University of British Columbia, Vancouver, Canada Vladimir L. Druskin [email protected] Schlumberger-Doll Research [email protected] MS33 Rob Remis Discrete Operator Upscaling for Well Models on Circuits and Systems Group Polyhedral Meshes Delft University of Technology [email protected] Well modeling is a critical component of reservoir simulations because wells drive strong localized gradients in Mikhail Zaslavsky the solution while typically being under-resolved. Many Schlumberger-Doll Research state-of-the-art well-models assume that the problem is dis- [email protected] cretized on orthogonal grids. However, to capture the influence of subsurface stratigraphy it is essential to use polyhedral meshes along with advanced discretization methods. Joern Zimmerling In this research we present a new methodology, which is Circuits and Systems Group based on model upscaling, to represent wells on general Delft University of Technology polyhedral meshes. [email protected] Daniil Svyatskiy Los Alamos National Laboratory MS33 [email protected] An Adaptive Enriched Algebraic Multiscale Solver (AE-AMS) David Moulton Los Alamos National Laboratory We present an Adaptive Enriched Algebraic Multiscale Applied Mathematics and Plasma Physics Solver (AE-AMS) within the AMS framework of Wang et [email protected] al. [JPC, 2014]. Our enrichment strategy is efficient, because it minimizes the number of additional basis functions by accounting for both the underlying problem character- MS33 istics and the solver settings. We study several enrichment Title Not Available at Time of Publication strategies through numerical test cases, and illustrate that the AE-AMS outperforms the original AMS for challenging Abstract not available at time of publication. heterogeneous problems. Hamdi Tchelepi Stanford University Abdulrahman M. Manea Energy Resources Engineering Department Stanford University [email protected] Energy Resources Engineering Department [email protected] MS34 Hadi Hajibeygi Active Subspace Dimension Reduction for Subsur- TU Delft face Sensitivity in Hydrology [email protected] Studying sensitivity of hydrology model outputs to subsur- Hamdi Tchelepi face properties is challenging due to the high dimensional- Stanford University ity of spatially varying subsurface fields. We apply recently Energy Resources Engineering Department developed active subspaces to reduce the dimension of the 106 GS15 Abstracts

sensitivity analysis and gain insight into the relationship [email protected], [email protected] between permeability and model outputs.

Paul Constantine MS34 Colorado School of Mines Applied Mathematics and Statistics Probabilistic Parameter Estimation and Prediction [email protected] for Groundwater Contamination

We compute approximate solutions to inverse problems MS34 for determining parameters in groundwater contaminant transport models with stochastic data. We utilize a Quantifying Uncertainties in Gulf of Mexico Circu- measure-theoretic inverse framework to perform uncer- lation Forecasts tainty quantification and estimation for these parameters. Adjoint problems, which are useful in determining a pos- The impacts of input uncertainties on the Gulf of Mex- teriori error estimates, are developed and solved numeri- ico circulation forecast are studied using Polynomial Chaos cally. The solutions are used to make predictions of future (PC) Expansions. Key issues are: characterizing the inputs contaminant concentrations and to analyze possible reme- probability density functions, their forward propagation, diation techniques. and the validation of the PC surrogate. We use Empiri- cal Orthogonal Functions to constrain the dimension of the Steven Mattis uncertain space, and an ensemble calculation to construct University of Texas at Austin the surrogate. Sea Surface Height variances indicate a loss [email protected] of predictability in the Loop Current region after 20 days. Troy Butler University of Colorado Denver Mohamed Iskandarani [email protected] Rosenstiel School of Marine and Atmospheric Sciences University of Miami Clint Dawson [email protected] Institute for Computational Engineering and Sciences University of Texas at Austin Matthieu Le Henaff [email protected] University of Miami matthieu le henaff ¡mlehenaff@rsmas.miami.edu¿ MS34 guotu Li Duke Bayesian Inference of Fault Slip Distribution Dur- [email protected] ing A Tsunami Event Using Polynomial Chaos

Omar M. Knio We present an efficient method to infer fault slip distri- Duke University bution using water surface elevation data obtained during [email protected] Tohoku earthquake and tsunami. We characterize the slip distribution by six different parameters assumed constant Ashwanth Srinivasan in six fault segments. The efficiency of our approach stems Tendral LLC from the use of polynomial chaos expansions to build an [email protected] inexpensive surrogate for the numerical tsunami GeoClaw model that can be used to perform a sensitivity analysis. The surrogate also reduces the computational burden of W. Carlisle Thacker the Markov Chain Monte-Carlo sampling needed for the CIMAS Bayesian inference. Our objective is to sharpen the initial [email protected] estimates of the uncertain slip distributions. We report results of the Maximum-A-Posteriori (MAP) values of the uncertain parameters. MS34 Uncertainties in Tsunami Simulations from Uncer- Ihab Sraj tain Bathymetry Duke University [email protected] VOLNA, a nonlinear shallow water equations solver, produces high resolution simulations of earthquake-generated Kyle T. Mandli tsunamis. However, the uncertainties in the bathymetry Columbia University (from irregularly-spaced observations) have an impact on Applied Physics and Applied Mathematics tsunami waves. We first employ a Gaussian field to quan- [email protected] tify uncertainties in these boundary fields. These uncertainties are then parametrised to be used as inputs of an Omar M. Knio emulator of VOLNA. We finally propagate uncertainties in Duke University the bathymetry to obtain an improved probabilistic assess- [email protected] ment of tsunami hazard. Ibrahim Hoteit Xiaoyu Liu, Serge Guillas King Abdullah University of Science and Technology University College London (KAUST) GS15 Abstracts 107

[email protected] Materials Design [email protected], myian- [email protected] MS34 Towards the Prototype Probabilistic Earth-System Model for Climate Prediction MS35 Assessing the Impacts of Multi-Rate Mass Transfer Our research is focused on making current climate model and Sorption in Heterogeneous Media simulations more consistent with preserved scaling symme- tries of the partial differential equations which govern the Direct numerical simulation of contaminant persistence in multi-scale nature of climate. This is achieved by moving heterogeneous subsurface formations is known to be a com- away from the traditional deterministic approach to the putationally challenging problem. We describe coupled closure problem in computational fluid dynamics, and to- desorption and diffusive exchange between mobile and im- wards a more novel description of physical processes near mobile zones by multiple first-order exchange terms. The and below the truncation scale of climate models, using link between effective first-order rates and geostatistical contemporary nonlinear stochastic-dynamic mathematics. medium descriptions is established, using regression based The proposed consequences of such an approach will be on fine-scale simulations. This approach facilitates efficient to reduce biases against observations, produce estimates of assessment of reactive transport in heterogeneous domains. uncertainty in its own predictions, and a model which can make use of emerging energy-efficient probabilistic proces- Maria T. Elenius, Eric Miller, Linda Abriola sor hardware. We will present results from efforts in various Tufts University fields of the climate model development in our group rang- [email protected], [email protected], ing from stochastic approaches in atmospheric convection [email protected] parameterization, land surface process parameterization, ocean eddy-induced mixing and sea-ice parameterization to stochastic hardware simulations of simple climate mod- MS35 els. Multi-Scale Multi-Component, Multi-Phase Flash with Applications to Salt Deposition and Light Aneesh Subramanian Tight Oil University of California, San Diego, USA [email protected] The Gibbs-Helmholtz Constrained (GHC) equation of state is used to predict phase properties and equilibrium Tim Palmer behavior in two applications of current interest - CO2 se- University of Oxford, UK questration and light tight oil (LTO). In CO2 sequestra- [email protected] tion, mixtures contain light gases, ions, amorphous silica and water and can exhibit three fluid phases plus solid salts. In contrast, LTO applications contain light gases, MS35 heavier hydrocarbons, and water and often exhibit differ- Molecular Simulation of Adsorption and Transport ent behavior in tight pores than in the bulk. in Shales Organic Matter Angelo Lucia, Heath Henley, Edward Thomas Using an atomistic description of the oil-shale organic Department of Chemical Engineering matter and Molecular Simulations [1], we generate quasi- University of Rhode Island experimental data to study adsorption and mass transfer at [email protected], heath [email protected], the nanoscale. First, we review reservoir simulators mod- edward [email protected] els of dry gas adsorption [2] and extend them to light oils [3]. Second, isothermal transport is studied: non-Darcean Denis Voskov behavior is obtained, as transport is dominated by a ther- Energy Resources Engineering Department mally activated diffusion process, like nanoporous carbons Stanford Univeristy [4], described in the Maxwell-Stefan framework. References [email protected] [1] Collell et al., Energy & Fuels 2014, 28 (12), 74577466. [2] Collell et al., Microporous Mesoporous Mater. 2014, 197, pp 194203. [3] Collell et al., J. Phys. Chem. C 2014, MS35 118 (45), 2616226171. [4] Botan et al., Langmuir 2013, 29, 99859990. PH Dependent Reaction Fronts in Porous Media

Julien Collell Multicomponent reactive transport in porous media gives Universite de Pau et des Pays de lAdour rise to reaction fronts with complex morphology. The ﬁrst- [email protected] order structure of these fronts can be analyzed in the hyperbolic limit of the governing equations. Field and experimental data show good agreement with analytical simula- Guillaume Galliero tions of ion-exchange reactions. New theoretical and exper- 1Laboratory of Complex Fluids and their Reservoirs imental results for reactive transport with pH-dependent Universite de Pau surface reactions show more complex front morphology and [email protected] highlight the eﬀect of nonlinear surface chemistry on transport behavior. Francois Montel, Magali Pujol TOTAL, CSTJF, Pau, France Marc A. Hesse [email protected], [email protected] University of Texas Department of Geological Sciences Philippe Ungerer, Marianna Yiannourakou [email protected] 108 GS15 Abstracts

Colin McNeece lems in 3D elastodynamics. The University of Texas Department of Geological Sciences, UT Austin Stéphanie Chaillat [email protected] Laboratoire POEMS (CNRS-ENSTA-INRIA) [email protected] MS35 Marion Darbas Discrete-Continuum Models of Transport Phenom- LAMFA UMR CNRS 7352 ena [email protected] Discrete, particle-based simulations offer distinct advantages when modeling solute transport and chemical re- Frédérique Le Louër actions. For example, Brownian motion is often used to LMAC, Université de Technologie de Compiègne model diffusion in complex pore networks, and Gillespie- [email protected] type algorithms allow one to handle multicomponent chemical reactions with uncertain reaction pathways. Yet such MS36 models can be computationally more intensive than their continuum-scale counterparts, e.g., advection-dispersion- Fast Frequency Domain Solvers and Seismic Mi- reaction equations. Combining the discrete and continuum croscale Inversion models has a potential to resolve the quantity of interest with a required degree of physicochemical granularity at Abstract not available at time of publication. acceptable computational cost. We present computational examples of such hybrid models and discuss the challenges Bjorn Engquist associated with coupling these two levels of description. Department of Mathematics and ICES, UT Austin [email protected] Daniel M. Tartakovsky, Joseph Bakarji University of California, San Diego [email protected], [email protected] MS36 Full Waveform Inversion for the Identifiable Sub- space Using Interior Point Methods MS35 Reactive Flow and Transport in Porous Media: Ap- Full-waveform inversion (FWI) optimizes subsurface model plications and Challenges estimates to derive high-fidelity geological models. A mathematically sound method is described for selecting the Thermal multiphase flow and multi-component reactive part of the geological parameters that is best identifiable transport in porous media is an important type of simula- from the seismic acquisition geometry. This is combined tion since it describes almost all energy- and environment- with either interior-point or sequential quadratic program- related industrial processes. Applications of practical inter- ming methods for performing FWI for the subset of param- est include, but are not limited to, modeling conventional eters that have been characterized as identifiable. Numer- and unconventional petroleum reservoirs, CO2 sequestra- ical results are presented on several examples of increased tion processes and advanced geothermal applications. In complexity. my talk I will discuss a robust implementation of chemical reaction with precipitation and dissolution of a solid phase Drosos Kourounis for Darcy scale and ideas of coarse scale reconstruction of USI - Università della Svizzera italiana fine-scale results. Several examples of practical interest will Institute of Computational Science be presented. [email protected] Denis Voskov Energy Resources Engineering Department Marcus J. Grote Stanford Univeristy Universität Basel [email protected] [email protected]

Hamdi Tchelepi Olaf Schenk Stanford University USI - Universit`a della Svizzera italiana Energy Resources Engineering Department Institute of Computational Science [email protected] [email protected]

MS36 MS36 A Well-Conditioned Fast Multipole BEM for 3-D Asymptotic Preconditioning Approach for Multi- Elastodynamics in the Frequency Domain Parameter Full Waveform Inversion

The Fast Multipole accelerated boundary element method Developing efficient and reliable multi-parameter ap- (FM-BEM) is a possible approach to solve 3D elastody- proaches for Full Waveform Inversion is an increasingly namic problems in unbounded domains. By nature the important issue in seismic imaging. The main difficulty FM-BEM is used in conjunction with an iterative solver. is related to potential trade-offs between different classes To reduce the number of iterations, we propose a judicious of parameters (P-wave velocity and density for instance). integral representation of the scattered field which natu- One could mitigate this issue by accounting accurately for rally incorporates a regularizing operator (a high-frequency the inverse Hessian operator within the inversion. To this approximation of the DtN). This OSRC-like preconditioner end, we propose to use an asymptotic approximation of this is applied efficiently to Dirichlet exterior scattering prob- operator as an efficient preconditioner within a truncated GS15 Abstracts 109

Newton algorithm. reflector and the illuminating array is complex and strongly scattering. In this setup traditional migration imaging fails Ludovic Metivier since the echoes from the reflector are lost in the noisy Grenoble backscattered echoes from the ambient medium. In virtual ludovic mtivier ¡[email protected] array imaging, noisy traces are recorded on an auxiliary receiver array that is located in the homogeneous slab above Ludovic Metivier the reflector and below the strongly scattering medium. LJK-CNRS Univ. Grenoble Alpes Imaging is performed by migrating the cross correlations ludovic mtivier ¡[email protected] of the recorded field. We will illustrate with numerical results the robustness of virtual array imaging and present an Romain Brossier analysis of the signal to noise ratio of the obtained image. ISTerre University Joseph Fourier Chrysoula Tsogka [email protected] University of Crete and FORTH-IACM [email protected] Stephane Operto GEOAZUR MS37 CNRS [email protected] Experimental Demonstrations of Some Computa- tional Challenges in Hydraulic Fracture Simulation Jean Virieux Hydraulic fracture modeling relies on a non-linear, non- ISTerre local moving boundary problem with multiple nested University Joseph Fourier length scales possesses a harsh numerical stability criterion [email protected] for explicit time-stepping methods and a demonstrable ten- dency for algorithmic details to have a first order impact MS36 on predictions. Bringing together predictions from a variety of types of hydraulic fracture simulators with data Accelerated Discontinuous Galerkin Time-Domain from both the field and laboratory, this talk will highlight Simulations for Seismic Imaging some lessons that have been learned over the past decade Improving both the accuracy and computational perfor- of research. mance of simulation tools is a major challenge for seismic imaging, and generally requires specialized algorithms to Andrew Bunger make full use of accelerator-aided clusters. We present a University of Pittsburgh strategy for reverse time migration based on a high-order [email protected] penalty-discontinuous Galerkin time-domain method, dealing with different wave models. Our implementation can MS37 be run on several architectures thanks to a unified multi- threading programming framework, and exhibits a good Hierarchical Modeling of Networks and Solution of load balancing and minimum data movements. Nonlinear Network Models via MYNTS-NL

Axel Modave We present a new methodology for hierarchical modeling of Computational and Applied Mathematics networks which can be applied to pipeline systems and frac- Rice University tured reservoirs. The setup of the finest-level network rep- [email protected] resentation heavily relies on Kirchhoffs laws and Darcy(- Weisbach) flow models. For solving the resulting system of Amik St-Cyr nonlinear equations and inequalities we developed a work- Computation and Modeling, flow employing analytical formulations and NL. The hier- Shell International E&P, Inc. archy is based on reduced-order modeling and is used for [email protected] speeding up simulations and/or comparative flow analysis. Tanja Clees Timothy Warburton Fraunhofer-Institute for Algorithms and Scientific Department of Computational And Applied Mathematics Computing Rice University Germany [email protected] [email protected] William A. Mulder Lialia Nikitina, Igor Nikitin Shell Global Solutions International B.V. Fraunhofer SCAI [email protected] High Performance Analytics HPA [email protected], MS36 [email protected] Signal to Noise Ratio Analysis in Virtual Source Array Imaging Nils Hornung Fraunhofer SCAI Bonn We consider the problem of virtual source array imaging. [email protected] Motivated by geophysical applications, we assume that the illuminating array is at the surface of the earth while the Bernhard Klaassen, Klaere Cassirer reflector to be imaged is located in a homogeneous slab at Fraunhofer SCAI some depth. We also assume that the medium between the High Performance Analytics HPA 110 GS15 Abstracts

[email protected], The University of Melbourne [email protected] [email protected]

Siroos Azizmohammadi MS37 Montanuniversitaet Leoben Eﬃcient and Robust Compositional Numerical Institute of Reservoir Engineering Modeling in Unfractured and Fractured Permeable [email protected] Media Based on New Concepts

An efficient and accurate numerical model for multicompo- MS37 nent compressible flow in fractured media is presented. The Effective Transmissivity of Two and Three- discrete-fracture approach is used where the fracture enti- Dimensional Fractured/porous Media ties are described explicitly in the computational domain. We invoke cross-flow equilibrium in fractures. This will al- A method to numerically compute the full permeability low large matrix elements in the neighborhood of the frac- tensor of a two- and three-dimensional fractured porous tures. We use an implicit FV scheme to solve species mass medium is proposed. It assumes that fluid flows through balance equation in fractures. Numerical model is devel- both the fractures and matrix, and calculates the full per- oped for 2D and 3D structured and unstructured meshes. meability tensor of the medium. The method is based on the element-wise averaging of pressure and flux. A derived Ali Zidane formulation approximates three-dimensional flow proper- Reservoir Engineering Research Institute ties in cases where only two-dimensional analysis is avail- [email protected] able, based on an alternative expression of the excluded area. Abbas Firoozabadi Yale University Adriana Paluszny abbas.fi[email protected] Imperial College [email protected] MS37 Philip Lang, Robert Zimmerman Modeling Subsurface Fractures using Enriched Fi- Imperial College London nite Element Method [email protected], [email protected] Extended finite element method (XFEM) allows accurate modeling of fractures without having to construct mesh to MS38 honor geometries of fracture. In this talk, we will present two applications of XFEM with improved formulation. The Adaptive Mesh Refinement for Dynamic Rupture first one concerns rapid evaluation of well productivity with Simulations in Complex Geometries fractured completions. Examples on using the new method Dynamic earthquake rupture simulations involve the cou- to quantify the impact of non-Darcy effect will be given. pling of wave propagation and frictional sliding fault inter- The second application concerns predicting natural frac- faces. The friction laws used in such simulations introduce ture characteristics (e.g. density, orientation, and connec- small-scale features (around the nearly singular rupture tivity) using a 3D geomechanical model which can simulate front) that would be prohibitively expensive to capture fracture initiation, growth, and intersection occurred in the with a static mesh. Since simulations involve both wave mechanical genesis of natural fractures. Simulation studies propagation and small-scale rupture features, here we pro- offered new insights on the factors that control the density pose the use of dynamically adaptive, high-order accurate and connectivity of natural fractures. discontinuous Galerkin methods for such problems. Hao Huang, Gauthier Becker, Rod Myers, Jichao Yin, Jeremy E. Kozdon Huaifei Sun Naval Postgraduate School ExxonMobil Upstream Research Company Department of Applied Mathematics [email protected], gau- [email protected] [email protected], ro- [email protected], [email protected], [email protected] Lucas Wilcox Department of Applied Mathematics Naval Postgraduate School MS37 [email protected] Dependence of the Equivalent Permeability of a Fractured Rock Mass on Fluid Pressure and Stress MS38 The fracture matrix ensemble permeability / anisotropy of A Coupled Model for Dynamic Wedge Failure, Co- outcrop analog models of naturally fractured layered sedi- seismic Landslides, and Tsunami Propagation for mentary rocks has been computed as a function of sample Shallow Subduction Zone Earthquakes size using finite-element models. As in situ fracture aperture, influences these parameters, a sensitivity analysis was We incorporate coseismic landslides and tsunami propaga- conducted with competing aperture models, also consider- tion in the dynamic rupture model of shallow subduction ing the influence of residual aperture. Our results indicate earthquakes with extensive wedge failure. An updated La- correlations with sample size and demonstrate the decisive grangian approach is used in which the equation of motion, role that aperture plays for fracture flow. failure criterion, and boundary conditions are evaluated at the deformed configuration. We investigate how inelastic Stephan K. Matthai wedge failure and landslides affect the arrival time, ampli- GS15 Abstracts 111

tude, and frequency content of tsunami waveforms. Claudia Piromallo Istituto Nazionale di Geofisica e Vulcanologia Shuo Ma [email protected] Department of Geological Sciences San Diego State University Alessio Piatanesi [email protected] Istituto Nazionale di Geofisica e Vulcanologia, Italy [email protected] MS38 Yoshihiro Ito Segmented Source Structures: When Do Earth- Disaster Prevention Research Institute, Kyoto University, quake Ruptures Jump Between Faults? Ja [email protected] How segmented fault systems host earthquakes is of primary importance to assessing seismic hazard. We ad- Dapeng Zhao dress the potential for jumping versus continuous slip dur- Department of Geophysics, Tohoku University, Sendai, ing the 1992 Landers earthquake in southern California, Japan which ruptured segments of 5 different right-lateral, strike- [email protected] slip faults. One of these faults is the 4km long Landers- Kickapoo Fault in the releasing step between the John- son Valley Fault to the southwest, where the earthquake Kenji Hirata nucleated, and the Homestead Valley Fault to the north- National Research Institute for Earth Science and east. Using boundary element method models incorpo- Disaster P rating 3D, non-planar faults, we find that slip along the [email protected] Landers-Kickapoo Fault is required to transfer slip through the step. This raises the question: when do ruptures jump Massimo Cocco across a step and when are secondary faults required to Istituto Nazionale di Geofisica e Vulcanologia transfer slip across a step? Addressing this requires the in- [email protected] corporation of structures present within steps into numerical models and a comparison of quasistatic model results such as these, which approximate the dynamic solution for the stress field near a slowly propagating rupture tip, with MS38 those from dynamic models, which capture slip accelera- tions and the seismic waves emitted from the rupture tip. The SeisSol Software Package for Large-Scale Tsunamigenic Earthquake Simulations

Elizabeth Madden University of Massachusetts We present the peta-scale software package SeisSol for [email protected] the simulation of tsunamigenic earthquakes. The dynamic earthquake faulting and the subsequent seismic wave prop- David Pollard agation is solved simultaneously by a high order ADER-DG Stanford University method implemented on unstructured tetrahedral meshes. [email protected] To demonstrate the advantages of the scheme we will present a subduction earthquake scenario. To this end, Frantz Maerten geometrically complex faults can be accurately discretized Schlumberger, Montpellier Technology Center and the impact of earthquake source dynamics on tsunami [email protected] initiation and propagation can be analysed.

MS38 Stephanie Wollherr Ludwig-Maximilians-Universität München 3D FEM-based Study of the 2011 Tohoku Earth- Department of Earth and Environmental Sciences quake Tsunamigenic Rupture Process [email protected] Tohoku earthquake is investigated by using a 3D-FEM Alice A. Gabriel model honouring the geometrical and structural complexi- Department of Earth and Environmental Sciences ties of the subduction interface up to the trench zone, and Ludwig-Maximilians-University Munich performing a joint inversion of tsunami and geodetic data. [email protected] Spatial correlation between slip and seismic velocity suggests structural control on the rupture. Sensitivity of re- trieved slip model to elastic subduction zone parameters, Alexander Breuer, Sebastian Rettenberger inclusion of horizontal displacement and nonlinear non- Technische Universität München hydrostatic dispersive versus linear shallow water tsunami Department of Informatics, Scientific Computing modelling is analysed as well. [email protected], [email protected]

Fabrizio Romano, Elisa Trasatti Alexander Heinecke Istituto Nazionale di Geofisica e Vulcanologia Parallel Computing Laboratory [email protected], [email protected] Intel Corporation, Santa Clara, CA, USA [email protected] Stefano Lorito Istituto Nazionale di Geofisica e Vulcanologia, Italy Michael Bader [email protected] Technische Universität München 112 GS15 Abstracts

[email protected] transport in porous media). The method is naturally par- allelizable, has optimal complexity and we provide sharp a-priori error estimates on its accuracy. MS38 Seismo-Thermo-Mechanical Modeling of Subduc- Houman Owhadi tion Zone Seismicity Applied Mathematics Caltech Seismo-thermo-mechanical modeling aims to improve our [email protected] physical understanding of spatiotemporal earthquake oc- currence in subduction zones. After validating this new continuum viscoelastoplastic geodynamic model with sim- MS39 ilar on- and off-fault physics, we demonstrate the impor- Partition of Unity Methods: Mass Lumping and tance of off-megathrust events on the megathrust cycle. Fast Solvers for Higher Order and Enriched Spaces Moreover, activation of steep off-megathrust fault planes could potentially generate larger than expected tsunamis, Meshless and generalized finite element methods are mod- especially for outerrise events. This additional long-term ern computational techniques designed to overcome some model component can provide self-consistent fault geome- of the shortcomings of classical mesh-based approaches. tries, stresses and strengths to dynamic rupture models. The Partition of Unity Method (PUM) not only provides the fundamental framework for generalized and extended finite element methods (GFEM/XFEM) but may also Ylona van Dinther be utilized to construct meshfree methods with problem- Department of Earth Sciences dependent approximation functions. In this talk we fo- ETH Zurich cus on such a meshfree PUM, its approximation proper- [email protected] ties when using higher order polynomials and problem- dependent enrichment functions, as well as its parallel im- Taras Gerya plementation. Here, we are concerned not only with the Geophysical Institute efficient assembly of the stiffness matrix but also with the ETH-Zurich fast solution of the resulting linear systems (i.e. the effi- [email protected] cient simulation of static problems or implicit dynamics). Moreover, we discuss the properties of a general mass lumping scheme which is applicable to higher order and arbitrar- Luis A. Dalguer ily enriched local approximation spaces to deal with large Swiss Nuclear scale explicit dynamics problems efficiently with the pro- [email protected] posed PUM.

Martin Mai Marc A. Schweitzer KAUST Institut für Numerische Simulation [email protected] 53115 Bonn, Germany [email protected] MS39 Meshless Discretization of Generalized Laplace Op- MS39 erator For Anisotropic Heterogeneous Media Oil and Gas Production Forecasting with Semi- Analytical Reservoir Simulation Reservoir simulations require complex discretizations due to presence of faults, fully discontinuous permeability Reservoir simulation is used by oil and gas companies to tensors. The smoothed particle hydrodynamic (SPH) model fluid flow in the subsurface. Because of the com- is an interpolation-based numerical technique that can plexity of reservoirs, forecasts and decisions regularly re- be used to solve underlying partial differential equations quire the use of computationally expensive numerical sim- (PDEs) describing fluid flow in porous media. The mesh- ulations. However, due to the high speed in model setup less multi-point flux approximation (MMPFA) for gener- and computation of results, the industry is experiencing alized Laplace operator is proposed describing fluid flow a growth in the application of analytical reservoir simu- in anisotropic heterogeneous porous media. The funda- lation. This paper reviews analytical reservoir simulation mentals, potential, and computational aspects will be pre- technology and its applications to conventional and uncon- sented. ventional resources.

Alexander Lukyanov Peter Tilke Schlumberger-Doll Research Schlumberger-Doll Research Cambridge, MA 02139, USA Cambridge, MA 02139, USA [email protected] [email protected]

Kees Vuik Wentao Zhou, Boris Samson, Shalini Krishnamurthy, Jeff Delft University of Technology Spath, Michael Thambynayagam [email protected] Schlumberger [email protected], [email protected], skrishna- [email protected], [email protected], [email protected] MS39 Meshless Multigrid with Rough Coefficients MS39 We introduce a meshless multigrid method for PDEs with Extending the Method of Fundamental Solutions rough coefficients (and in particular for PDEs arising in to Non Homogeneous Elastic Wave Propagation GS15 Abstracts 113

Problems define the failure boundary (in the stochastic space) corresponding to the threshold of a rare event. The training We consider the numerical solution of the Cauchy-Navier samples for the classification algorithm are obtained using a equations of elastodynamics, assuming time-harmonic vari- multilevel splitting algorithm and Monte Carlo (MC) sim- ation for the displacement field in an isotropic material. In ulations. Once the training of the classifier is performed, a the absence of body forces, the method of fundamental full MC simulation can be efficiently performed using the solutions (MFS), a meshfree procedure for solving homo- classifier as a reduced order model replacing the full sim- geneous elliptic PDEs, is applied. The formulation of the ulator. The developed rare events sampling algorithm sig- MFS is then modified in order to extend it to the non ho- nificantly outperforms direct MC and multi-level splitting mogeneous case. More precisely, the unknown solution is methods in terms of efficiency and precision on a standard approximated by superposition of fundamental solutions benchmark for CO2 leakage through a leaky abandoned (Kupradze tensors) of the Navier operator with different well. In this test case, CO2 is injected into a deep aquifer source points and test frequencies. The applicability of and then spreads within the aquifer and, upon reaching the method is justified in terms of density results and its an abandoned well; it rises to a shallower aquifer. The accuracy is illustrated trough numerical examples. The rare events sampling algorithm estimates the probability of performance of the method is also tested for interior wave leakage of a pre-defined amount of the injected CO2 given scattering problems and materials with non constant den- a heavy tailed distribution of the leaky well permeability. sity. The proposed algorithms efficiency and reliability enables us to perform a sensitivity analysis to study the effects of Svilen S. Valtchev the different modeling assumptions including the different CEMAT, IST, University of Lisbon prior distributions on the probability of the rare event of 1049-001 Lisbon, Portugal CO2 leakage. [email protected] Ahmed H. ElSheikh Institute of Petroleum Engineering MS39 Heriot-Watt University, Edinburgh, UK Large Scale Compuation of Fluid-Solid-Fracturing [email protected] Using SPH with Application to Hydro-Fracturing

Conventional stimulations of strong, stiff, brittle rocks have MS40 in general been successful. However, the more ductile plays The Ensemble Kalman Filter and Beyond have been less successful. That is, current fracturing technology is limited to the more brittle formations. Labora- The ensemble Kalman filter (EnKF) has proven to be one tory tests with gelatin show that the fracture development of the most efficient algorithms for inverse modeling of is sensitive to material properties, such as anelasticity and transient phenoma in a stochastic context. Its main ad- ductility. MIT has developed an Open Source SPH code vantage being that it does not rely on a computer-intensive to investigate hydro-fracturing of tight formations. It is optimization algorithm, but it is an assimilation algorithm capable of handling coupled multi-phase non-Newtonian that incrementally updates the inverse estimates as new fluids, elasto-visco-plastic solids with brittle or ductile frac- state data are acquired. Its main disadvantage is that ture. The use of SPH for fracture means that the fracture the updating is computed on the basis of the two-point can be handled discretely without the need for special el- auto- and cross-covariances between parameters and states, ements. The fracture geometry can be complex and non- what, in the long run, yields the estimates multiGaussian. planar. The code is built on a parallel library capable of To go beyond the standard EnKF we need to get away from optimizing the execution across multi-core machines with the multiGaussian curse. large numbers of compute nodes. Jaime Gomez-Hernandez John R. Williams Research Institute of Water and Environmental Massachusetts Institute of Technology Engineering Cambridge, MA, 02139, USA Technical University of Valencia - Spain [email protected] [email protected]

Nadir Akinci, Gizem Akinci, Bruce Jones, Kai Pan, Abel Sanchez, Maitham Aluhbail, Abdulaziz Albaiz, Zeid MS40 Alghareeb Model Calibration under Uncertain Geologic Sce- MIT narios Using Sparse Representation Techniques [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], Inverse modeling and uncertainty quantification in subsur- [email protected], [email protected] face flow and transport systems are typically performed without accounting for the uncertainty in the conceptual Peter Tilke geologic continuity model (e.g., variogram or training im- Schlumberger-Doll Research age). The geologic scenario, however, can present one of Cambridge, MA 02139, USA the most dominant and persistent sources of uncertainty [email protected] in predicting the flow and transport behavior. We present effective formulations that are inspired by sparse representation techniques to discriminate against several proposed MS40 geologic continuity models during model calibration. Machine Learning Approaches to Rare Event Sam- pling and Estimation Reza Khaninezhad Electrical Engineering An efficient rare events sampling algorithm have been de- University of Southern California veloped using machine learning classification methods to [email protected] 114 GS15 Abstracts

Azarang Golmohammadi ability,etc.) from training data images are used to create an Electrical Engineering, USC informative prior distribution, which combined with a like- [email protected] lihood function of the geophysical data leads to a much better representation of the subsurface than commonly used Benham Jafarpour deterministic penalized least squares inversion methods. ViterbiSchoolofEngineering The proposed methodology reduces the ambiguity inher- University of Southern California ent in the inversion of high-dimensional parameter spaces, [email protected] and accommodates a wide range of summary statistics and geophysical forward problems.

MS40 Jasper Vrugt University of California Irvine Recent Advances and Trends in the Geostatistical [email protected] Approach to Inverse Modeling and Data Assimila- tion MS41 The Geostatistical Approach (GA) is a method to solve al- gebraically underdetermined problems including quantifi- A Floe Size Distribution in the Cice Sea Ice Model cation of uncertainty in the context of objective empirical cice Bayes statistical inference. In the last few years, like other The sea ice model is a popular component of climate Bayesian methods, GA is revolutionized by high perfor- and forecasting models. However, it does not contain infor- mance computing, particularly the introduction of fast lin- mation on the size of ice floes. This is likely to inhibit its ac- ear algebra that uses approximate methods with controlled curacy, particularly in a vicinity of the ice edge, where floe cice error. We review recent advances and trends in GA. sizes are relatively small. An extended version of in the Antarctic will be presented. The extended model con- Peter K Kitanidis tains a floe size distribution based on mathematical models Stanford University of ice break-up. [email protected] Luke Bennetts University of Adelaide MS40 [email protected] Determination of Geological Scenario Using an Op- timization Procedure Siobhan O’Farrell CSIRO, Australia Uncertainty in the geological scenario or training image siobhan.o’[email protected] is often ignored in oil reservoir history matching. In this talk, a systematic procedure for the determination of the Petteri Uotila most likely geological scenario, along with model realiza- Finnish Meteorological Institute tions within that scenario, is presented. The approach uses petteri.uotila@fmi.fi continuous parameterizations of uncertain training image attributes and optimization to determine attribute values. Results demonstrate that the approach can provide mod- MS41 els that lead to uncertainty reduction and appropriately Free-boundary Problems in Cryosphere Models bracket future reservoir performance. Thin flowing layers, such as ice sheets, ice shelves, sea ice, Matthieu A. Rousset, Louis J. Durlofsky subglacial liquid water, and supraglacial liquid water, are Department of Energy Resources Engineering common components of cyrospheric climate models. These Stanford University flows are characterized by interaction with other climate [email protected], [email protected] components (e.g. atmosphere and ocean), which adds or removes fluid. Thus there are free boundaries, in the map- plane, between where the fluid is present and not. We advo- MS40 cate a common approach to the construction of numerical Formal Uncertainty Quantification in Geophysics: models for these thin layer flows: semi-discretize in time, Likelihood Free Inference Using Summary Statis- treat the nonnegativity of layer thickness as a constraint, tics from Training Data Images and solve a well-posed spatial free boundary problem at each time step. Advanced numerical tools are available for In the past decades, Bayesian methods have found solving each time step problem, namely parallel-scalable widespread application and use in environmental systems and constraint-respecting Newton solvers based on Krylov modeling. Despite the progress made, hypothesis(model) subspace methods. The approach clarifies the degree to refinement has proven to be very difficult in large part be- which exact discrete conservation, a goal of climate mod- cause of the poor diagnostic power of residual based like- eling, is achievable. Non-trivial examples will be shown. lihood functions. In a series of recent papers we have made the case for a diagnostic approach to model eval- Ed Bueler uation. This statistical methodology relaxes the need for University of Alaska Fairbanks an explicit likelihood function in favor of one or multiple [email protected] different summary statistics rooted in environmental theory that together have a much more compelling diagnostic power to detect epistemic errors than some average mea- MS41 sure of the size of the error residuals. In this talk, I will How Climate Model Complexity Influences the Sea demonstrate the prospects of diagnostic model evaluation Ice Stability to improve probabilistic inversion of geophysical data. The distributions of global summary metrics (roughness, vari- Two types of idealized climate models find bifurcations GS15 Abstracts 115

and associated instabilities during the retreat of sea ice [email protected] under global warming: (i) latitudinally-varying annual- mean diffusive energy balance models (EBMs) and (ii) seasonally- varying single-column models (SCMs). Com- MS41 prehensive global climate models, however, typically find An Anisotropic Elastic-Decohesive Constitutive no such instabilities. To bridge this gap, we develop an Relation for Modeling Sea Ice idealized model that includes both latitudinal and seasonal variations. The model reduces to a standard EBM or SCM Satellite imagery indicates that much of the winter Arc- as limiting cases in the parameter regime. We find that the tic ice deformation is concentrated in linear features, like stability of the sea ice cover vastly increases with the in- cracks. The aim of this research is to build on a previously clusion of spatial communication via meridional heat trans- formulated elastic-decohesive constitutive model that pre- port or a seasonal cycle in solar forcing, being most stable dicts the initiation, orientation and extent of cracks and tie when both are included. This implies that the sea ice cover it more closely to the thermodynamics and the distribution may be substantially more stable than has been suggested ice thickness. Examples are given to illustrate aspects of in previous idealized modeling studies. the model when simulating the failure of sea ice.

Till Wagner Deborah Sulsky Scripps Institution of Oceanography Department of Mathematics University of California San Diego University of New Mexico [email protected] [email protected]

Ian Eisenman Scripps Institution of Oceanography MS42 [email protected] Effective Properties of Realistic Oil Shale Stackings This work aims at numerically characterizing some macro- MS41 scopic properties of realistic computer-generated block stackings. The complex geometries studied represent the Sea Ice, Climate, and Homogenization for Compos- stacking configuration of the Ecoshale in-capsule configu- ite Materials ration. The permeability tensor of this porous media is determined as well as the inertial correction. Concerning The polar sea ice pack is an important component of the the thermal dispersion tensor, a classic local equilibrium Earths climate system undergoing rapid change. Complex volume averaging method is used. physical processes in sea ice play a critical role in regu- lating polar climate. Understanding these processes and Romain Guibert developing methods to monitor changes in the ice pack Institut de Mécanique des Fluides de Toulouse are thus important for making accurate predictions of the [email protected] Earths future climate. Homogenization has proven to be a powerful mathematical tool for understanding the effective Iryna Malinouskaya properties of composite media, and sea ice exhibits com- TOTAL posite structure on multiple length scales over ten orders [email protected] of magnitude. As such, homogenization techniques can be applied to understand ice properties such as fluid permeability, electrical conductivity and large-scale rheological Bernard Corre properties.In this talk I will discuss and highlight models TOTAL E&P France developed for sea ice using homogenization and how they TOTAL help advance our understanding of the role of sea ice in the [email protected] climate system, and improve projections of climate change Gérald Debenest Christian Sampson Institut de Mécanique de Fluides de Toulouse University of Utah [email protected] [email protected] Michel Quintard Institut de Mécanique des Fluides de Toulouse MS41 [email protected] Stochastic Dynamics and Critical Phenomena in Sea Ice Models Alexandre Lapene TOTAL E&P France The evolution of melt ponds on the surface of Arctic sea TOTAL ice is a complex stochastic process that is important in [email protected] climate modeling. We propose two models describing the stochastic dynamics of melt pond geometry – an analogue of the Ising model from statistical mechanics, and a low- MS42 order stochastic dynamical system model of energy balance Towards a Coupled Thermo-mechanical and Heat in the climate system. These models facilitate investigation and Mass Transfer Model for Source Rock Matu- of critical phenomena in Earths cryosphere, and melting ration and Retorting sea ice in particular. Thermal degradation of source rock, exogenous or not, in- Ivan Sudakov volves kerogen conversion resulting in rock structure evolu- University of Utah tion from non-permeable to permeable. Pyrolysis reactions Mathematics Department produce oil and gas, locally increasing pressure and stress. 116 GS15 Abstracts

The rock fails and cracks propagate enhancing the perme- [email protected] ability of the medium. This represents a new challenge for porous media research as the system to be model evolves in time and exhibits strong coupling between mass and heat MS42 transfer, and rock mechanics. A 3D numerical method is Transport in Porous Media with Surface Sources: proposed to model the thermo-mechanical phenomena in- Non-Equilibrium Models and Distribution Coeffi- volved in the in-situ oil shale retorting process. The me- cients chanical model is based on an original hybrid approach between two discrete methods. A lattice-type discretization We present several Darcy-scale models obtained via the is used to describe the underlying micro-structure of the method of volume averaging for a generic pore-scale prob- continuum. A particulate model is used for handling the lem of transport by advection and diffusion with multiple crack interfaces and their interactions. Heat conduction phases and sources/sinks on the interfaces. We review the and thermal expansion are solved by a finite-volume algo- different classes of approximations that can be used (eg lo- rithm. Different mechanical and thermal validation tests cal equilibrium, non-equilibrium, asymptotic) and discuss are presented and compared to experimental results found their limitations. We also present a multiple temperature in the literature. They show the abilities of this frame- model with a distribution coefficient that captures the par- work to simulate and predict the mechanical behavior and titioning between the different phases. the failure of materials undergoing significant structural changes. Yohan Davit, Quintard Michel Institute of Fluid Mechanics of Toulouse Alexandre Lapene University of Toulouse and CNRS TOTAL E&P France [email protected], [email protected] TOTAL [email protected] MS42 Rafik Affes Non-Newtonian Flow Through Porous Media: Mi- total cro and Macro-Scale Properties of Power-Law Flu- rafik.aff[email protected] ids In this work, we study polymer flow through porous struc- Bernard Corre tures in the context of Enhanced Oil Recovery methods. TOTAL E&P France We consider a non-Newtonian polymer flow described by TOTAL a power-law fluid and generalized incompressible Stokes [email protected] equations at the pore-scale. Our strategy is based on the method of volume averaging, CFD calculations, x-ray imaging of realistic structures and statistical tools. We MS42 show that this combination of approaches provides signif- Modelling In-Situ Upgrading of Heavy Oil with icant insight into the complexity of the micro-scale flow, Non-Equilibrium Reactions Using Operator Split- allowing us to better characterize its behavior and explicit ting Method links with macro-scale properties.

We present a mathematical model that describes the Frederic Pierre In-Situ Upgrading of bitumen and oil shale. A non- Institute of Fluid Mechanics of Toulouse equilibrium reaction model is used to describe the transfer University of Toulouse between the liquid and vapour phases. We use operator [email protected] splitting to solve separately the transport equation and the chemical reactions describing pyrolysis and phase transfer. Yohan Davit Dimensionless Analysis is used to study the sensitivity of Institute of Fluid Mechanics of Toulouse the reaction parameters and identify ﬂow regimes in a two- University of Toulouse and CNRS phase model. [email protected] Julien Maes Imperial College Michel Quintard [email protected] Institut de M´ecanique des Fluides de Toulouse [email protected] Matthew Jackson Department of Earth Science and Engineering Romain De Loubens Imperial College London, South Kensington Campus Total [email protected] [email protected]

Ann Muggeridge MS42 Imperial College [email protected] Pore Scale Simulation of Carbonate Dissolution We have developed a numerical tool to simulate dissolution Michel Quintard phenomena at pore-scale. The model allows to dissolve a Institut de M´ecanique des Fluides de Toulouse solid in presence of liquid acid into dissolved species. It [email protected] is based on a Darcy-Brinkman framework to diﬀerentiate solid phase and void spaces. The volume fraction of solid in Alexandre Lapene each cell of the computational domain varies with chemical TOTAL E&P France reaction at the solid surfaces. It can, therefore, change the TOTAL morphology of the solid skeleton. The model has shown GS15 Abstracts 117

promising results to capture the aperture evolution of a it with classical Discontinuous Galekin methods. fracture due to dissolution and has demonstrated a good ability to simulate dissolution wormholes. First results also Marie Bonnasse-Gahot showed that the model can capture CO2 gas bubbles gen- INRIA Nachos and Magique 3D eration at the solid walls. [email protected]

Cyprien Soulaine Henri Calandra Stanford University Total [email protected] CSTJF, Geophysical Operations & Technology, R&D Team Hamdi Tchelepi [email protected] Stanford University Energy Resources Engineering Department Julien Diaz [email protected] Team-Project Magique-3D INRIA Bordeaux Sud-Ouest Michel Quintard [email protected] Institut de M´ecanique des Fluides de Toulouse [email protected] Stephane Lanteri INRIA [email protected] MS43 High-Order Ipdg Approximations for Elasto- MS43 Acoustic Problems Dg for Large-Scale Inverse Problems in Time Do- main: Opportunities and Challenges We develop a solution methodology for the direct elasto-acoustic scattering problem based on Discontinuous This talk discusses various challenges of statistical inverse Galerkin approximations. The method distinguishes itself problem using high-order DG methods in geosciences, par- by combining high-order polynomials, local stabilizations ticularly global seismic inversion in time domain. In partic- and curved element edges on the boundaries. Numerical ular, we will talk about scalability of DG, issue with gradi- results illustrate the salient features and highlight the per- ent/Hessian computation, discretize-then-optimize versus formance of the solution methodology. Moreover, the de- optimize-then-discretize, compactness of the Hessian, chal- signed method ensures a convergence order with a gain of lenges in high dimensional parameter spaces, among many two order of magnitude compared to polygonal boundaries, others. Numerical results for statistical inversion over 1M and a potential to address high-frequency regimes. parameters will be presented.

Hélène Barucq, Lionel Boillot Tan Bui Team-Project Magique-3D University of Texas at Austin INRIA Bordeaux Sud-Ouest [email protected] [email protected], [email protected] MS43 Henri Calandra Total High order DG Methods on Hybrid Meshes CSTJF, Geophysical Operations & Technology, R&D High order time-explicit nodal discontinuous Galerkin Team (DG) methods have grown in popularity over the past [email protected] decade for reasons both mathematical and computational in nature. Sharp trace inequalities with explicit constants Elodie Estecahandy allow for explicit expressions for optimal CFL and penalty Team-Project Magique-3D constants, and the computational structure of DG methods INRIA Bordeaux Sud-Ouest on simplices and hexahedra allows for efficient implementa- [email protected] tion on accelerators and graphics processing units. In this talk, we present extensions of these aspects of DG meth- Rabia Djeloulli ods to high order pyramidal elements, and discuss the de- Calfornia State University at Northridge/IRIS velopment of a GPU-accelerated solver for wave equations [email protected] on hybrid meshes containing hexahedra, wedges, pyramids, and tetrahedra.

MS43 Jesse Chan Rice University Performance Assesment on Hybridizable Dg Ap- [email protected] proximations for the Elastic Wave Equation in Fre- quency Domain MS43 Seismic Imaging in frequency domain represents a very A Simple and Accurate Discontinuous Galerkin challenging task when considering realistic 3D elastic me- Scheme for Modeling Wave Propagation in Media dia because of the huge size of the linear system to be with Curved Interfaces inverted. To reduce the number of unknowns of the linear system, we propose to consider a hybridizable DG method. Conventional high-order discontinuous Galerkin schemes We analyze the performance of the method on realistic test suﬀer from interface errors caused by the misalignment be- case in a parallel programming framework and we compare tween straight-sided elements and curved material inter- 118 GS15 Abstracts

faces. We develop a novel discontinuous Galerkin scheme tical and more prevalent. As the usage has increased, to reduce the errors. We modify the numerical fluxes to new challenges have emerged, and we continue to develop account for the curved interface. Our numerical modeling new finite volume methods and workflows to meet those example demonstrate that our new discontinuous Galerkin needs. Here, we will share recent progress on extending scheme significantly suppresses the spurious diffractions our methodology and applying it to study recovery mecha- seen in the results obtained using the conventional scheme. nisms in naturally fractured reservoirs. Specifically, we will The computational cost of our scheme is similar to that of address consistent discretization, flow-based upscaling, and the conventional scheme. Our new discontinuous Galerkin comparison between gridded and embedded DFM simula- scheme is thus particularly useful for large-scale wave mod- tions. eling involving complex subsurface structures. Brad Mallison, Sarah Vitel, Robin Hui Xiangxiong Zhang Chevron Energy Tech. Co. Purdue Universityogy [email protected], [email protected], Department of Mathematics [email protected] [email protected]

MS44 MS44 Reactive Transport Modeling in Fractured Porous Cvd-Mpfa Mixed-Dimensional Coupled Fracture Media: Role of Fluid-Rock Interactions on Flow Approximation and Transport

A novel cell-centred control-volume distributed multi-point In deep geological media heat and chemical stresses can flux approximation (CVD-MPFA) finite-volume formula- cause physical alterations, which may have a significant ef- tion is presented for discrete fracture-matrix simulations. fect on flow and reaction rates. As a consequence it will The grid is aligned with the fractures and barriers which lead to changes in permeability and porosity of the for- are modelled as lower-dimensional interfaces with frac- mations due to mineral precipitation and dissolution. We ture network located between the matrix cells. The demonstrate the results of a numerical scheme considering CVD-MPFA formulation naturally handles fractures with material discontinuities in fractured porous media used to anisotropic permeabilities on unstructured grids. solve a system of nonlinear transport models.

Raheel Ahmed Hamid Nick, David Bruhn Swansea University Delft University of Technology [email protected] [email protected], [email protected]

MichaelG.Edwards Swansea University MS44 School of Engineering Generalized Multiscale Finite Element Method for [email protected] Flows in Fractured Media In this work, we present a multiscale approach for shale MS44 gas transport in fractured media. Our approach uses an Phase Transition and Reverse Pumping During upscaled model in the form of nonlinear parabolic equa- Flow Induced Slip Failure tions to represent the matrix that consists of organic and inorganic matter. The interaction of matrix and the frac- Shear or tensile failure due to fluid injection leads to the ture is represented by multiscale basis functions. We follow creation of new volume, which is accessible by fluid. De- Generalized Multiscale Finite Element Method to extract pending on the ratio of mechanical to flow time scales, the the leading order terms that represent the matrix and the pressure in such volumes temporarily decreases, which can fracture interaction. Numerical results are presented. result in a flow from the adjacent matrix into the fracture. This phenomenon is supported by simulation studies show- Yucel Akkutlu ing that this reverse pumping mechanism can be exploited Dept of Petroleum Engineering to extract significant amounts of fluid from the matrix. Texas A&M University [email protected] Rajdeep Deb ETH Zurich Yalchin Efendiev Institute of Fluid Dynamics Dept of Mathematics [email protected] Texas A&M University [email protected] Patrick Jenny Institute of Fluid Dynamics Maria Vasilyeva ETH Zurich North-Eastern Federal University [email protected] Russia [email protected]

MS44 New Directions and Practical Application of Fi- MS44 nite Volume Methods for Discrete Fracture-Matrix Diﬀusive Zone Fracture Modeling for Porous Media Simulations Applications

In recent years, application of discrete fracture-matrix We discuss modeling fractures in a poroelastic medium us- (DFM) simulations to ﬁeld studies has become more prac- ing a phase-ﬁeld formulation. The fracture is treated as GS15 Abstracts 119

a diffuse interface in the reservoir domain. The coupled [email protected], [email protected] reservoir-fracture flow problem is formulated as a single, pressure diffraction equation. We provide numerical examples demonstrating the effectiveness of this approach. Ad- MS45 ditionally a comparison between two modeling approaches, Nonhydrostatic Correction for Shallow Water fracture/matrix flow as an interface versus a diffusive zone, Equations with Quadratic Vertical Pressure Dis- is also presented. tribution: A Boussinesq-Type Equation

Mary F. Wheeler Two common approaches for dispersive long wave equa- Center for Subsurface Modeling, ICES tions are compared namely the Boussinesq-type equations University of Texas at Austin and the nonhydrostatic pressure correction for the shallow [email protected] water equations. If the latter is derived with a quadratic vertical interpolation for the nonhydrostatic pressure, we Gurpreet Singh show that both approaches are equivalent for special cases. The University of Texas at Austin The comparison of numerical dispersion relations is per- Center for Subsurface Modeling formed with a testcase implemented in a tsunami model [email protected] based on an adaptive triangular mesh with ﬁnite element space discretization. Sanghyun Lee Center for Subsurface Modeling, ICES Anja Jeschke UT Austin, TX, USA CliSAP/CEN, University of Hamburg [email protected] [email protected]

Thomas Wick Stefan Vater Johann Radon Institute for Computational and Applied University of Hamburg, KlimaCampus Math : Research group ”Numerical Methods in Geosciences Austrian Academy of Sciences [email protected] [email protected] Jörn Behrens KlimaCampus, University of Hamburg MS45 [email protected] Tsunami-Hysea Model: a Multi-Gpu Finite- Volume Solver for the Italian Tsunami Early Warn- ing System MS45 Modeling Coastal Hazards Using the Multi-Layer The INGV in collaboration with the EDANYA Group Shallow Water Equations (UMA) are developing and implementing a FTRT (Faster Than Real Time) Tsunami Simulation approach for the Currently earthquake based tsunami modeling usually in- Italian candidate Tsunami Service Provider, namely the volves the use of a depth-averaged model of the ocean for Centro Allerta Tsunami (CAT). The numerical model used computational efficiency and the suitability of such mod- for this purpose, named Tsunami-HySEA, implements in els to the problem. Models containing multiple layers have the same code the three phases of an earthquake generated usually not been applied to such events as the single layer tsunami: generation, propagation and coastal inundation. model tends to be sufficient. In this talk I will outline The HySEA model uses nested meshes with different res- results looking into whether certain earthquake scenarios olution and multi-GPU environment, which allows much may warrant a multi-layer approach and what the pros and FTRT simulations, computing within a few minutes wall cons of the approach are. clock time the evolution of a seismically generated tsunami in the whole Mediterranean Sea. Kyle T. Mandli Columbia University Manuel J. Castro Applied Physics and Applied Mathematics University of Malaga, Spain [email protected] [email protected]

JoséMGonzález-Vida, Jorge Mac´ıas-Sánchez, Marc de la MS45 Asunción Managing Parallel Dynamic Adaptivity for University of Málaga, Spain Tsunami Simulations with Time-Dependent [email protected], [email protected], [email protected] Source Terms

Daniele Melini We present recent work on coupled tsunami and earth- Istituto Nazionale di Geofisica e Vulcanologia, Italy quake simulation. As tsunamis may need hours to develop [email protected] and reach the shores whereas earthquakes happen within minutes, we need to tackle the problem of different time scales of those processes. On the computational side, we Fabrizio Romano discuss using adaptive parallel grids for the tsunami sim- Istituto Nazionale di Geofisica e Vulcanologia ulation and show speedup results due to vectorizing over [email protected] simultaneous tsunami simulations.

Roberto Tonini, Stefano Lorito, Alessio Piatanesi, Irene Kaveh Rahnema Molinari Technische Universität München Istituto Nazionale di Geofisica e Vulcanologia, Italy Chair of Scientific Computing [email protected], [email protected], [email protected] 120 GS15 Abstracts

Michael Bader tiotemporal evolution of solutes, a process that is mainly Technische Universität München controlled by the heterogeneity of K. In sedimentary [email protected] aquifers at the local scale, vertical variations of K are typically larger than horizontal variations and thus exert more control on the plume evolution. The K layering can be in- MS45 ferred by combining the Lagrangian formulation of trans- Dynamic Models of Earthquakes and Tsunamis port with the assimilation of tracer test data via the ensem- from Dip-Slip Faults Offshore Ventura, California ble Kalman filter (EnKF). In this work, the data for the assimilation procedure are provided by the monitoring of The Ventura basin in southern California is becoming in- tracer tests with electrical resistivity tomography (ERT). creasingly recognized for seismic and tsunami hazards. Our main objective is to show the possibility of directly us- Within the region is a network of coastal dip-slip faults, po- ing ERT resistivity data collected across a control plane by tentially producing earthquakes of magnitude 7 or greater. assimilating the solute travel times, instead of the concen- We construct a 3D dynamic rupture model of an earth- tration values, thus avoiding the need for a petrophysical quake on the Pitas Point fault to model ground motion and law. The methodology is applied to both a synthetic and the resulting tsunami. Our corresponding tsunami model a real test case and gives a satisfactory retrieval of the matches the seafloor displacement to the final seafloor dis- K vertical distribution, as well as of the solute evolution. placement from the rupture model. The performance of the method depends on the distance between the control plane and the injection source. Kenny J. Ryan Department of Earth Sciences Elena Crestani, Matteo Camporese, Paolo Salandin University of California, Riverside Università degli Studi di Padova [email protected] [email protected], mat- [email protected], [email protected] Eric L. Geist US Geological Survey [email protected] MS46 A Data Assimilation Framework for Fully Coupled Michael Barall Hyperresolution Subsurface - Land Surface Models Invisible Software [email protected] Data assimilation (DA) is increasingly applied to not only update states of terrestrial system models, but also parameters. We compared different DA methodologies for joint David D. Oglesby state-parameter estimation for (1) saturated groundwater Department of Earth Sciences, Univ. of CA, Riverside flow problems and (2) 1D land surface model columns. Ex- 900 University Ave. Riverside, CA 92521 periments with 3D land surface models and large scale cou- [email protected] pled subsurface- land surface models show the feasibility of the approach, and the current limitations and challenges. MS45 Harrie Jan Hendricks-Franssen Towards Operational Adaptive Tsunami Modeling Agrosphere (IBG-3) - Validating Adaptive Discontinuous Galerkin In- Forschungszentrum Jülich undation Schemes [email protected] We present a tsunami simulation framework, which is based on adaptive triangular meshes and a Runge-Kutta discon- Wolfgang Kurtz tinuous Galerkin (RKDG) discretization. This approach IBG-3, Forschungszentrum Julich allows for high local resolution and geometric accuracy, [email protected] while maintaining the opportunity to simulate large spatial domains. While the specific components of the framework Xujun Han, Johannes Keller, Hongjuan Zhang have numerically been validated, in this study the appli- IBG-3, Forschungszentrum Julich GmbH cability to realistic scenarios is considered. We compute [email protected], [email protected], well-known benchmark problems and compare simulation [email protected] results to recent tsunami events. Harry Vereecken Stefan Vater Forschungszentrum J University of Hamburg, KlimaCampus Agrosphere Institute IBG-3 : Research group ”Numerical Methods in Geosciences [email protected] [email protected]

Jörn Behrens MS46 KlimaCampus, University of Hamburg Recent Advancements in Data Assimilation [email protected] Through EnKF Coupled with Moment Equations of Groundwater Flow MS46 We discuss the key elements of a novel data assimila- Assessment of Hydraulic Conductivity at the Local tion technique we propose that is grounded on coupling Scale via Assimilation of Travel Time Data From the EnKF algorithm with the moment equations (MEs) of ERT-monitored Tracer Tests groundwater flow. Accuracy and feasibility of the approach are successfully tested and compared against its more tra- Assessing the spatial distribution of hydraulic conductivity ditional (Monte Carlo based) counterpart through a suite (K) in natural aquifers is fundamental to predict the spa- of synthetic studies and by way of a field-scale application GS15 Abstracts 121

performed in an alluvial aquifer. Displacement Data

Marco Panzeri, Monica Riva, Alberto Guadagnini Fluid extraction from producing hydrocarbon reservoirs is Politecnico di Milano one of the most frequent causes of anthropogenic land sub- [email protected], [email protected], al- sidence. A geomechanical model is used to predict the land berto [email protected] surface displacements above a gas ﬁeld where displacement observations are available. An ensemble-based data assimilation (DA) algorithm is implemented that incorporates MS46 these observations into the response of the geomechani- Groundwater Flow Data Assimilation with a cal model. The calibration focuses on the uniaxial vertical Reduced-Order Model Based on Stochastic Mo- compressibility CM which is assumed heterogeneous within ment Equations the reservoir.

We present a computationally efficient methodology to es- Claudia Zoccarato timate the spatial distribution of heterogeneous hydraulic Università degli Studi di Padova conductivity fields in random geologic media using a Monte [email protected] Carlo-based data assimilation (DA) approach. The computational burden associated with the forecast step of the Domenico Ba DA scheme is reduced by projecting the groundwater flow University of Sheffield equation into the space of few basis functions. These basis d.bau@sheffield.ac.uk functions are obtained from the solution of the equations satisfied by the ensemble moments of groundwater flow. Massimiliano Ferronato Dept. ICEA - University of Padova Damiano Pasetto [email protected] Institut National de la Recherche Scientifique (INRS-ETE) Giuseppe Gambolati Centre Eau Terre Environnement University of Padova [email protected] DMMMSA [email protected] Mario Putti Department of Mathematics Pietro Teatini University of Padua Università degli Studi di Padova [email protected] [email protected]

Alberto Guadagnini Los Almos National Laboratory MS47 [email protected] A Stochastic Bulk Rate Parameterization of Cloud Microphysical Processes Driven by a Turbulent Collision Kernel MS46 Iterative Ensemble Smoothers in the Annealed Im- Collision and coalescence of cloud droplets to form rain portance Sampling Framework droplets is a poorly understood area of cloud microphysics. Detailed models are prohibitively expensive. Var- Iterative ensemble techniques for solving inverse problems ious bulk models have been proposed, but require an as- has recently gained a lot of interest in many geophysical sumed droplet distribution and rely on ad-hoc parameters. communities. Although several variants exist, we focus A stochastic bulk rate parametrization that avoids the use on the ensemble smoother with multiple data assimila- of any specific apriori distribution and includes only phys- tion (ESMDA). The first part of this study discuss the ically meaningful parameters is presented. A droplet dis- similarity between the iterative smoother and other exist- tribution is assumed to exist and to have a spectral mean. ing techniques such as particle flow and annealed impor- Values of physically meaningful parameters are acquired tance sampling. The second part is devoted to how we from data. This new parametrization, possibly the first can use a sequential Monte Carlo sampler in combination stochastic one, can accommodate realistic turbulent ker- with an annealing process to weight-correct the iterative nels. Results are presented. sampling procedure and discuss possible approximations David Collins in large scale models. University of Victoria Andreas Stordal [email protected] International Research Institute Of Stavanger (IRIS) Bergen 5008, Norway MS47 [email protected] A Normal Mode Perspective of Intrinsic Ocean- climate Variability Ahmed H. ElSheikh Institute of Petroleum Engineering Observations of the sea surface temperature field over more Heriot-Watt University, Edinburgh, UK than a century indicate that there is pronounced variabil- [email protected] ity in the climate system. Understanding the mechanisms of this variability is crucial to determine the role of ocean heat content variations in past and future climate changes. MS46 When a steady background state in an ocean-climate model Estimation of a Spatially Distributed Reservoir is slightly perturbed, the long-time response is determined Compressibility by Assimilation of Ground Surface by the spatial patterns of the normal modes. Here, the type 122 GS15 Abstracts

and patterns of normal modes for a range of diﬀerent equi- slows down the sinking. This negative feedback mechanism librium states in a hierarchy of ocean-climate models are is thought to be responsible for the existence of a 60-70 presented. The rather elegant organization of these normal year cycle in AMOC. We present underwater data of heat, modes is demonstrated and prototype physical mechanisms salinity and AMOC overturning rate to reveal how this explaining patterns of sea surface temperature variability mechanism works in the real world, and suggest that the based on these normal modes are provided. current hiatus in global warming is caused by this AMOC variability. Henk A. Dijkstra IMAU, Utrecht University, Utrecht, the Netherlands Ka-Kit Tung [email protected] University of Washington [email protected] MS47 Carbon-weather Data Assimilation MS48 Global-local Multiscale Model Reduction for Flows Abstract not available at time of publication. in Heterogeneous Porous Media

Inez Fung We combine discrete empirical interpolation techniques, University of California, Berkeley global mode decomposition methods, and local multi- [email protected] scale methods, such as the Generalized Multiscale Fi- nite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly- MS47 heterogeneous porous media. To solve the nonlinear gov- Modeling and Evaluation of Hurricane Storm Surge erning equations, we employ the GMsFEM to represent the Mitigation solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse Recent hurricane events in the Gulf of Mexico have demon- grid. Computing the GMsFEM solution involves calculat- strated the vulnerability of coastal populations and infras- ing the residual and the Jacobian on the fine grid. As such, tructure to hurricane storm surges. The authors have been we use local and global empirical interpolation concepts to at the forefront in the development of the Advanced Circu- circumvent performing these computations on the fine grid. lation (ADCIRC) storm surge model. This finite element The resulting reduced-order approach enables a significant model has been used in design/planning mode prior to the reduction in the flow problem size while accurately captur- hurricane season, in predictive mode as storms approach ing the behavior of fully-resolved solutions. We consider land, and in hindcasting mode after the event. We present several numerical examples of nonlinear multiscale partial recent results of Hurricane Ike validation, as well as pro- differential equations that are numerically integrated us- posed structural gates and levees constructed to mitigate ing fully-implicit time marching schemes to demonstrate the effect of storm surges on significant areas such as Galve- the capability of the proposed model reduction approach ston Bay and the Houston Shipping Channel. to speed up simulations of nonlinear flows in high-contrast Jennifer Proft porous media. University of Texas at Austin Victo Calo [email protected] Applied Mathematics & Computational Science and Earth Science & Engineering, KAUST MS47 [email protected] Quantifying Inter-annual to Decadal Uncertainty Related to Initial Ocean Conditions MS48 Smith et al. (2012) discuss the importance of initial condi- Residual-driven Online Generalised Multiscale Fi- tions on long time scale forecasts and Krger et al. (2012) nite Element Methods and Matei et al. (2012) illustrate how various reanalysis products influence decadal outcomes. In this talk we dis- The construction of local reduced-order models via multi- cuss the next steps that are necessary in the quantification scale basis functions has been an area of active research. of uncertainty: how to comprehensively quantify the down- In this talk, we present online multiscale basis functions stream forecast uncertainty, as it relates to initial condition which are constructed using the offline space and the cur- uncertainty, in a statistically rigorous manner. We present rent residual. Online multiscale basis functions are con- some early outcomes of the research. structed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows Robin Tokmakian that one needs to have an offline space with certain prop- Naval Postgraduate School erties to guarantee that additional online multiscale ba- [email protected] sis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are MS47 constructed using Generalized Multiscale Finite Element Global Warming Hiatus and AMOC Variability Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee Atlantic Meridional Overturning Circulation (AMOC), is that additional online multiscale basis functions will reduce also called the Great Heat Conveyor Belt. When AMOC the error independent of contrast. We note that the con- speeds up it transports more heat and salinity from the struction of online basis functions is motivated by the fact subtropical Atlantic to the sub polar latitudes of the North that the offline space construction does not take into ac- Atlantic, where it sinks. The warm water melts ice in the count distant effects. Using the residual information, we polar latitudes; the fresh water dilutes the salty water and can incorporate the distant information provided the offline GS15 Abstracts 123

approximation satisfies certain properties. In the talk, the- offering greater flexibility in certain applications. oretical and numerical results are presented. Our numerical results show that if the offline space is sufficiently large Daniel W. Meyer (in terms of the dimension) such that the coarse space con- Institute of Fluid Dynamics tains all multiscale spectral basis functions that correspond [email protected] to small eigenvalues, then the error reduction by adding online multiscale basis function is independent of the con- Florian Muller trast. We discuss various ways computing online multiscale Institute of Fluid Dynamics, ETH basis functions which include a use of small dimensional of- fl[email protected] fline spaces. The research is supported by Hong Kong RGC General Research Fund (Project 400411). Patrick Jenny Institute of Fluid Dynamics Eric Chung ETH Zurich CUHK [email protected] [email protected]

MS48 MS48 Spatiotemporal Adaptive Methods for Multi- Generalized Multiscale Finite Element Method physics Modeling

In this talk, I will discuss multiscale model reduction tech- We discuss how Multiscale methods, which have been de- niques for problems in heterogeneous media. I will focus vised to efficiently solve large reservoir models, provide an on recently proposed methods that are based on Multiscale effective framework to deal with multiphysics problems. In- Finite Element Method (MsFEM). The main idea of this deed, they allow using different physical descriptions at dif- approach is to systematically incorporate the small-scale ferent scales and adapting the spatiotemporal resolution to information into multiscale basis functions. These meth- the problem of interest. We focus on the Multiscale Finite ods are intended for multiscale problems without scale sep- Volume method, which is basedonanumericalvolume- aration and high contrast. I will discuss the issues related averaging paradigm and can be easily applied to different to multiscale basis construction and a number of applica- systems of conservation equations. tions. I will also discuss some applications to parameter- dependent problems. Pavel Tomin Premier Assistant (Postdoc) Yalchin Efendiev University of Lausanne Dept of Mathematics [email protected] Texas A&M University [email protected] Ivan Lunati University of Lausanne [email protected] MS48 Algebraic Multiscale Method for Fractured Porous Media MS49 Coupling Deformation and Flow in Fractured An accurate and efficient algebraic multiscale method is de- Poroelastic Materials veloped for naturally fractured porous media, with a wide range of fracture length scales and fracture-matrix conduc- We introduce a coupled system of PDEs for the modeling tivity contrasts. Local basis functions for both matrix and of the fluid-fluid and fluid-solid interaction in a fractured, fractures are solved to construct fracture-matrix coupled poroelastic material. The fluid flow in the fracture is mod- multiscale coarse system. Combined with a second stage eled by a lower-dimensional equation, which interacts with smoother, our development leads to an iterative multiscale surrounding rock matrix and the fluid it contains. To de- strategy for heterogeneous fractured media. Several nu- termine the mechanical and hydrological equilibrium of the merical studies illustrate applicability of our method for system numerically, we combine an XFEM discretization real field studies. for the rock matrix deformation and pore pressure with a lower-dimensional grid for the fracture. The resulting Hadi Hajibeygi coupled discrete problem is solved using a substructuring TU Delft method. Analytical aspects of the proposed procedure are [email protected] discussed and illustrated with numerical examples in two and three dimensions.

MS48 Katja K. Hanowski Fast Uncertainty Quantification of Two-phase Flow IGPM and Transport with Multi-level Monte Carlo RWTH Aachen University [email protected] Multilevel Monte Carlo (MLMC) combines traditionally a multigrid technique with Monte Carlo (MC) sampling to Oliver Sander arrive at an MC simulation framework that is substantially IGPM RWTH Aachen University faster than conventional MC. Here, we apply instead of [email protected] grids of different resolution a hierarchy of solution methods of different accuracy. In the context of two-phase flow and transport, we demonstrate that the resulting solver MLMC MS49 leads like traditional MLMC to significant speedups while Iterative Methods for Coupled Flow and Geome- 124 GS15 Abstracts

chanics for Fractured Porous Media Center for Subsurface Modeling, ICES University of Texas at Austin Fractures play an important role in determining the flow [email protected] profile and at the same time are vulnerable regions for the mechanical deformations. We consider an iterative scheme for solving a coupled mechanics and flow problem in a frac- MS49 tured poroelastic medium. We provide an iterative scheme Modeling of Quasi-static Hydraulic Fracture Prop- to solve the coupled problem and our scheme is an adap- agation in Porous Media Using XFEM tation due to the presence of fractures of a classical fixed stress-splitting scheme. We prove that the iterative scheme We present a numerical model in 2D that describes hy- is a contraction in an appropriate norm. Moreover, the so- draulically driven fracture growth. The model is based on lution converges to the unique weak solution of the coupled the theory of poroelasticity and simulates the propagation problem. We also provide multi rate algorithms and their of a single embedded fracture in a fully saturated, linear analysis for such problems. elastic, isotropic, porous material. Fluid flow in the open flow in the fracture is approximated by a parallel plate Kundan Kumar model. The numerical model is set up using Finite El- Center for Subsurface Modeling, ICES University of ements and the fracture is described using the Extended Texas at Finite Element Method (XFEM). We discuss implantation [email protected] of the interface conditions and show test cases.

Tameem Almani Insa Neuweiler CSM, ICES, UT Austin Institute for Fluid Mechanics and Environmental Physics [email protected] in C University of Hannover [email protected] Vivette Girault University of Paris VI [email protected] Alina Juan-Lien Ramirez, Stefan Loehnert University of Hannover [email protected], [email protected] Mary F. Wheeler hannover.de Center for Subsurface Modeling, ICES University of Texas at Austin [email protected] MS49 An Xfem Approximation of Coupled Flow and Me- chanics in Fractured Rocks MS49 Phase Field Modeling for Fracture Propagation XFEM are often used in the simulation of fracture mechanics. In this work we employ XFEM also to the dis- In this talk, we consider phase-field-based fracture prop- cretization of the flow problem, so that grids can be set agation in elastic and poroelastic media. The main pur- irrespectively of the position of fractures thanks to suitable pose is the development of a robust and efficient numer- enrichment functions. Inside the fractures, whose aperture ical scheme. To enforce the entropy condition; namely, depends dynamically on the effective normal stress, flow is crack irreversibility, we use a robust primal-dual active set computed by a suitable reduced model coupled with the strategy. This is merged with the outer Newton iteration flow in the surrounding porous matrix. for the variational inequality of the fully-coupled nonlinear partial differential equation system, resulting in a sin- Anna Scotti gle, rapidly converging nonlinear iteration. In addition, it MOX, Department of Mathematics, Politecnico di Milano is well known that phase-field models require fine meshes [email protected] to accurately capture the propagation dynamics of the crack. Because traditional estimators based on adaptive Alessio Fumagalli mesh refinement schemes are not appropriate, we present Institut Fran¸cais du Pétrole Energies´ nouvelles a predictor-corrector scheme for local mesh adaptivity to [email protected] reduce the computational cost. Our proposed approach is substantiated with different numerical tests in two and Bianca Giovanardi three dimensions considering crack propagation in elastic MOX, Politecnico di Milano media as well as multiple pressurized fractures in hetero- [email protected] geneous media. Collaborators: Mary F. Wheeler, Thomas Wick, Timo Heister MS50 Sanghyun Lee Center for Subsurface Modeling, ICES Toward Stochastic Nonlinear Wave Models UT Austin, TX, USA The use of deterministic simulations for marine applica- [email protected] tions is a common practice in coastal and off-shore engineering. In recent years, we have proposed a i) massively Thomas Wick parallel and ii) high-order numerical strategies for highly Johann Radon Institute for Computational and Applied efficient and accurate prediction of wave propagation and Math wave kinematics and iii) a stochastic formulation for wave Austrian Academy of Sciences propagation. In this talk, we present our ongoing work on [email protected] extending the previous works and applying it to the case of hydrodynamic loads on offshore wind turbines. We will Mary F. Wheeler outline the development of a new unstructured and robust GS15 Abstracts 125

spectral element method for the potential flow equations. Costas Synolakis The model is aimed at large-scale wave propagation in ma- Department of Civil and Environmental Engineering rine settings with complex geometric structures. The com- University of Southern California putational methods are applied to estimate the uncertain- [email protected] ties in the hydrodynamic loads acting on the monopile of the IAE1s OC3 Phase 1 test case. Here uncertainties in the Patrick Lynett input data (e.g. bathymetry, wave spectra, geometry) are University of South Carolina investigated using traditional and novel uncertainty quan- [email protected] tification techniques. The objective of the study is to combine and deliver new advanced methodologies for efficient, Argiris Delis systematic and rigorous engineering analysis. Technical University of Crete School of Production Engineering & Management Claes Eskilsson [email protected] Chalmars University of Technology Gothenburg, Sweden. [email protected] MS50 Integrated Coastal and Ocean Process Modeling Allan P. Engsig-Karup for Management of Coastal Flooding and Morpho- Technical University of Denmark logical Changes Department of Informatics and Mathematical Modeling [email protected] This paper presents applications of integrated coastal and ocean process modeling for management of coastal flooding Daniele Bigoni and morphological changes induced by waves, storm surges, The Technical University of Denmark sediment transport, and sea level changes. It emphasizes [email protected] the advancement of the integrated modeling to simulate and predict hydrodynamic and morphodynamic processes in coasts and estuaries. This paper provides engineering MS50 application examples for comprehensive impact assessment of coastal flooding and erosion due to combined hazardous Harbour Modelling Via Depth Averaged and Non- storm conditions in coasts. Hydrostatic Models: Comparison and Validation Mustafa Altinakar In this work a numerical study of the wave conditions in NCCHE - University of Mississippi the old Venetian harbor in Chania, Crete in Greece, is [email protected] presented using two numerical models/codes, namely the COULWAVE code and the TUCWave one. Field measure- Yan Ding ments are also used to validate the simulations. In the NCCHE, University of Mississippi well-established COULWAVE code, the 2D fully nonlinear [email protected] weakly dispersive Boussinesq-type equations of Wei at al. (1995) are solved. The numerical model uses a predictor- corrector scheme to march forward in time and a Finite MS50 Volume (FV) solver on structured meshes. The resulting scheme is of fourth-order of accuracy, both in space Spectral Collocation Simulation of Non-Periodic and time. In the TUCWave code the 2D weakly nonlin- Long Waves in Nonlinear Dispersive Systems ear weakly dispersive Boussinesq-type equations of Nwogu We are concerned with collocation methods based on Her- (1993) are solved by implementing a novel high-order ac- mite and Laguerre functions in order to solve Cauchys curate, in space and time, well-balanced FV numerical problems attached to nonlinear wave equations with non- method on unstructured triangular meshes. A MUSCL- linear (regularized long-wave) or linear dispersion (KdV, type reconstruction technique is implemented for enhanc- Nonlinear Schrdinger, Gordons equations, etc.) on infinite ing the spatial accuracy while a strong stability preserving domains. We avoid the domain truncation or periodicity Runge-Kutta method is used for the time stepping. Here and use the scaling parameter hidden in these methods in we examine the contribution of harbor resonance in the ex- order to get accurate conservation of some time invariant citation of the Venetian harbor basin during typical winder and to capture a large picture of the wave propagation. storms. An extensive comparison of the two models is performed under the same conditions obtained from the field Calin I. Gheorghiu measurements. Romanian Academy ”T. Popoviciu” Institute of Numerical Analysis, Maria Kazolea Cluj-Napoca INRIA Bordeaux Sud-Ouest [email protected] [email protected]

Nikos Kalligeris MS50 University of Southern California Coupling of Non-hydrostatic Models for Shallow Department of Civil and Environmental Engineering Water Flows [email protected] The motion of water in a complex hydrodynamic conﬁg- Nikos Maravelakis uration is characterized by a wide spectrum of space and Technical University of Crete time scales. Consequently, the numerical simulation of a School of Environmental Engineering hydrodynamic system of this type is characterized by a [email protected] large computational cost. In this talk we will address the 126 GS15 Abstracts

problem of coupling 1D, 2D and 3D non-hydrodstatic and [email protected] hydrostatic models.

Edie Miglio MS51 Politecnico di Milano (Italy) Distribution Functions of Water Saturation for MOX, Dept. of Mathematics Stochastic Nonlinear Two-Phase Problems [email protected] We give an analytical expression for the one-point cumulative distribution and probability density functions of the MS50 water saturation for the stochastic Buckley-Leverett prob- Sensitivity Analysis Via Anova Decomposition for lem with uncertainty in porosity and total Darcy flux. Wave Runup on Complex Bathymetries With the use of a streamline approach and appropriate random processes, the one-point distributions can be de- We use uncertainty quantification tools to study the sensi- rived exactly, leading to any one-point statistics. We pro- tivity wave runup to variations of wave amplitude, slope, vide comparisons with Monte Carlo simulations and low and friction coefficient. Sensitivity indexes are computed order approximations to illustrate the performance of the from an Analysis of Variance based on a non-intrusive poly- method. nomial chaos method (Crestaux-LeMaitre-Martinez, 2009). To guarantee the repeatability of the experiments, two in- Fayadhoi Ibrahima dependent numerical codes are used, developed in (Ricchi- Stanford University uto, JCP 2015) and (Nikolos and Delis, 2009), respectively, fi[email protected] and several 2D and 3D inundation bechmarks are used to investigate runup physics. Daniel W. Meyer Institute of Fluid Dynamics Anargyros Delis [email protected] Technical University of Crete [email protected] Hamdi Tchelepi Stanford University Mario Ricchiuto Energy Resources Engineering Department INRIA [email protected] [email protected]

Pietro M. Congedo MS51 INRIA Bordeaux Sud-Ouest (FRANCE) A Stochastic Galerkin Method for Two-Phase Flow [email protected] in Heterogeneous Porous Media We consider the dynamics of two-phase flow in a two- MS51 dimensional heterogeneous porous medium with randomly located interfaces. In the deterministic case discontinuities A Multilevel Monte Carlo Method for Estimating of the flux function occur due to the change of the ma- Failure Probabilities of Two-Phase Flow Systems terial parameters. Based on the capillarity-free fractional This talk presents a multilevel Monte-Carlo method for flow formulation a hybrid Stochastic Galerkin finite volume computing failure probabilities of subsurface two-phase method (HSG-FV) is presented. The classical polynomial flow systems for carbon dioxide storage. We study sweep chaos expansion is extended by a multi-element discretiza- efficiency and breakthrough time as indicators for stor- tion. This yields a weakly coupled deterministic system age capacity, and denote by failure the events that these which allows for efficient parallelization. are below critical values. The flow is governed by the Markus Köppel,IljaKröker Buckley-Leverett equation, and the permeability field is University of Stuttgart modeled with uncertainty. We apply a multilevel Monte- Institute for Applied Analysis and Numerical Simulation Carlo method specialized for failure probabilities to reduce [email protected], the computational effort. [email protected] Fritjof Fagerlund Department of Earth Sciences Christian Rohde Uppsala University University of Stuttgart [email protected] Institut für Angewandte Analysis und Numerische Simulation [email protected] Fredrik Hellman Department of Information Technology Uppsala University MS51 [email protected] Dimension Reduction with Inverse Regression for High-dimensional Stochastic Modeling of Subsur- Axel M˚alqvist face Flows Department of Mathematical Sciences Chalmers University of Technology Stochastic modeling of subsurface flows often involves [email protected] many uncertain parameters, such as permeability on each grid-block, and hence suffers the “curse of dimensional- Auli Niemi ity”. This difficulty is alleviated if we can represent the Department of Earth Sciences high-dimensional parameter vector on a lower-dimensional Uppsala University subspace. The inverse regression method greatly reduces GS15 Abstracts 127

model dimensionality while preserving the nonlinear uncer- (2006), tainty propagation from model parameters to the quantity to be predicted, and is shown to be more effective than Lynn S. Bennethum traditional methods like K-L expansion. University of Colorado Denver [email protected] Weixuan Li Pacific Northwest National Laboratory [email protected] MS52 Role of Sorption in Effective Stress in Variably Sat- urated Soil MS51 Uncertainty Quantification Using Transformed Abstract not available at time of publication. Probabilistic Collocation Method for Strongly Nonlinear Problems Ning Lu Department of Civil and Environmental Engineering In uncertainty quantification, the traditional probabilistic Colorado School of Mines collocation method (PCM) may produce nonphysical os- [email protected] cillation and inaccurate estimation in case of strong nonlinearity/unsmoothness. To address this issue, we develop a new transformed probabilistic collocation method MS52 (TPCM), in which model response is represented by the A Multi-Scale Form of Terzaghi’s Effective Stress location or arrival time of a particular response value. We Principle for Unsaturated Expansive Clays show that the TPCM is more accurate than the PCM and is much more efficient than the Monte Carlo method. A multi-scale approach of Terzaghis effective stress principle for unsaturated swelling clays is presented that is rigor- Qinzhuo Liao ously derived by homogenization starting from micro- and University of Southern California nano-mechanical analyses. The resulting macroscopic elas- [email protected] tic stress captures coupling between electrochemical dis- joining forces at the clay platelet scale and capillary ef- Dongxiao Zhang fects at the clay cluster scale. Numerical simulations allow Peking University conclusions about water transfer between intra- and inter- [email protected] particle pores during wetting and thus about the evolution of the resulting swelling pressure.

MS51 Julia Mainka Energie and Transfer Stochastic Galerkin Methods and the Problem of LEMTA - Universite de Lorraine - CNRS High Stochastic Dimensionality in CO2 Storage [email protected] The complexity of numerical simulation of transport of CO2 in subsurface storage formations necessitates Marcio A. Murad simplified-physics models that are subject to significant National Laboratory of Scientific Computation uncertainty in modeling assumptions and material parame- LNCC/MCT ters. A stochastic Galerkin solver for stochastic CO2 trans- [email protected] port is presented along with numerical results and analysis of the most prominent sources of uncertainty. Special care Christian Moyne is needed to accurately capture quantities of interest, e.g., Universite de Lorraine, LEMTA, UMR 7563, probability of CO2 leakage to the atmosphere and ground- Vandoeuvre les Nancy, France water resources. [email protected]

Per Pettersson Tran Van Duy Uni Research LEMTA - Universit´e de Lorraine -CNRS UMR 7563 [email protected] [email protected]

MS52 MS52 Introduction to Terzaghi Stress Principle and a An Analytical Approach to Link Effective Stress, Theoretical Formulation Based on Total Differen- Shear Strength and Moisture at the Micro-scale tials The link from water content and water tension to effective Here we present results on the derivation of the Terzaghi stress and shear strength is unclear. Particle contact forces Stress Principle theoretically using total differentials from and the effect of a small amount of water on them are for- a thermodynamic framework. We use thermodynamic defi- mulated through analytical calculations of probability and nitions of the drained and unjacketed compressibilities and geometry, for identical rigid spheres. Findings are com- total differentials to theoretically determine how the total pared to triaxial shear test results on specimens of uniform pressure relates to strain and changes in fluid pressures. We glass spheres. The effect of water is found to be different show that under simplifying assumptions we recover the from applying an external isotropic stress to the soil. varying forms of the Biot coefficient for saturated porous media and the bishop parameter for partially saturated Kartal Toker porous media. Results are compared with other approaches Deaprtment of Civil Engineering such as the differential approach of Wang (2000), and the Middle East Technical University mixture theoretical approach of Coussy (1995) and Borja [email protected] 128 GS15 Abstracts

John Germaine tions, and naturally introduce a path function, which is Massachusetts Institute of Technology proven to be a monotonic function of the spatial coordinate [email protected] variable. By using the linear transformation and the path function, we overcome the above difficulties and develop Patricia Culligan the efficient methods for calculating the interface and its Columbia University interior compositions. Moreover, the computation of the [email protected] surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. MS52 Numerical examples are tested to verify the efficiency of Effective Stress Tensor in Unsaturated Pendular- the proposed methods. State Granular Media Jisheng Kou The expression of a proper effective stress tensor in un- Hubei Engineering University saturated granular media has been a longstanding issue [email protected] essentially because of the difficulty to account for interfacial effects. While the analysis of unsaturated conditions Shuyu Sun goes beyond Terzaghi’s effective stress, the commonly used Division of Mathematical and Computer Sciences & Bishop’s effective stress is fraught with many issues, one of Engineering them being empirical. In this connection, we derive a sin- King Abdullah University of Science and Technology gle effective stress tensor that encapsulates evolving liquid (KAUST) bridges, interfaces, particle packing, and water saturation [email protected] through a micromechanical analysis of force transport in an unsaturated pendular-state granular material. Discrete Xiuhua Wang Element Method (DEM) numerical simulations of triaxial Hubei Engineering University compression tests of pendular-state granular samples at dif- [email protected] ferent matric suctions are conducted to verify the proposed effective stress equation. MS53 Richard G. Wan Weak Galerkin Method for Steady Diffusion Prob- Civil Engineering lems with Highly Anisotropic Coefficients University of Calgary [email protected] In petroleum reservoir simulation, a family of control- volume methods has been developed for solving the general tensor pressure equation while satisfying flux-continuous, MS53 local mass conservative and discrete maximum principle. A Multi-stage Bayesian Prediction Framework for Weak Galerkin method is a type of finite element method Subsurface Flows which can meet all these requirements under general finite elements framework. In the talk, we will compare the finite In this talk, we discuss the development of computationally volume method with Weak Galerkin finite element method efficient procedures for subsurface flow prediction that re- specifically on high anisotropic diffusion problem. Second- lies on the characterization of subsurface formations given order convergence rate and monotonicity of Weak Galerkin static (measured permeability and porosity at well loca- method are verified with numerical examples. tions) and dynamic (measured produced fluid properties at well locations) data. We describe a predictive proce- Yan Li dure in a Bayesian framework, which uses a single-phase Chevron flow model for characterization aiming at making predic- [email protected] tion for a two-phase flow model. The quality of the characterization of the underlying formations is accessed through Lin Mu the prediction of future fluid flow production. Michigan State University Victor Ginting [email protected] University of Wyoming [email protected] Xiu Ye University of Arkansas, Little Rock [email protected] MS53 Efficient Numerical Methods for Simulating Sur- face Tension of Multi-component Mixtures with MS53 the Gradient Theory of Fluid Interfaces Weak Galerkin Finite Element Methods for Darcy Flow on Hexahedral Meshes Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a ma- For some real applications (petroleum reservoir simula- jor immiscible two-phase flow mechanism for systems with tions, in silico for biological and medical problems), hex- a strong wettability preference. We consider the numerical ahedral meshes are natural choices for spatial discretiza- simulation of the surface tension of multi-component mix- tion of 3-dim irregular domains. In this talk, we present tures with the gradient theory of fluid interfaces. Major preliminary results of developing weak Galerkin finite el- numerical challenges include that the system of the Euler- ement methods for solving the Darcy equation on hexa- Lagrange equations is solved on the infinite interval and the hedral meshes. In particular, we shall discuss these is- coefficient matrix is not positive definite. We construct a sues: error estimates, algorithm implementation and in- linear transformation to reduce the Euler-Lagrange equa- tegration with the visualization package VisIt, numerical GS15 Abstracts 129

experiments, and comparison with results on tetrahedral [email protected] meshes. This is a joint work with Farrah Sadre-Marandi (Colorado State University) and Min Yang (Yantai Univer- sity, China). MS54 The Importance of Physical and Numerical Ap- James Liu proximations in Hydraulic Methods for Aquifer Department of Mathematics Characterization Colorado State University [email protected] Inversion of hydraulic data for purposes of transport modeling is a nonlinear, ill-posed Bayesian inverse problem in which the forward model may be extremely expensive due MS53 to model extent, model transience, and model nonlinearities. We will review approaches to reducing the compu- Multi-Dimensional Eulerian-Lagrangian Advection tational burden of this problem. We will focus on useful Schemes using Quadrature physical and numerical approximations for reducing the expense of forward model evaluations, in addition to effective We develop an Eulerian-Lagrangian scheme to solve linear methods for data or parameter reduction. advectionproblems,whichintheoryhavenoCFLcon- straint. We integrate mass using a quadrature rule, af- Michael Cardiff ter converting cell average masses into high order accurate University of Wisconsin, Madison values at quadrature points. We develop a new WENO cardiff@wisc.edu reconstruction technique for the primitive function on several local stencils, weight them based on the smoothness of David Lim the solution to avoid shock-like discontinuities, and differ- University of Wisconsin-Madison entiate. Numerical results demonstrate the capabilities of [email protected] the scheme.

Todd Arbogast MS54 University of Texas at Austin Parallel Preconditioner Updates in Parameterized [email protected] Nonlinear Inverse Problems

Chieh-Sen Huang We consider combinations of preconditioner updates and ational Sun Yat-sen University recycling Krylov subspace methods that yield fast conver- Kaohsiung, Taiwan gence for parameterized systems of equations and allow ef- [email protected] ﬁcient ﬁne-grained parallel implementations. We consider applications in UQ for inverse problems. Jamie Pool, Mary Wheeler University of Texas at Austin Eric De Sturler [email protected], [email protected] Virginia Tech [email protected]

MS53 MS54 Approximate Solution to the Boussinesq Equation Joint Probabilistic Inference of Multi-Gaussian Near A Well Conductivity Fields and Their Associated Vari- ograms from Indirect Hydrological Data Flows near wells in unconfined aquifers are commonly modeled by the Boussinesq equation. We analyze the recharge We present a Bayesian approach for simultaneous esti- by well of an initially dry aquifer. Using similarity vari- mation of high-dimensional conductivity fields and asso- ables we reduce the original problem to a boundary-value ciated variograms. Our approach merges periodic embed- problem for a nonlinear ordinary differential equation. We ding with dimensionality reduction to decouple the vari- construct an approximate analytical solution to this prob- ogram from the random numbers, and facilitate MCMC lem having a singular term, to model behavior near the simulation. Using the Matérn variogram allows for infer- wellbore, and a polynomial part, to approximate the be- ence of the field smoothness. Conditioning on direct mea- havior in the far field. surements is straightforward. We illustrate our method using a synthetic flow and transport experiment involving Aleksey S. Telyakovskiy a 10,000-dimensional conductivity field, and provide com- Department of Mathematics and Statistics parison against other state-of-the-art approaches. University of Nevada [email protected] Eric Laloy Belgian Nuclear Research Centre Myron B. Allen [email protected] University of Wyoming Department of Mathematics Niklas Linde [email protected] University of Lausanne [email protected] Satoko Kurita University of Nevada, Reno Jasper Vrugt Department of Mathematics and Statistics University of California Irvine 130 GS15 Abstracts

[email protected] characterization and control.

Dennis McLaughlin MS54 Civil Engineering MIT Inversion of the Co-seismic Slip from GPS Data [email protected]

Remote sensing and geodetic measurements are providing a new wealth of observational data that have the ability to MS54 improve our understanding of co-seismic rupture and slow Statistical Tests for L1 Regularization Parameter slip events in subduction zones. We formulate a Bayesian Selection inverse problem to infer the slip distribution on the plate interface using an elastic finite element model and GPS sur- Choice of regularization parameter for the L1 norm is an face deformation measurements. We present an application open question and here we view the term as the result of to the co-seismic displacement during the 2012 earthquake maximizing the probability parameters errors are from an on the Nicoya Peninsula in Costa Rica, which is uniquely exponential distribution. In this case the regularization positioned close to the Middle America Trench and directly term should be weighted with the mean of the error in the over the seismogenic zone of the plate interface. From this initial guess, which is unknown. We use a statistical test to study we identify a locked patch that is likely to release estimate the mean, and hence find a regularization param- stress in the future. eter. The approach will be demonstrated on an inversion of resistivity data in the near surface. Kimberly McCormack University of Texas at Austin Jodi Mead [email protected] Boise State University Department of Mathematics Marc A. Hesse [email protected] University of Texas Department of Geological Sciences [email protected] MS55 Effective Large Scale Simulations of Discrete Frac- Georg Stadler ture Network Flows with a Pde-Constrained Opti- Courant Institute for Mathematical Sciences mization Approach New York University [email protected] Focusing on the Discrete Fracture Network model for fractured media, we consider a PDE-constrained optimization approach for flow simulations which allows for non- MS54 conforming grids, i.e. meshes on the fractures are required Model Reduction and Ensemble Kalman Filtering to be neither conforming each other, nor conforming to their intersections. The method is therefore well suited Ensemble versions of Bayesian inference are convenient for for dealing with large scale complex geometries, and it is estimating unobservable spatially variable properties from well suited for parallel implementation. Effectivity of the measurements of related state variables. Ensemble meth- method on rather complex networks will be shown. ods are especially usefu when the properties have complex spatial structures that do not conform to Gaussian descrip- Stefano Berrone tions. However, ensemble methods can be time consum- Politecnico di Torino ing for high-dimensional problems. This paper describes a Dipartimento di Scienze Matematiche ”G.L. Lagrange” reduced- order approach to ensemble characterization that [email protected] is particularly well suited for subsurface flow and transport problems. It uses a truncated discrete cosine transform Sandra Pieraccini to reduce the dimensionality of spatially variable time- Dipartimento di Matematica invariant model parameters and a nonlinear extension of Politecnico di Torino, Italy principle orthogonal decomposition to reduce the dimen- [email protected] sionality of dynamic model states. The resulting nonlinear reduced-order model can be included in the forecast step Stefano Scialo‘ of a reduced-order ensemble Kalman filter. We illustrate Politecnico di Torino these concepts in a subsurface solute transport problem, Dipartimento di Scienze Matematiche comparing the ensembles produced by full- and reduced- [email protected] order filters. The reduced-order Kalman filter does at least as well as the full-order filter in characterizing a dynamic solute plume, even though its augmented state dimension MS55 is only 2% of the dimension of the full-order state. This Upscaling Techniques for Highly Fractured Porous substantial increase in efficiency implies that 1) a reduced- Media with Non-Matching Discretization order filter with the same ensemble size as its full-order counterpart can give comparable performance for orders of The aim of this contribution is to present a novel methodol- magnitude less computational effort or 2) it can use a much ogy for a flow-based upscaling technique applied to highly larger ensemble for the same computational effort. The fractured reservoirs. To derive the upscaled properties we possibility of substantial increases in ensemble size could solve local problems where the numerical scheme adopted lead to performance improvements through reductions in removes parts of the geometrical constraints for the grid sampling error and in the rank of the ensemble null space. generation. A sub-region method is considered to enhance Also, a reduced-order model similar to the one described the intra porous matrix communication. Effectiveness of here could be used in ensemble real-time control applica- the method in comparison to more classical implementations, where it can decrease the effort required for both tions is proved through synthetic but representative prob- GS15 Abstracts 131

lems. Louis Durlofsky Stanford University Alessio Fumagalli [email protected] Institut Fran¸cais du Pétrole Energies´ nouvelles [email protected] MS55 Stefano Zonca An Integrated Approach To Upscaling And History Politecnico di Milano Matching Of Fractured Reservoirs [email protected] Fracture statistics are commonly used to generate macroscale parameters such as permeability. The upscaled Paola Panfili parameters are often adjusted using EnKF or similar meth- Eni E&P ods, where simulator predictions are compared with field paola.panfi[email protected] data. We show that these adjustments may be inconsis- tent with the underlying fracture structure, under certain Luca Pasquale conditions. We propose a new workflow to eliminate the MOXOFF problem, where the upscaling procedure is integrated into luca.pasquale@moxoff.com the history matching workflow. Synthetic field case examples are provided.

MS55 P˚al N. Svik, Inga Berre HPC Discrete Fracture Network Modeling for Sub- Department of Mathematics surface Flow and Transport Applications University of Bergen [email protected], [email protected] A workflow, dfnWorks, generates discrete fracture networks (DFN) of planar polygons, creates a high quality Martha Lien conforming Delaunay triangulation of the intersecting DFN Octio AS polygons, assigns properties (aperture, permeability) using Bergen geostatistics, sets boundary and initial conditions, solves [email protected] pressure/flow in single or multi-phase fluids (water, air, CO2) using the parallel PFLOTRAN, and solves for transport using Lagrangian particle tracking. Applications are MS55 shown for nuclear waste repository, CO2 sequestration and Imposing Convergence Constraints on Multiscale hydraulic fracturing and extraction of unconventional hy- Mehods for the Efficient Solution of Multiphase drocarbon resources. Flow Through Naturally Fractured Porous Media

Carl Gable, Jeffrey Hyman, Satish Karra, Nataliia This work investigates the possibility of using an incom- Makedonska pletely converged pressure solution in the sequentially im- Los Alamos National Laboratory plicit loop, traditionally used to simulate multiphase flow Earth and Environmental Sciences Division through porous media. This is made possible through the [email protected], [email protected], [email protected], Multiscale Finite Volume (MSFV) formulation, which was [email protected] recently extended to include fully integrated basis functions which account for contributions from wells and fractures Scott Painter [Tene et al, SPE RSS 2015]. Here, we take this method Oak Ridge National Laboratory one step further towards multiphase flows, by adding a Environmental Sciences Division conservative flux reconstruction stage and pairing it with [email protected] a fine-scale transport solver. In our experiments we monitor the convergence behaviour while adaptively varying the Hari Viswanathan tolerance level for the pressure solution. Finally, we con- Los Alamos National Laboratory clude that only few iterations of the multiscale pressure Earth and Environmental Sciences Division solver are sufficient to obtain results which are meaning- [email protected] ful for decision-making, especially given the fact that, in practice, the reservoir specification is subject to geological uncertainties. MS55 Adaptive Mesh Refinement for Modeling Flow Matei Tene Through Three-Dimensional Fracture Networks Delft University of Technology [email protected] Fractured formations with low matrix permeability are sometimes modeled using only a fracture network, with the Hadi Hajibeygi matrix contributions neglected completely. In this work TU Delft we present an adaptive mesh refinement (AMR) technique [email protected] applicable to three-dimensional fracture networks. The method is illustrated by simulating transport in complicated fractured models. We show that our AMR procedure MS56 can effectively reduce the size of the discrete model by in- Dynamically Adaptive Storm Surge Simulations troducing resolution in the active parts of the network. with a Slope-Limited Discontinuous Galerkin Model Mohammad Karimi-Fard Stanford Discontinuous Galerkin models have recently been used to [email protected] produce accurate and robust storm surge simulations. The 132 GS15 Abstracts

computational eﬀort, however, is still its major weakness. [email protected] In order to reduce the latter, we introduce a dynamically adaptive triangular mesh with problem-dependent reﬁne- Lucas Wilcox ment indicators to resolve local features. Our nodal slope- Department of Applied Mathematics limited Bernstein approach guarantees a correct handling Naval Postgraduate School of wetting and drying. Near-realistic test cases demon- [email protected] strate the potential of our non-uniform mesh.

Nicole Beisiegel Francis X. Giraldo University of Hamburg Naval Postgraduate School [email protected] [email protected]

Joern Behrens MS56 University of Hamburg A Trace Fem for a Coupled Transport and Diffusion Department of Mathematics over Surfaces and in a Bulk [email protected] In this talk, we consider a system of advection-diffusion Cristobal Castro equations in a bulk domain coupled to an advection- Escuela Universitaria de Ingeneria Mecanica diffusion equation on an embedded surface. Such systems Universidad de Tarapaca, Arica of coupled partial differential equations arise in, for exam- [email protected] ple, the modeling of transport and diffusion of surfactants in two-phase flows. The model considered here accounts for adsorption-desorption of the surfactants at a sharp in- MS56 terface between two fluids and their transport and diffusion Discontinuous Galerkin Methods for Coupled Hy- in both fluid phases and along the interface. We present a drologic/Hydrodynamic Flows well-posedness analysis for the system of bulk-surface equations and introduces a finite element method for its numer- Tropical storms lead to rainfall runoff and storm surge ical solution. The finite element method is unfitted, i.e., which may interact during a storm event, especially in the mesh is not aligned to the interface. The method is low-lying coastal areas. Overland flow, rainfall runoff into based on taking traces of a standard finite element space channels and streams, and storm surge occur at different both on the bulk domains and the embedded surface. The spatial/temporal scales, and may be modeled using cou- numerical approach allows an implicit definition of the sur- pled 1D/2D and possibly 3D hydrodynamic models. In face as the zero level of a level-set function. Optimal order this talk, we will discuss a discontinuous Galerkin based error estimates are proved for the finite element method framework for modeling overland flow and rainfall runoff both in the bulk-surface energy norm and the L2-norm. through a network of connected channels. The analysis is not restricted to linear finite elements and a piecewise planar reconstruction of the surface, but also Clint Dawson covers the discretization with higher order elements and a Institute for Computational Engineering and Sciences higher order surface reconstruction. University of Texas at Austin [email protected] Maxim A. Olshanskii Department of Mathematics Prapti Neupane University of Houston Institute for Computation, Engineering and Sciences [email protected] University of Texas at Austin [email protected] Arnold Reusken, Sven Gross Numerical Mathematics RWTH Aachen University, Aachen, Germany MS56 [email protected], [email protected] Atmospheric Simulations on the Sphere with the aachen.de Nonhydrostatic Unified Model of the Atmosphere (NUMA): Advances Using Parallel Grid Genera- tion with P4est MS56 Unfitted Finite Element Methods Using Bulk The Non-hydrostatic Unified Model of the Atmosphere Meshes for Surface Partial Differential Equations (NUMA) developed at the Naval Postgraduate School is the dynamical core inside the Naval Research Laborato- In this talk I will introduce a family of novel finite ele- rys next-generation weather prediction system NEPTUNE. ment methods for partial differential equations posed on Recent advances include interfacing NUMA with the p4est surfaces. The key idea is that the finite element space is library, which allowed for parallel grid generation. The re- based on continuous piecewise linear finite element func- sults of 3D unstable jet simulations on the sphere using 2D tions on a bulk triangulation which is independent of the mesh decomposition and 1D IMEX time integration will surface. I will introduce both a sharp interface and narrow be presented, along with scalability results up to 1,555,200 band version of the method for stationary problems and million MPI ranks. show how these methods can be combined to solve equations on evolving surfaces. I will present robust numerical Michal A. Kopera, Simone Marras, Andreas Mueller analysis for a simple model problem and provide computa- Naval Postgraduate School tional examples to show the flexibility and efficiency of the [email protected], [email protected], [email protected] methods. TOBIN Isaac Thomas Ranner ICES, University of Texas at Austin University of Leeds GS15 Abstracts 133

UK [email protected] [email protected]

MS57 MS56 Evaluating Numerical Weather Prediction Data Frozen Landscapes in Transition: Improving Pre- Common numerical weather prediction models provide dictions of Ice Sheet Stability in a Warming World gridded data for various meteorological parameters in a by Numerical Modeling certain temporal and spatial frame. We discuss methods to allow the comparison of different model outputs either We will present the FROZEN-project that has the over- to other model outputs for detecting general biases and all aim to develop a numerical simulation tool for ice sheet consistency considerations, or to ground truth based on modeling. Within a Finite Element Method framework, we actual observations for quality evaluation. For the quali- develop a tool that allows for high-resolution ice simulation tative comparison of gridded data sets we focus on novel over large areas and time intervals up to 100 000 years, error measures based on optical flow algorithms. and features appropriate treatment of grounding line migration at an ice sheet’s marine margin. This is done by the Thorsten Riess Ice Sheet Coupled Approximation Levels (ISCAL) method, W3 Data GmbH that couples the full Stokes equations and a Shallow Ice Ap- [email protected] proximation [1], and by introducing a subgrid-scale model for grounding line migration. We will present the current status of the project and discuss its continuation. MS57 Modeling of Free Groundwater Table in a Coastal Josefin Ahlkrona, Lina von Sydow Aquifer in Northern Germany Uppsala University josefi[email protected], [email protected] The finite volume code d3f (distributed density driven flow), based on the UG toolbox, handles free surface Nina Kirchner groundwater flow using level set methods. The progress of Stockholms Universitet application of d3f to a regional 3d model of a coastal aquifer [email protected] near the German North Sea is presented, taking into account variable recharge, river discharge and the pumping wells of three waterworks. The objective is forecasting the Per Lotstedt impact of several scenarios to the seawater-freshwater in- Department of Information Technology terface. Uppsala University, Sweden [email protected] Anke Schneider, Hong Zhao, Jens Wolf Gesellschaft für Anlagen- und Reaktorsicherheit Braunschweig, Germany MS57 [email protected], [email protected], Some Recent Developments of Level Set Methods [email protected] for Flow and Transport in Porous Media Peter Frolkovic Level set methods are useful numerical tool for capturing Department of Mathematics and Descriptive Geometry evolving interfaces in computational modelling of processes Slovak University of Technology that involve moving curves and surfaces. In this talk some [email protected] applications of such methods will be discussed together with several recent developments that make such numer- Dmitry Logashenko ical methods robust enough to be applied in problems of Steinbeis Forschungszentrum 936 flow and transport in porous media. Germany [email protected] Peter Frolkovic Department of Mathematics and Descriptive Geometry Sebastian Reiter Slovak University of Technology Goethe-Center for Scientific Computing [email protected] Goethe-Universität Frankfurt [email protected]

MS57 MS57 Evolving Surfaces in Geodesy Derivation and Analysis of a Multiscale Model for Biofilm Growth in Porous Media We present evolving manifold approaches for geodetic applications, namely for building the computational grids in We consider the growth of biofilms made by bacteria within solving large-scale geodetic boundary value problems re- a saturated porous media and obtain in a level-set frame- lated to Earth gravity potential modelling, for filtering of work an upscaled model. By periodic homogenization we EarthobservationdatagivenonclosedsurfacesasEarth derive Darcy’s law and modified transport equations with topography or satellite orbits and for processing of digital degenerating effective coefficients given by the evolving mi- terrain models. crostructure at the pore-scale. In case of non-degenerating coefficients, uniqueness and existence of strong solutions Karol Mikula are shown up to possible closure of some pores. Department of Mathematics Slovak University of Technology Raphael Schulz 134 GS15 Abstracts

Department of Mathematics spherical harmonics and radial basis functions) can by com- University of Erlangen bined to inherit their particular advantages as the “best [email protected] of both worlds”. The obtained iterative sequence of approximations is stable (also in the presence of noise) and Peter Knabner converges to solutions with well-known theoretical justi- Friedrich-Alexander University Erlangen-Nurenberg, fications (Moore-Penrose inverse or Tikhonov-regularized Germany normal equation). Department of Mathematics [email protected] Volker Michel Geomathematics Group Universität Siegen MS57 [email protected] Fire and Ice: Evolving Interfaces in Magma and Ice Flows MS58 Multi-phase interactions are fundamental to many ques- Localized Bandlimited Inversion of Planetary tions in Earth science. Given the nonlinear nature of the Magnetic-Field Data governing equations, numerical methods play an important role in advancing our basic understanding and pre- When estimating planetary crustal magnetic fields from dictive capabilities of multi-phase flows. One important satellite data, the satellite altitude and noise limit the challenge in computational approaches for simulating geo- maximum achievable spatial resolution. For only locally physical flows is the accurate representation and tracking available data, the conditioning of the crustal magnetic of interfaces between different phases. In this study, we field inversion is exacerbated. We present a method that focus on evolving interfaces in magmatic and ice flows to only solves for the well-conditioned components of the local illustrate when and how interface dynamics can have pro- crustal magnetic field inversion in an efficient way and es- found influence on the overall behavior of the geophysical timate local magnetic field features from local high-quality system. satellite data for the Martian South Pole.

James Sethian Alain Plattner University of California, Berkeley Department of Earth and Environmental Sciences Department of Mathematics California State University, Fresno [email protected] [email protected]

Jenny Suckale Frederik J. Simons Massachusetts Institute of Technology Princeton University [email protected] [email protected]

MS58 MS58 HPC Solutions for Long-Term Lithospheric Dy- The Treatment of Systematic Bias in Geomagnetic namics Inverse Problems

High spatio-temporal resolution forward models of the Given the excellent magnetic measurements available in the mantle-lithosphere and crust are of industrial and soci- modern era from observatories and satellites, and most re- etal interest. Over million year timescales, the lithosphere cently from the Swarm constellation, geomagnetic models evolves as a highly viscous, incompressible non-linear fluid. are now striving to describe more subtle field sources. This To enable efficient 4D models, algorithmic and compu- requires a more robust treatment of noise, particularly sys- tationally scalable preconditioners are essential. Here I tematic bias, which can drive estimation error more than present a new FE methodology and multilevel precondi- larger variance zero-mean processes. A strategy to mitigate tioner which exploits hardware characteristics of modern this bias is discussed which seeks to maximize signal-to- HPC facilities. Significant speedups compared to tradi- noise ratios of model parameter subsets within data subsets tional methods are demonstrated through simulations of leading to improved field models. continental rifting and subduction. Terence Sabaka Dave A. May Goddard Space Flight Center ETH Zurich NASA [email protected] [email protected]

Jed Brown Mathematics and Computer Science Division MS58 Argonne National Laboratory and CU Boulder Inverse Modelling in Ionospheric Research [email protected] The Earth’s ionosphere is most important for radio wave propagation in space and between satellites and terrestrial MS58 observation sites. GPS observations, for instance, provide Greedy Algorithms for Regularization of Inverse information on the slant total electron content which is Problems in the Geosciences the integral over the electron density along the ray path between transmitter and receiver. The estimation of the We present a new greedy algorithm for the regularization electron density is strongly underdetermined and an ill- of ill-posed inverse problems in the geosciences. The par- posed inverse problem. For solving this problem we use ticular features are: diﬀerent kinds of basis functions (like data adaptive techniques based on B-spline series expan- GS15 Abstracts 135

sions. resulted from the averaging procedure.

Michael Schmidt Jie Chen Bayerische Akademie der Wissenschaften Xi’an Jiaotong University (China) Munich, Germany [email protected] [email protected] Shuyu Sun MS59 King Abdullah University of Science and Technology [email protected] Fractal Analysis of Spontaneous Imbibition in Gas- water-rock Systems Xiao-Ping Wang Spontaneous imbibition is a ubiquitous natural and fun- Hong Kong University of Science and Technology damental phenomenon existing in a variety of processes. [email protected] Since first theoretical model for liquid moving through a horizontal capillary and then Lucas-Washburn (LW) equation were proposed, the static and dynamical problems MS59 connected with the penetration of a wetting liquid into Measuring and Upscaling Hydraulic Properties of a capillary or porous medium in contact with bulk liq- Variably-Saturated Porous Media uid, have been investigated both analytically and experimentally. There was considerable controversy over the Hydraulic properties of variably-saturated porous media LW equation. For the spontaneous imbibition, some re- are crucial for modeling multiphase flow and transport in searchers modified the LW model by considering the geo- many energy and environmental related applications. Up- metrical shape of capillaries, the effect of tortuosity, and scaling small scale measurements to a suitable scale for corrections relating to microstructure of rocks. But, these numerical modeling has been a research focus for decades. model predictions were not in good agreement with exper- Recent advances in nondestructive testing methods, such imental data. It has been shown that the pore space and as neutron imaging, combined with new upscaling tech- tortuous streamtubes/capillaries of natural porous media niques have improved our capability to measure hydraulic exhibit the fractal behavior. However, study of the sponta- properties and model multiphase flow and transport. neous imbibition based on the fractal characters of porous media was limited. By introducing the fractal dimension Chu-Lin Cheng for a tortuous capillary, analytical expression for time evo- University of Texas – Pan American lution of the height/weight of capillary rise is obtained. [email protected] Based on the assumption that porous media are comprised of a bundle of independent different sized parallel capillaries, the spontaneous imbibition in porous media also can Edmund Perfect be analyzed. In particular, (1) The mass of imbibed liquid University of Tennessee Knoxville is expressed as a function of the fractal dimensions, the [email protected] minimum and maximum hydraulic diameter of pores, and the ratio for minimum to maximum hydraulic diameters, Misun Kang porosity, fluid properties as well as the fluid-solid interac- University of California-Davis tion. (2) the behavior of imbibed weight versus time is [email protected] consistent with the LW equation, regardless of the imbibition in a single tortuous capillary and porous media. (3) Clark Cropper An explanation from the effect of the convolutedness prop- University of Tennessee Knoxville erty of tortuous capillaries on the spontaneous imbibition [email protected] is given. Richard T. Mills Jianchao Cai Oak Ridge National Laboratory China University of Geosciences and The University of Tennessee, Knoxville [email protected] [email protected]

Chu-Lin Cheng Jianchao Cai University of Texas – Pan American China University of Geosciences [email protected] [email protected]

MS59 MS59 From Stokes-Cahn-Hilliard Equations to Darcy’s Law for Two-Phase Flow in Porous Media Using DFN Modeling of Water Coning in Naturally Frac- Volume Averaging tured Heavy Oil Reservoirs, and Comparison to Dual-Porosity Approach A technique of local volume averaging is applied to a two- phase fluid mixture system and general equations are ob- We discuss a compositional Discrete Fracture Network tained which depict mass and momentum transport in (DFN) finite element model with capillarity and diffusion, porous media. Starting from the system of coupled Stokes- and verify its performance by reproducing experimental Cahn-Hilliard equations for incompressible two-phase fluid data for water injection into a fractured stack at different flow, the volume averaging is performed without signifi- rates. The agreement is excellent. We then simulate wa- cantly idealizing either the porous medium or the fluid me- ter coning in a densely fractured heavy oil reservoir with chanical relations. The resulting equations are generalized an underlying aquifer. The results are compared to those Darcy’s law for two-phase flow with medium parameters from a dual-porosity type representation for the fractures, 136 GS15 Abstracts

which cannot capture all the relevant physics. pressure build-up in the aquifer due to injection and the buoyancy of CO2. The underlying Eulerian- Lagrangian Joachim Moortgat framework has high potential to improve the efficiency and Ohio State University accuracy for the numerical simulation of complex flow [email protected] and transport processes in CO2 sequestration. We note that the sparse grid probabilistic collocation framework, Abbas Firoozabadi which adds computationally efficient uncertainty quantifi- Yale University cation functionality onto pre-existing Eulerian-Lagrangian abbas.fi[email protected] methods in a nonintrusive manner and also provides a scalable framework to consider uncertainty in a straightforward parallel manner, sometimes yield nonphysical results such MS59 as negative variance. We plan to conduct preliminary Pore-Scale Modeling of Multi-Component Multi- study on this issue and their possible remedies Phase Flows Hong Wang We consider the modeling and simulation of possibly com- University of South Carolina pressible, partially miscible, fully compositional two-phase Department of Mathematics hydrocarbon systems using a diffuse interface model to- [email protected] gether with Peng-Robinson Equation of State (EOS). Our modeling scheme utilizes molar densities as the order pa- Yongqiang Ren, Jianya Liu rameters, and the approach is based on the coupling of Shandong University (China) the Navier-Stokes equation for flow and a Cahn-Hilliard- [email protected], [email protected] like equation with Peng-Robinson chemical potentials for phase behaviors of hydrocarbon fluids. Our modeling ap- Jinhong Jia proach can be used to predict volumetric behaviors, solubil- University of South Carolina ity, miscibility, and interface tensions of common hydrocar- [email protected] bon liquid (oil) and vapor (gas) accurately. Moreover, the entire modeling approach is self-consistent and complies MichaelA.Celia with the principles of non-equilibrium thermodynamics in- Princeton University cluding the second law of thermodynamics, the maximum Dept of Civil Engineering entropy production principle (MEPP) and the Onsager [email protected] reciprocity principle. The continuum model is formulated mathematically in a coupled nonlinear partial differential equation (PDE) system, which usually does not have ana- MS60 lytical solutions. We thus propose an efficient numerical so- Multiscale Hybrid Models of Flow and Transport lution of the modeling system, focusing on discrete energy Through Complex Porous Media stability, local mass conservation and numerical accuracy. For spatial discretization, we apply a finite volume-based Hybrid models combine pore-scale and continuum-scale method to turn the partial differential equations (PDE) representations. Desirable features of hybrid models are 1) into an ordinary differential equation (ODE) system. For their ability to track where and when in space and time to temporal discretization, the resultant ODE system is de- use pore-scale simulations, i.e. their adaptability to time- coupled by using an asymmetric splitting scheme, and then and space-dependent phenomena, and 2) their flexibility integrated in time using a semi-implicit marching scheme. in implementing the coupling boundary conditions. In this In addition, targeting the specific features of each of the work, we construct criteria for adaptive hybridization and three terms in Peng-Robinson chemical potentials, we pro- a non-intrusive non-overlapping hybridization scheme to pose a convex splitting-based semi-implicit time scheme, model reactive flow through a chemically heterogeneous which is proved to be unconditionally energy stable under porous medium with complex structure. certain conditions. We compare our computational results with laboratory experimental data reported in the litera- Ilenia Battiato ture, which have good agreement. Department of Mechanical Engineering, Clemson University Shuyu Sun [email protected] Division of Mathematical and Computer Sciences & Engineering King Abdullah University of Science and Technology MS60 (KAUST) How to Charaterize Porosity from Image Process- [email protected] ing

This talk aims at discussing how to characterize the poros- MS59 ity of media by means of image processing. We mainly A Probabilistic Collocation Eulerian-Lagrangian focus on the problem of describing accuretaly the multi- Localized Adjoint Method for Assessing CO2 Leak- scale information by means of geometric and/or statistical age Through Wells in Randomly Heterogeneous descriptors. These descriptors may be used for 3-D re- Prous Media construction and vizualisation. We will also discuss the problem of dealing with percolation properties regarding We develop a probabilistic collocation Eulerian-Lagrangian the connectedness of the poral space and how to modify localized adjoint method for assessing CO2 leakage through this connectedness using image processing tools. wells in randomly heterogeneous porous media, by utilizing the intrinsic mathematical, numerical, and physical prop- Catherine Choquet erties of the mathematical model. We model the process University of Marseille in which CO2 is injected intbate, which depends on the [email protected] GS15 Abstracts 137

Michel Berthier tionally efficient reconstruction of multiscale pore network University of La Rochelle for digital rock physics. France [email protected] Hongkyu Yoon, Thomas Dewers Geoscience Research and Applications Sandia National Laboratories MS60 [email protected], [email protected] Hybrid Reduced Models for Evolving Porescale Ge- ometries MS61 We consider algorithms which account how macroscale Depth-Averaged Models for Debris Flows in properties of porescale geometries such as permeability K Rugged Terrain change due to, e.g, biocementation, or other reactive transport and/or phase transitions. Our approach combines cal- We have developed a mathematical model and software (D- culations of K for modifications of geometry generated with Claw) for simulating landslides and debris flows, seamlessly (i) ”brute force” exhaustive search, (ii) stochastically gen- from initiation to deposition. The depth-averaged model erated representative modifications, and (iii) actual tran- is a two-phase particle-fluid model incorporating princi- sient process simulations. We discuss the advantages and ples from granular and soil mechanics. The result is a disadvantages of each approach. nonconservative hyperbolic system of five PDEs, similar to shallow-water models for free-surface flows in topography. Timothy Costa The mathematical model, and the challenge of accurately Oregon State University incorporating topographic effects in steep and rugged ter- [email protected] rain, will be described.

Malgorzata Peszynska David George Department of Mathematics U.S. Geological Survey Oregon State University Cascades Volcano Observatory [email protected] [email protected]

Richard Iverson MS60 USGS Computational and Experimental Study of Isolat- Cascades Volcano Observatory ing Properties of Soil Mixtures at Pore and Core [email protected] Scales in Environmental Applications

Computational modeling is applied to study isolating prop- MS61 erties of mixtures of clays and sand which are used as seal- Semi-Implicit Central-Upwind Scheme for Shallow ing barriers of waste disposal sites. Core scale properties Water Models with Friction Terms of 3D samples of soils are assessed by simulating flows at porescale and upscaling. Experimental measurements are I will introduce a new semi-implicit central-upwind scheme used at porescale in order to provide realistic data describ- for the Saint-Venant system of shallow water equations ing geometry of mixtures, as well as to obtain core scale with the Manning friction terms. In the case of very shal- parameters to be compared with results of computations. low water, for example, when the drainage of rain water is modeled, the friction terms become stiff and thus re- Anna Trykozko quire a special treatment. We propose a new semi-implicit University of Warsaw method, which is not only highly accurate and efficient, [email protected] but also remains well-balanced and preserves positivity of the water depth. Beata Luczak-Wilamowska Faculty of Geology, University of Warsaw, Poland Alexander Kurganov [email protected] Tulane University Department of Mathematics Marek Dohnalik [email protected] Institute of Oil and Gas, Cracow, Poland [email protected] MS61 A Parallel, Terrain-Follow-Grid Transform for In- MS60 tegrated Surface and Subsurface Flow: Moving to Multiscale Reconstruction of Nano-Pore Geomate- Exascale Simulations over the Continental US rials and Representative Sampling for Digital Rock Physics Interactions between surface and groundwater systems are well-established theoretically and observationally. While Geomaterials containing nano-pores (shales and carbonate numerical models that solve both surface and subsurface rocks) have become increasingly important for unconven- flow equations in a single framework (matrix) are increas- tional gas and oil resources and geological carbon storage. ingly being applied, computational limitations have re- Accurate prediction of coupled geophysical and chemical stricted their use to local and regional studies. As a step to- processes in multiscale pore network systems requires re- ward enabling integrated simulation over large extents and alistic representation of pore structure and topology. In high spatial resolution, a terrain-following grid formula- this work, we apply multiscale imaging techniques for char- tion (TFG) is presented for simulation of coupled variably- acterizing pore structures at nano-to-centimeter scale and saturated subsurface and surface water flow. The TFG is representative sampling of ensemble members for computa- introduced into the integrated hydrologic model, ParFlow, 138 GS15 Abstracts

which uses an implicit, Newton Krylov solution technique. [email protected] The analytical Jacobian is also formulated and presented and both the diagonal and non-symmetric terms are used Mario Putti to precondition the Krylov linear system. Using this TFG, UniversitàdiPadova efficient scaling to a large number of processors (16,384) [email protected] and a large domain size (8.1 Billion unknowns) is shown. An integrated hydrologic simulation of surface and subsurface flow at high spatial resolution (1 km) over much MS61 of continental North America (6.3 million square km) is presented. This demonstrates the applicability of this for- Bedload Sediment Transport on Gpu mulation to high resolution, large spatial extent hydrology applications where topographic effects are important. In this work we propose a PVM path-conservative numerical scheme for the numerical simulation of bedload sed- Reed M. Maxwell iment transport. This first order scheme is extended by Department of Geology and Geologic Engineering means of a MUSCL-type reconstruction operator in or- Colorado School of Mines der to achieve second order accuracy on triangular meshes. [email protected] The CUDA implementations of both numerical schemes are described, and some numerical tests with real applications Laura Condon are presented. Colorado School of Mines [email protected] Marc de la Asunción University of Málaga, Spain Stefan Kollet [email protected] Meteorological Institute University of Bonn Manuel J. Castro [email protected] University of Malaga [email protected]

MS61 Tom´as Morales Ice Sheet Dynamics: High-Order Approximation University of C´ordoba on the Sphere [email protected]

Large ice sheets such as Antarctica play a significant role in Jorge Mac´ıas climatology and, in particular, in sea level rise. Ice sheets University of Málaga behave like shear thinning fluids and can be modeled with [email protected] nonlinear Stokes equations. In order to reduce the computational costs we use an high order approximation of the Stokes model that can be derived considering the ice sheet MS62 geometry as a shell. We compare results obtained using the Stokes model and its approximation. Dynamic Earthquake Rupture Simulations on Non- planar Faults Embedded in 3D Geometrically Com- Mauro Perego plex Heterogeneous Elastic Solids CSRI Sandia National Laboratories [email protected] Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The corresponding initial boundary value MS61 problems are both numerically and computationally chal- Modeling Shallow Water Flow on General Terrain lenging. We present a high order accurate finite difference method for: a) enforcing nonlinear friction laws, in Shallow water equations are commonly used in many ap- a consistent and provably stable manner, suitable for effi- plications. Their formal derivation should account for cur- cient explicit time integration; b) dynamic propagation of vatures of the terrain model. However this task is not well earthquake ruptures along non-planar faults; and c) accu- understood. We derive a general form of SWE accounting rate propagation of seismic waves in heterogeneous media for terrain geometry by performing depth integration along with free surface topography. normals to bed surface rather than to streamlines. We discuss by theoretical and numerical results the errors arising Kenneth Duru from this approximation as well as the role of curvatures Department of Geophysics, Stanford University, Stanford in different applications. CA Ilaria Fent Stanford University Université catholique de Louvain [email protected] Belgium daff[email protected] Eric M. Dunham Department of Geophysics Carlo Gregoretti Stanford University University of Padova [email protected] [email protected] MS62 Stefano Lanzoni University of Padova Goal Oriented Estimates for Interface Problems: Italy Applications in Two Phase Transport Problems in GS15 Abstracts 139

Heterogeneous Porous Media [email protected]

In oil reservoir simulation practitioners are interested in Ken Mattsson some specific feature of the solution to the system describ- Uppsala University, Sweden ing the multiphase flow in heterogeneous porous media [email protected] such as the oil production (goal functional). We develop an fully computable goal-oriented error estimate for discontin- Gunilla Kreiss uous in time and space Galerkin method for interface prob- Division of Scientific Computing lem for saturation equation. The error estimate is used in Uppsala University an adaptive strategy that allows accurate approximation [email protected] of the goal functional at reduced computational cost.

Igor Mozolevski Margot Gerritsen Federal University of Santa Catarina Dept of Energy Resources Engineering [email protected] Stanford University [email protected] Serge Prudhomme {É}cole Polytechnique de Montr{é}al MS62 Montr{é}al, Qu{é}bec, Canada [email protected] Stable Projection Operators For High-Order Finite Difference Methods

MS62 A methodology for coupling high-order finite difference Effective Slip Law for General Viscous Flows over methods is proposed based on projecting the finite dif- An Oscillating Surface ference solution along a coupling interface into a space of discontinuous polynomials. In this talk we show coupling We consider the non-stationary three-dimensional viscous to differing finite difference methods, including “hanging flow in a bounded domain with a rough boundary. Under node’ block interfaces, as well an unstructured, triangle- the assumption of a smooth flow in the domain without based discontinuous Galerkin method. Numerical exam- roughness, we prove existence of a smooth solution to a ples will be provided to demonstrate the accuracy and sta- problem with rough boundary. Using boundary layers and bility of the proposed method for acoustic wave propaga- results on solenoidal vector fields, we obtain the Navier tion. friction condition. It is valid when the size of the asprities tends to zero. Error estimates for the velocity and pressure Lucas Wilcox are shown. Department of Applied Mathematics Maria Neuss-Radu Naval Postgraduate School University of Erlangen-Nuremberg [email protected] Mathematics Department [email protected] Jeremy E. Kozdon Naval Postgraduate School Andro Mikelic Department of Applied Mathematics Institut Camille Jordan, Departement de Mathématiques [email protected] UniversitéLyon1 [email protected] MS62 Sarka Necasova A New Reconstruction Algorithm for Flow and Re- Mathematical Institute of Academy of Sciences active Transport Simulation in Porous Media on Czech Republic Cartesian Grids [email protected] Source terms in immersed boundary methods (IBMs) are MS62 determined by the difference between the interpolated values on the boundary points and the desired (physical) A Finite Difference Framework for Porous Media boundary values. In presence of subgrid discontinuity of Flow state variables across solid boundaries, one-sided stencil reconstruction is generally employed. We propose a novel We design and construct finite difference operators for ap- second-order reconstruction scheme based on an interpola- plications in porous media. The new operators possess tor defined along the outward normal of the solid boundary. properties that facilitates boundary and interface treat- We demonstrate the interpolator flexibility and improved ments, and in many cases lead to provably robust discreti- accuracy with different boundary conditions. sations and error estimates. The framework is in particular suitable for coupling regions with different continuity requirements using different discretisation accuracy, where Mehrdad Yousefzadeh the second order method is directly comparable to a finite University of California San Diego volume discretisation. We demonstrate the applicability of San Diego State University the framework through numerical experiments. [email protected]

Anna Nissen Ilenia Battiato Department of Mathematics Department of Mechanical Engineering, Clemson University of Bergen University 140 GS15 Abstracts

[email protected] tion contributions. The solvation contribution dominates at lower temperatures and is based on the Born model for determining the free energy of solvation, where formation MS63 water permittivity is calculated using Johnson and Nor- SubFlow, an Open-Source Tool for Modeling Car- ton regression coefficients. The nonsolvation contribution bon Dioxide Sequestration in Geological Forma- dominates at higher temperatures and is empirically deter- tions mined. Activity coefficients of electrically charged solutes are approximated using the B-dot model, which is an ex- The capture of carbon dioxide for its subsequent storage in tended Debye-Hckel model. The HKF derived partial molal brine saturated reservoirs or depleted oil fields has become heat capacity and enthalpy of charged aqueous species aris- a significant part of the US energy policy. In this work, ing from the interaction of CO2-rich brine with sandstone we focus on the design and development of a novel appli- are used in the source term of a transient heat transfer cation for modeling the time-evolution of the sequestration model. The heat transfer model accounts for the advective process. SubFlow is written in C++ and uses a relational and diffusive energy transport of aqueous CO2 in a porous database to store simulation data. It provides 3D real-time sandstone formation. Advective transport is modeled us- visualization and parallel execution. SubFlow uses either, ing Darcy’s law for pressure driven-flow and solved using finite volume or mimetic discretization methods to solve a finite volume method on a staggered grid. Formation for the governing partial differential equations. It employs pressure is computed using a poroelastic pore pressure dif- Gear’s method to solve the mechanism modeling geochem- fusion model and solved using the finite element method. ical kinetics. Results are compared with those obtained by We present the effect of ion and electrolyte solute inter- TOUGHREACT and STOMP. action on reservoir temperature as high pressure (228-372 bar) CO2-rich water is injected into a lower pressure (152- Johnny Corbino Delgado 255 bar) sandstone formation. Computational Science Research Center SDSU Christopher Paolini [email protected] SDSU [email protected]

MS63 Numerical Simulation of Fluid Pressure and Frac- MS63 turing in CO2 Sequestration Mimetic Finite Differences to Simulate Carbon Dioxide Subsurface Mass Transport CO2 sequestration in underground aquifers shows significant potential in reducing greenhouse gas emissions. How- We present Mimetic Finite Differences as an alternative nu- ever, rock fractures, formed during injection, may release merical method to solve for the mass transport equation. toxic species into the water table and release CO2 into the In this work, this equation models the long-term behav- atmosphere. Because rock fractures develop as a result of ior of geologically sequestered CO2.Wediscusshowcan stresses, a model to compute the internal rock stresses in- we construct higher-order 1D mimetic operators, as well duced by the injection of CO2-rich water was developed. as how to construct their higher-dimensional counterparts. A finite element model was used to calculate the fluid pres- Finally, we provide simulation results within the framework sure, stresses and strains induced by injection of CO2 into a of the Mimetic Methods Toolkit (MTK), an API imple- geologic sandstone formation. The Terzaghi effective stress menting mimetic discretization and quadrature schemes. was determined from the calculated overburden pressure and fluid pressure. When the Terzaghi-effective stress ex- ceeded the critical fracture gradient, simulated fractures Eduardo J. Sanchez were induced. The effect of the simulated fractures was es- Computational Science Research Center timated as an incremental permeability by means of Odas San Diego State University permeability tensor. This poroelastic pressure and frac- [email protected] ture module was used to approximate formation pressure during injection of CO2 rich water into the Oligocene Frio Formation along the Texas Gulf Coast, with simulation MS63 parameters derived from the Frio Test Pilot Experiment. Pore Dynamics and Calcite Solubility in Carbona- Simulation results were compared to bottom-hole pressure ceous Aquifers Used in Energy Storage Applica- data obtained from an observation well 30 meters away tions. from the injection well, during a 35-day injection phase. Geothermal energy harvesting applications use deep Jonathan Mathews groundwater aquifers to store energy. The impact of this San Diego State University additional energy to the aquifer chemistry is crucial for [email protected] long-term operation. Gaseous CO2 is added to the injected water to compensate potential precipitates of carbonates and to prevent structural changes to the aquifer. To bet- MS63 ter understand this thermal and chemical coupling on the Effect of Aqueous Electrolytic Reactions on Reser- aquifer structure, we consider a long-wave model of this voir Temperature during CO2 Injection process for a single axisymmetric pore where gaseous CO2 concentration, temperature, fluid flow and hydrochemistry A well-known model for computing the thermodynamic modify the pore radius in space and time. Substrates are properties of aqueous electrolytic solutions at geologic composed of calcite and dolomite, whose composition evo- conditions of high temperature and pressure is the re- lution is part of the full pore problem. The concentration vised Helgeson-Kirkham-Flowers (HKF) model. The HKF footprint of the dissolved solid calcite concentration over model is based on computing properties of dilute aqueous many seasonal cycles of the energy harnessing system is species by separately considering solvation and nonsolva- found. The impact of these results on the efficiency of these GS15 Abstracts 141

systems, along with the chemical impact on the aquifer is University of Texas at Austin discussed. [email protected]

Burt S. Tilley Worcester Polytechnic Institute PP1 Mathematical Sciences Department [email protected] Test Condition for Obtaining the Global Optimum Value of a Function Using Discarding Algorithm Daniel Brady Mathematical Sciences Department The problem of finding the global minimum of a vector Worcester Polytechnic Institute function is very common in science, economics and engi- [email protected] neering. One of the most notable approaches to find the global minimum of a function is that based on interval analysis. In this area, the exclusion algorithms (EAs) are Martina Ueckert, Thomas Baumann a well-known tool for finding the global minimum of a func- Institute of Hydrochemistry tion over a compact domain. There are several choices for Technische Universitaet Munich the minimization condition In this paper, we introduce a [email protected], [email protected] new exclusion test and analyze the efficiency and computational complexity of exclusion algorithms based on this PP1 approach.We consider Lipschitz functions and give a new minimization condition for the exclusion algorithm. Then Parallel Computation of Bayesian Model-Based we study the convergence and complexity of the method Geostatistics for Improved Reservoir Characteri- zation Ibraheem Alolyan King Saud University Instead of spatial distribution in simple kriging, Bayesian [email protected] kriging has been done to take into account the uncertainty in a form of posterior-distribution to avoid unrealistic small regions for optimal linear interpolation. Multiple equiprobable realizations have been created, statistically ranked and PP1 sampled to select P10, P50, and P90. The procedure was A Structure-Preserving Split Finite Element Dis- expedited through R parallel computing package. Rmpi cretization of the 1D Wave Equation allowed to create R code to run in multiple CPUs on one machine for more quick results. We introduce a finite element (FE) discretization of the 1-dimensional wave equation that is written in split form, Watheq J. Al-Mudhafar i.e. the equation is split into topological and metric parts. Louisiana State University We provide a proof of concept that this FE discretization [email protected] consisting of initially independent pairs of FE spaces which are then connected by a Galerkin Hodge operator is stable. We compare this discretization with a standard mixed PP1 finite element approach with respect to accuracy and effi- Convergence Analysis of Multirate Coupling ciency. Schemes for Coupled Flow and Geomechanics Werner Bauer Coupling of geomechanics and flow in poroelastic media University of Hamburg has several environmental and petroleum engineering ap- KlimaCampus plications. In this work, we have rigorously formulated [email protected] and analyzed multirate iterative coupling schemes for solving coupled geomechanics and flow problems in poro-elastic and fractured poro-elastic media. Multirate schemes bet- Jörn Behrens ter exploit the different time scales of mechanics and flow KlimaCampus, University of Hamburg by allowing for multiple finer time steps for flow within one [email protected] coarser geomechanics time step, reducing the overall CPU run time considerably. PP1 Tameem Almani The Mathematics Behind Severe Thunderstorm CSM, ICES, UT Austin Prediction and Alerting [email protected] The weather forecast system of the future will have to Kundan Kumar deal with massive amounts of data and still be able to Department of Mathematics produce personalized weather alerts. We present our re- University of Bergen, Bergen, Norway search on generating and communicating thunderstorm [email protected] forecasts, nowcasts and analyses using post-processed numerical weather prediction (NWP), radar and lightning ob- Gurpreet Singh servations and human forecaster interaction. We focus on The University of Texas at Austin a few specific tasks: generation of probabilistic areas from Center for Subsurface Modeling NWP forecasts, time-interpolation, tracking from radar [email protected] and lightning data, and object-based verification.

Mary F. Wheeler Dominique Brunet, Dave Sills Center for Subsurface Modeling, ICES Environment Canada 142 GS15 Abstracts

[email protected], [email protected] curate boundary closure for wave propagation problems. Unfortunately, the PML does not give us an indication about appropriate boundary conditions needed to close the PP1 edges of the PML, or how boundary conditions should be Combining Optical and Atomic Force Microscopy enforced in a numerical setting. We analyze initial bound- Measurements with Numerical Simulations Re- ary value problems for PMLs using the normal mode anal- veals Nanoscale Wetting Phenomena ysis and present a stable numerical approximations of the PML with the boundary conditions. Numerical experi- We investigate nanoscale oil droplets on well-characterized ments verify theoretical results. glass surfaces by combining optical microscopy and atomic force microscopy. By comparing experimental results with Kenneth Duru simulations at the molecular scale of the liquid-solid in- Department of Geophysics, Stanford University, Stanford terface, we reveal how the local surface properties aﬀect CA wetting properties such as contact angle and surface cov- Stanford University erage. The results will enable technology development for [email protected] enhanced oil recovery and on-chip catalysis.

Peter Bryant, Mathias B. Steiner PP1 IBM Research - Brazil Relative Importance of Sorption Versus Aggrega- [email protected], [email protected] tion over Soil Carbon Stocks and Dynamics

Michael Engel We couple BAMS1 [Riley et al., 2014] and AggModel IBM TJ Watson Research Center [Segoli et al., 2013] to understand the impact of vari- [email protected] ous protection mechanisms (e.g., sorption, aggregation) on SOM dynamics. BAMS1 includes microbes, multiple carbon substrate groups, and mechanistic sorption processes; Ronaldo Giro AggModel includes multiple aggregate size classes. Pre- IBM Research - Brazil liminary results suggest clay mineral surface area and soil [email protected] aggregates are as dominant controls of soil carbon stocks and its long residence times, respectively. Rafael R. Del Grande Universidade Federal do Rio de Janeiro Dipankar Dwivedi, William Riley, Margaret Torn [email protected] Lawrence Berkeley National Laboratory [email protected], [email protected], [email protected] Rodrigo F. Neumann IBM Research - Brazil Johan Six [email protected] ETH Zurich [email protected] Phaedon Avouris, Claudius Feger IBM TJ Watson Research Center [email protected], [email protected] PP1 Combining Global Optimization and Boundary In- tegral Methods to Robustly Estimate Seismic Ve- PP1 locity Models Information-Theoretic Characterization of Long- Memory Gaussian Processes We combine a fast Helmholtz solver using boundary integral methods with particle swarm optimization to globally We derive explicit expressions for the mutual information estimate a seismic velocity model without an initial guess. and conditional mutual information between states of a Our forward solver constrains model space to a layered long-memory, Gaussian stochastic process, and speciﬁcally, model with perturbations to achieve computational saving ARFIMA(p,d,q). We give information-theoretic character- and allows the use of global optimization methods that re- izations of the transition from stationary long-memory to quire numerous evaluations and few unknowns. We apply nonstationarity, and from long-memory to anti-persistence. our technique to estimate a velocity model from real tele- We also give an explicit connection between information seismic regional data and synthetic exploration scale data. available for prediction and the moving average representation. For comparison we derive the same quantities for the short-memory, Markovian, AR(1) process. We men- Gregory Ely tion a potential application to the evaluation of predictive massachusetts institute of technology models. Massachusetts Institute of Technology [email protected] Gordon V. Chavez New York University Alison Malcolm [email protected] Memorial University of Newfoundland [email protected]

PP1 The Impact of Boundary Conditions and Numeri- PP1 cal Boundary Procedures on the Stability of Per- Numerical Study of the Propagation of Acoustic fectly Matched Layers Waves Around and Inside an Underground Cavity

The perfectly matched layer (PML) has emerged as an ac- Motivated by the need to detect an underground cavity GS15 Abstracts 143

within the procedure of an On-Site-Inspection (OSI) of University of California, Berkeley the Comprehensive Nuclear Test Ban Treaty Organiza- [email protected], [email protected], frys- tion (CTBTO), which might be caused by a nuclear ex- [email protected], [email protected] plosion/weapon test, we provide a basic numerical study of the wave propagation around and inside such an underground cavity. Our computations are done with the paral- PP1 lel ﬁnite element library Ngsolve on top of the automatic Inversion of Postseismic Deformation for Litho- 2D/3D tetrahedral mesh generator Netgen. spheric Viscosity and Fault Slip

Sofi Esterhazy We present an inverse method which discerns the mech- University of Vienna anisms driving postseismic deformation, namely, afterslip Department of Geophysics and Meteorology and viscous relaxation in the lithosphere. Our method is sofi[email protected] based on a linearized approximation for postseismic deformation which greatly simplifies an otherwise expensive Ilaria Perugia forward problem. This approximation allows us to quickly University of Vienna infer fault slip over the postseismic period as well as image Faculty of Mathematics the lithospheres viscosity structure with unprecedented res- [email protected] olution. We apply our method to postseismic deformation following the 2010 El Mayor-Cucapah earthquake. Götz Bokelmann University of Vienna Trever T. Hines,EricHetland Department of Geophysics and Meteorology University of Michigan [email protected] [email protected], [email protected]

Joachim Schöberl PP1 Vienna University of Technology A Posteriori Diagnosis Tools for Improved Data As- Institute for Analysis and Scientific Computing similation System Performance [email protected] The information content of atmospheric measurements in PP1 data assimilation is closely determined by the representation of the model and observation error statistics. Evalu- SVM with Uncertainty for Mineral Prospectivity ation of short-range forecast error sensitivities to observa- Mapping tion error variance and innovation-weight parameters provides guidance to improve the system performance. A case Over the last 20 years mineral exploration has begun study is presented for various observing instruments as- adopting advanced data mining techniques to assimilate similated in NASAs GEOS-5 system. Statistical analysis large data sets and identify prospective targets. Numerous of data assimilation products indicates that, in general, in- machine learning algorithms exist, however regardless of creasing the observation weight would improve the forecast the method all are plagued by the existence of uncertain- skill. ties in both the training data and training labels (known mineralization occurrences). To address this an algorithm Austin Hudson was developed based on support vector machines which ex- Portland State University plicitly incorporates these uncertainties into the objective Portland, OR, USA function. [email protected] Justin Granek,EldadHaber University of British Columbia Dacian N. Daescu [email protected], [email protected] Portland State University Department of Mathematics and Statistics [email protected] PP1 Characterizing Roughness and Connectivity Prop- Ricardo Todling erties of Aquifer Conductivity Using Bayesian In- NASA/GSFC Global Modeling and Assimilation Office version [email protected]

In our study, we investigate two different properties of subsurface conductivity fields that are hard to detect using PP1 classic characterization schemes; roughness and connectiv- Local Refinement in Simulation of Wave Propaga- ity. To circumvent this difficulty we use the Method of tion Anchored Distributions (MAD), a fully Bayesian inversion tool. Since MAD does not assume any formal relationship An algorithm for the local refinement of both time and between the target variable and the data, we are able to space steps in staggered grids is introduced. It is based on determine the ability of a wide variety of data to detect a locally variable time-step scheme that matches with dis- these two aforementioned properties. continuous grids in finite-difference method for the efficient simulation of wave propagation. The first-order velocity- Falk Hesse stress formulations are used to obtain the spatial deriva- UFZ-Helmholtz Center for Environmental Research tives using finite-difference operators on a staggered grid. Leipzig, Germany In principle, this algorithm may give the fast and accurate [email protected] numerical solutions for any hyperbolic problem.

Carlos Murillo, Jon Sege, Heather Savoy, Yoram Rubin Tae-Seob Kang 144 GS15 Abstracts

Department of Earth and Environmental Sciences [email protected] Pukyong National University [email protected] PP2 Statistical Analysis and Simulation of the Spatial PP2 Distribution of Deformation Bands in Fault Dam- Multiscale Vertically-Integrated Models with Ver- age Zone. tical Dynamics and Heterogeneity for Co2 Migra- tion in Geological Formations Based on 106 outcrop scanlines, the distribution of deformations bands in damage zones of extensional faults in To overcome the vertical equilibrium (VE) limitation of porous sandstones has been characterized as follows: loga- conventional vertically-integrated models for CO2 storage, rithmic decrease of the bands away from the fault core and we develop a new vertically-integrated model by casting the clustering of the bands. A statistical simulation method for equations in a multiscale framework. The coarse scale is deformation bands spatial distribution is presented. The the vertically-integrated domain similar to the VE model, proposed algorithms reproduce the observed frequency and while the fine scale is a one-dimensional problem in the clustering of the deformation bands. The application and vertical direction that solves the vertical dynamics of CO2 validity of the developed algorithms are discussed. and brine. The end result is a multiscale model that relaxes the VE assumption while maintaining most computational Dmitriy Kolyukhin advantages of VE models. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS Bo Guo [email protected] Princeton University Princeton University Sylvie Schueller [email protected] Uni CIRP, Bergen, Norway; now at IFP Energies nouvelles, Rueil-Malmaison, France Karl Bandilla [email protected] Princeton University [email protected] PP2 Jan M. Nordbotten Inverse Modeling of Contaminant Transport with Department of Mathematics Implicit Sampling University of Bergen Monitoring and predicting groundwater flow and contam- [email protected] inant transport is one of the primary concerns of the De- partment of Energy. Advanced Simulation Capability for Eirik Keilegavlen Environmental Management (ASCEM) software package University of Bergen was developed to support efficient development of hydro- [email protected] logical models for predictive analysis, uncertainty quantification, and decision-making. We study the use of im- Florian Doster plicit sampling, which generates sample beams toward the Heriot-Watt University high probability regions of target probability density func- fl[email protected] tions, in the calibration of influential model parameters. We demonstrate the efficiency of the method in accurately Michael A. Celia characterizing the uncertainty of a calibrated 3D model for Princeton University the F-Area basin at Savannah River Site. Dept of Civil Engineering [email protected] Yaning Liu, George Shu Heng Pau, Haruko Wainwright Lawrence Berkeley National Laboratory [email protected], [email protected], [email protected] PP2 Adaptive Multi-Scale Pore Network Method for Stefan Finsterle Two-Phase Flow in Porous Media Lawrence Berkeley National Laboratory (LBNL), Berkeley For typical two-phase flow through porous media, capillary Hydrogeology & Reservoir Dynamics Department forces are dominant at the pore scale and viscous forces at [email protected] larger scales. We present a multiscale pore-network simulator which exploits this behavior. A pore-network, repre- Xuemin Tu senting a porous medium, is subdivided into subnetworks. University of Kansas The fluid-fluid interface in each subnetwork is evolved us- Lawrence, KS 66045-7594 ing either a quasi-static or dynamic pore-network solver, [email protected] depending on the local capillary number. A meso-scale equation is solved to couple the flow in the subnetworks. PP2 Karim Khayrat Ensemble-Based Framework for Geosteering ETH Zurich [email protected] Geosteering aims to steer an oil/gas well to optimize its coverage in the targeted reservoir zone. In this work, we Patrick Jenny propose an ensemble-based framework that uses logging- Institute of Fluid Dynamics while-drilling (LWD) data to continuously update the ge- ETH Zurich omodel, and optimize the well placement accordingly. A GS15 Abstracts 145

2D case is investigated under the proposed framework, Josep de La Puente in which synthetic electromagnetic (EM) data generated Barcelona Supercomputing Center from an advanced EM tool are assimilated. Satisfactory Spain geosteering performance is obtained, conﬁrming the bene- [email protected] ﬁts of the proposed framework.

Xiaodong Luo PP2 International Research Institute Of Stavanger (IRIS) Spatio-Temporal Upscaling of Reactive Transport Bergen 5008, Norway in Porous Media for Ultra-Long Time Predictions [email protected] STRICTLY POSTER PRESENTATION In most practi- Peder Eliasson cal applications it is satisfactory to know the macroscopic SINTEF, Norway (averaged in space and/or time) values of the state vari- [email protected] ables. Predictions of subsurface transport for ultra-long times require the formulation of continuum scale models for time-averages. In the current study we perform a spatio- Sergey Alyaev temporal upscaling for pore-scale advection-diffusion equa- IRIS, Norway tions with nonlinear heterogeneous reaction using homoge- [email protected] nization method to (i) obtain macro-time continuum-scale equations and (ii) identify their applicability regimes in Anouar Romdhane terms of relevant dimensionless groups. SINTEF, Norway [email protected] Farzaneh Ra jabi University of California San Diego Erich Suter, Erlend Vefring San Diego State University IRIS, Norway [email protected] [email protected], [email protected] Ilenia Battiato Department of Mechanical Engineering, Clemson PP2 University Determining Most Informative Measurements for [email protected] Geostatistical Characterization Via Inverse Mod- eling PP2 In order to use inverse modeling to infer the geostatisti- Terrain Correction Considering the Isostatic Com- cal parameters for a field, informative measurements are pensation of the Terrain necessary. The Method of Anchored Distributions allows multiple forms of data to constrain the uncertainty in these Terrain correction in the gravity anomaly at a point would parameters. This method is a Bayesian technique and relies require the Bouguer gravity anomaly values for the sur- on likelihood values determined from comparing measure- rounding terrain to account for the isostatic compensation ments to stochastic realizations. This poster focuses on of the surrounding terrain. It is demonstrated through a using Principal Component Analysis to determine which two-dimensional model (i.e. two rectangular columns of measurements have more informative distributions and the rigid material separated by a horizontal distance X ,hav- resulting impact on posteriors. ing density ρ ,heightsH1, H2 , and unit width floating in a viscous fluid having density ρf ,volumeV contained in Heather Savoy, Carlos Osorio Murillo, Yoram Rubin a rectangular box of width Y ). University of California, Berkeley [email protected], [email protected], ru- Amol D. Sawant, William Mohanty [email protected] Department of Geology and Geophysics Indian Institute of Technology Kharagpur [email protected], [email protected] PP2 Performance of Parallel Linear Solvers in Electro- PP2 magnetic Geophysics Coupled Multiphase Flow and Reactive Transport: Effects of Compressibility and Solubility on Gas The size and complexity of 3D electromagnetic modelling Storage Simulation problems present a serious challenge for computational methods. Complex linear systems arising from the finite- This work demonstrates an extension of the reactive trans- element or finite-difference discretizations on very large port software HYTEC – reactive two-phase flow and trans- grids need to be solved multiple times during the geo- port. Applying appropriate equation of state made it possi- physical inversion process. In this presentation we will dis- ble to precisely represent compressible multicomponent gas cuss different iterative and direct solvers for large complex phase, its thermodynamic properties and relevant fluxes. systems of linear equations. We will evaluate robustness, Integrated geochemical software CHESS allowed modeling speed and parallel efficiency of these methods for large- phase exchange and complex geochemical system. The de- scale electromagnetic problems, making a special focus on veloped coupling provides an analysis of gas compressibility the reusability for similar coefficient matrices. and dissolution role in CO2 plume formation in the context of impure supercritical CO2 injection. Vladimir Puzyrev Barcelona Supercomputing Center Irina Sin [email protected] MINES ParisTech 146 GS15 Abstracts

[email protected] griﬃ[email protected]

Vincent Lagneau Ziad S. Haddad, SIMONE Tanelli Geosciences Center Jet Propulsion Laboratory MINES ParisTech California Institute of Technology [email protected] [email protected], [email protected]

Jérôme Corvisier MINES ParisTech, PSL-Research University, PP2 Centre de Géosciences, France Data-Driven Stochastic Representations of [email protected] Mesoscale Ocean Eddies

Mohamed Azaroual We investigate how to use sample data, generated by BRGM a fully resolved quasi-geostrophic ocean model, to con- [email protected] struct stochastic representations of unresolved processes (so-called mesoscale eddies) in a reduced ocean model. These representations are formulated as stochastic pro- PP2 cesses, conditioned on a covariate (the resolved model state). We demonstrate that the tested strategies signif- On the Different Coupling Choices in Joint Hydro- icantly reduce the degrees of freedom of the respective geophysical Inversion model, while retaining the driving force of the unresolved processes. Hydrogeophysical studies combine different data types to improve the estimates of hydrological states, e.g. in so- Nick Verheul lute transport studies. But solving a coupled inverse prob- CWI (Centrum Wiskunde & Informatica) lem faces two main challenges: determining the relation- [email protected] ship between geophysical and groundwater variables; and fitting two different sources of data. We investigate two computational approaches; first, using the alternate direc- Daan Crommelin tion method of multipliers and second, a block coordinate Centrum voor Wiskunde en Informatica descent method for minimization of the coupled objective (CWI) function. Both methods provide a huge computational ad- [email protected] vantage. Geophysical and groundwater models were developed in Matlab to test the joint inversion framework for PP2 different cases, with or without knowledge of the petrophysical relationship. The Aurora: Electron Transport in the Upper At- mosphere Klara Steklova University of British Columbia For millennia, people have been fascinated with the natu- Department of Earth, Ocean and Atmospheric Sciences ral light shows of the aurora. Recently, advances in physics [email protected] have been made in modeling the aurora to help us understand more about this phenomenon. There are many challenges in making predictions given an auroral model. In Eldad Haber particular, the problem can be stated as a free boundary University of British Columbia, Vancouver, Canada value problem. To date, all computational investigations [email protected] have avoided the free boundary aspect of the problem. Nu- merical experiments are given showing that including the PP2 free boundary feature is necessary to obtaining physically meaningful solutions. Disambiguated Characterization of Rain from Radar Measurements Using An Alternate Repre- Mark Woods sentation of Hydrometeor Size Distributions Rensselaer Polytechnic Institute Sandia National Laboratories We present a method to disambiguate the interpreta- [email protected] tion of radar measurements when estimating mean masses and sizes of hydrometeors. The method hinges on partial mass integrals (PMI) of arbitrary particle size dis- PP2 tributions, without assuming gamma distribution. Opti- Constrained Optimization for the Inversion of 2 mized canonical-correlation analyses yield eigenvectors of and 3-Dimensional Bouguer Gravity Anomalies the PMI with a maximum correlation to eigenvectors of the radar observables. The potential of this method for rain We propose a constrained optimization approach applied retrieval algorithms is illustrated using ground-based and over Bouguer gravity anomalies to improve 2- and 3- airborne disdrometer measurements and simulated radar Dimensional models of Earths structures. Based on observations. Primal-Dual Interior Point methods, we develop density constraints for transitional areas obtained from previous Ousmane O. Sy geological observations (e.g., borehole data). We apply the Jet Propulsion Laboratory algorithm to synthetic data and gravitational datasets from California Institute of Technology a Porphyry Cu-Mo deposit formation (Cooper Flat Mine, [email protected] Sierra County, NM) focusing only on those feasible models meeting the constraints. Kaelyn Griffin Rose-Hulman Institute of Technology Azucena Zamora GS15 Abstracts 147

University of Texas at El Paso [email protected]

Aaron A. Velasco, ADRIAN E. Gutierrez University of Texas at El Paso Geological Sciences [email protected], [email protected]