58 GS11 Abstracts

IP1 tional perspective. Multiscale Model Reduction Techniques for Flows in High-contrast Heterogeneous Media and Appli- Jörn Behrens cations KlimaCampus University Hamburg The development of numerical algorithms for simulations [email protected] of flow processes in large-scale highly heterogeneous porous formations is challenging because properties of natural geologic porous formations (e.g., permeability) display high IP3 variability and complex spatial correlation structures which Recent Advances in Full Waveform Global Seismic can span a hierarchy of length scales. It is usually necessary Tomography of the Earth’s Mantle to resolve a wide range of length and time scales, which can be prohibitively expensive, in order to obtain accurate pre- Over the last 20 years, several generations of global tomo- dictions of the flow, mechanical deformation, and transport graphic models of the earth’s mantle elastic structure have processes under investigation. In practice, some types of been developed, relying on simple theoretical approxima- coarsening (or upscaling) of the detailed model are usually tions to the 3D wavefield (i.e. ray theory and first order performed before the model can be used to simulate com- normal mode perturbation theory). Now, it is possible to plex processes. Many approaches have been developed and compute accurate synthetics in spherical geometry for ar- applied successfully when a scale separation adequately de- bitrary 3D structures using numerical approaches, such as scribes the spatial variability of the subsurface properties the Spectral Element Method, which is particularly well (e.g., permeability) that have bounded variations. The suited for global waveform tomography. The challenge has quality of these approaches deteriorates for complex het- been shifted from theoretical limitations to the length of erogeneities without scale separation and high contrast. In computations involved. I will discuss and illustrate current this talk, I will describe multiscale model reduction tech- steps towards the development of next generation, high res- niques that can be used to systematically reduce the de- olution whole mantle models. grees of freedoms of fine-scale simulations and discuss ap- Barbara Romanowicz plications to preconditioners. Numerical results will be University of California, Berkeley presented that show that one can improve the accuracy [email protected] of multiscale methods by systematically adding new coarse basis functions and obtain contrast-independent preconditioners for complex heterogeneities. IP4 Yalchin Efendiev Computational Challenges in Applications of Cou- Dept of Mathematics pled Reservoir Geomechanics Texas A&M University Recent years have seen dramatic increase in the application [email protected] of coupled hydro-thermo-mechanical numerical solutions to petroleum industry. In this context they are often referred IP2 to as Coupled Reservoir Geomechanics, and involve coupled solution of multiphase, thermal flow in porous me- The Role of Applied Computational Mathematics dia, stress and deformation, and fracture mechanics. This in the end-to-end Near-field Tsunami Early Warn- growing discipline encompasses diverse problems such as ing System in Indonesia wellbore stability, sand production, hydraulic fracturing, In the aftermath of the 2004 Indian Ocean Tsunami, the compaction and subsidence, fault reactivation etc. Such German Federal Government funded the development of a applications invariably involve large, complex fields and new near-field tsunami early warning system (GITEWS) they pose serious computational challenges. This talk will for Indonesia as a multi-national multi-institutional sci- discuss some of them, including: Current state of the iter- entific collaboration. The system is in operation since ative strategies for the flow and stress coupling Grid con- November 2008 and is being handed over to the Indonesian struction, grid repair and generation of the geomechani- Government in the days of the SIAM Geosciences Meeting. cal grid from the flow grid Creation and upscaling of the Several tsunami events have occurred since the inaugura- geomechanical characterization and dealing with complex tion of the system and have demonstrated the performance media (such as naturally fractured reservoirs) Scale issues of this highly sophisticated and integrated tool for mitigat- and dealing with local accuracy requirements All of these ing the effects of natural disaster. In the core of the system, topics will be illustrated by examples of actual studies from several mathematical and computational techniques and studies of petroleum reservoirs and CO2 sequestration in procedures play a key role to interpret earth observation aquifers. data and to make use of the information gained. Simulat- Antonin Settari ing the specific components of the earth system is just the University of Calgary start of the chain of mathematical processes involved. A Taurus Reservoir Solutions rigorous (but simple and robust) uncertainty propagation [email protected] and reduction model helps in determining the potential impact of a rupture. Statistical methods are used to develop hazard maps and define risk zones. The presentation will IP5 give an overview of the diverse technical components and 3-D Finite-element Simulation of Transient Elec- societal considerations involved in the GITEWS Tsunami tromagnetics in Complex Earth Media Early Warning System. An emphasis will be laid on the computational mathematics aspects and their core role in The diffusion of low frequency EM fields in conductive solving the problem of near-field tsunami detection and media is the basis for controlled-source electromagnetic early warning. From this development, and the constraints (CSEM) remote sensing of Earths subsurface. Over the of real-time robust operational service, several conclusions past decade, there have been many numerical approaches can be drawn for a more general geo-scientific computa- developed for simulating CSEM in complex geological GS11 Abstracts 59

media, including direct implementation of the coupled CP1 Maxwells equations, the popular double-curl electric field Seismic Velocity Modeling Using Genetic Algo- formulation, and the coupled vector and scalar potentials rithms, Binary Versus Real Valued Searches formulation derived under the Coulomb gauge condition. In this talk, we present a new formulation that uses a From a statistical view seismograms are interpreted as ran- variation of the Lorenz gauge that is well suited to finite- dom variables. The random component can be attributed element (FE) modeling. Our formulation decouples the to sources such as distant-dependent measurement error, vector and scalar potentials into a separate diffusion equa- human error in picking arrival phases, and random noise tion for the vector potential and Poissons equation for the attributed to travel path. Stochastic modeling of such phe- scalar potential. It reduces the larger FE system that re- nomenon quantifies these random processes. Genetic algo- sults from the Coulomb gauge into two smaller decoupled rithms are iterative stochastic models that evaluate pro- systems of FE equations. Moreover, this Lorenzian-gauge gressively improved mathematical models. We explore the formulation retains the advantages of both the double-curl benefits of using binary versus real valued based genetic electric field and the Coulomb-gauge approaches; the re- algorithms in modeling seismic velocity structures. sulting FE system not only has the minimum number of unknowns but also can be used in the static limit using K B. Boomer an iterative solver. We illustrate the method for large 3-D Bucknell University geophysical CSEM problems and compare results with the [email protected] finite-element double-curl electric field approach and the finite-difference Maxwell equation approach. Richard A. Brazier The Pennsylvania State University Dubois Campus Jerry M. Harris Commonwealth College (Math Division) Stanford University [email protected] [email protected]

CP1 IP6 Appropriate Formulation of the Objective Function Atmospheric Convection in Weather and Climate for a Better Integration of 4D Seismic Data to Con- Simulations strain Reservoir Models. Convection in the atmosphere, whether driven by heat- Calibrating reservoir models to flow data involves history ing of the earth’s surface or by condensational heating in matching processes. Model parameters are iteratively ad- clouds, is one of the most difficult processes to represent justed to minimize the misfit between the real data and the in our climate and weather models, and representing these corresponding simulated responses. The current formula- processes is critical given the large uncertainty associated tion used to quantify the seismic data mismatch is neither with clouds in climate assessments and weather prediction. representative of the difference between two images, nor of Convective updrafts are not resolved in climate model sim- matching quality. We describe an alternative formulation, ulations that use horizontal mesh spacings of 0(100 km), using methods rooted in image processing, to extract rel- and they are severely under-resolved in weather prediction evant information from seismic images and compute their where the smallest horizontal mesh spacings are O(1 km). dissimilarity. The issues associated with representing convection have significant implications for the design of the Navier-Stokes Ratiba Derfoul solvers used atmospheric models. In this talk I will briefly IFP Energies nouvelles outline and provide examples of these issues and and dis- Laboratoire de Mathématiques de l’INSA, INSA Rouen cuss their implications. [email protected]

William C. Skamarock Sebastien Da Veiga, Elodie Tillier National Center for Atmospheric Research IFP Energies nouvelles [email protected] [email protected], [email protected] CP1 Traveltime Computation and Two-Point Seismic Christian Gout Ray-Tracing in Complex Velocity Models. INSA Rouen Lab. de Mathematiques de l’INSA The problem of tracing seismic ray between two given [email protected] points plays a central role in many implementations, for example in tomographic velocity analysis. Traditional ways of two-point ray-tracing, such as shooting or ray bend- CP1 ing methods appear to be unstable and computational On the Stability of the Perfectly Matched Layer in expensive in complex velocity anisotropic 3D models. A Time-Dependent Elastic Wave Guides. new approach based on eikonal ﬁnite-diﬀerence solvers is proposed. Numerical experiments using high-contrast There are many wave propagation problems where bound- isotropic and transversal isotropic models demonstrate the ary phenomenon such as surface or glancing waves are dom- accuracy of proposed two-point ray-tracing algorithms. inant. Typical examples are in seismology and earthquake engineering, which can be described by the elastic wave Serdyukov Aleksander equation in a waveguide. It has also been reported that INGG Russia when an elastic waveguide is accompanied by free-surface [email protected] (vanishing stresses) boundary conditions or clamped (vanishing displacements) boundary conditions, the PML becomes unstable and can not be used to truncate the computational domain. This is in part due to the existence 60 GS11 Abstracts

of backward propagating modes supported by the bound- CP2 ary conditions. In this talk we will discuss how to avoid Elastic Effect on the Stability of Viscoelastic Shear this instability. Analysis and numerical experiments will Flows in the Limit of Infnite Weissenberg and be presented highlighting the practicality of our technique. Reynolds Numbers This work is concerned with the linear stability of viscoelas- Kenneth Duru, Gunilla Kreiss tic shear flows of an Upper Convected Maxwell fluid under Division of Scientific Computing the effect of elasticity. We are focused on the stability prob- Uppsala University lem of a few classes of simple parallel flows in the limit of in- [email protected], [email protected] finite Weissenberg and Reynolds numbers. We will discuss the numerical stability results. We consider plane Couette and Poiseuille flow, the hyperbolic tangent shearlayer and CP1 the Bickley jet flows. For all these flows, we shall consider Identification of Multiple Layers in Geophysics Us- free surface boundary conditions as well as wall boundary ing Optimization and Level Set Methods conditions. In the inviscid case, all the flows are unstable for free surfaces. For wall bounded flows, the Couette A shape reconstruction method for geophysical objects by and Poiseuille flows are stable, while stability of the shear temperature or hydraulic head measurements is presented layer and Bickley jet depends on the ratio of the channel which uses adjoint equations and a level set function ap- width to the characteristic length scale of the profile. In all proach. Temperature is measured on subdomains, e.g. rep- cases, we find that elasticity stabilizes and ultimately sup- resenting boreholes. This information is used to recon- presses the instability. Our numerical approach is based struct the shape of the geophysical layers. For this pur- on the spectral Chebyshev collocation method. We shall pose shape optimization techniques are applied. Synthetic also show that some flows, such as plane Poiseuille flow examples demonstrate the use of the inverse method and between two parallel free surfaces, also have short wave in- its behavior in different configurations. stabilities. This is in marked contrast to the wall bounded Michael Herty case. In this case, no smooth velocity profiles unstables RWTH Aachen Universtiy to short waves are known, and for certain classes of flows Department of Mathematics there are even results ruling out short wave instability [email protected] Ahmed Kaffel virginia tech CP1 kaff[email protected] Estimation of Transmission Eigenvalues and the In- dex of Refraction Using Cauchy Data CP2 Transmission eigenvalues have import applications in in- A Computational Framework for Ocean and Atmo- verse scattering theory. We show that transmission eigen- sphere Modeling Based on Parallel Adaptive FEM values can be computed from the near field Cauchy data. for Unstructured Meshes In addition, we apply an optimization method to estimate We present a computational framework based on paral- the index of refraction based on the lowest transmission lel adaptive FEM for atmosphere and ocean simulations eigenvalues. The numerical results validate the effective- as part of the Unicorn project. In order to achieve effi- ness of the method. cient representation of spatial scales we use adaptive mesh Jiguang Sun refinement. The framework can utilize massively parallel Department of Mathematics, Delaware State University architectures to achieve the required model resolutions. In [email protected] our framework we treat the ocean/atmosphere as a turbulent incompressible fluid with variable density. We present results on the ongoing work. CP2 Kaspar Müller Spectral Methods on Semi-Infinite Domains for Im- School of Computer Science and Comunication plementation of Open Boundary Conditions Royal Institute of Technology KTH We adopt a spectral approach to open boundary conditions [email protected] [Givoli, 2008] using Generalized Laguerre functions [Wang et al. 2009], discretizing the equations in a semi-infinite Johan Hoffman, Johan Jansson domain attached to a finite region of interest. We consider School of Computer Science and Communication 1D Shallow Water Equations, with a spectral collocation Royal Institute of Technology KTH in space, semi-implicit semi-Lagrangian discretization in jhoff[email protected], [email protected] time. Coupling with different finite-domain discretizations shows that a reasonable number of base functions is sufficient to reach accuracy and efficiency without spurious CP2 reflections at infinity. Characteristics-Based Methods for Atmospheric Simulation on Modern Hardware Tommaso Benacchio Fachbereich Mathematik und Informatik, Freie Immense distributed memory parallelism requires priori- Universität tizing the lowering of communication burden in numeri- Berlin, Germany cal methods. Focusing on atmospheric simulation, I pro- [email protected] pose herein various characteristics-based (CB) integration methods. With fully discrete explicit time stepping, CB methods reduce communication and synchronization while allowing large-CFL time steps. I will discuss the theory, GS11 Abstracts 61

large-CFL accuracy, handling of source terms and multi- ﬂow and transport and yields a geometric inversion scheme dimensionality, limiting of oscillations, and eﬃciency on requiring no explicit regularization still capable of resolving accelerator-based computing architectures. highly detailed structure.

Matthew Norman Alireza Aghasi, Eric Miller, Andrew Ramsburg, Linda North Carolina State University Abriola Raleigh, NC Tufts University [email protected] [email protected], [email protected], [email protected], [email protected] CP2 Under-Resolved Les of Rayleigh-Benard Convec- CP3 tion; Effects of Prandtl Number Anisotropy Different Types of Parametrization for History- matching In [Piotrowski et al., JCP 228, 2009] the effects were discussed of anisotropic numerical filtering in under- One of the main goals of the reservoir characterization is to resolved large-eddy simulation (LES) on the organization provide geologically realistic reservoir property estimates of Rayleigh-Benard convection at a finite Prandtl number. that incorporate all relevant information. Preservation of This study extends the linear stability theory of that ear- spatial structure is a crucial aspect of geologically realis- lier work to anisotropic Prandtl numbers, to asses the role tic estimation. A key element in solving this issue is rep- of disparate approximations to the governing equations in resented by parameterization. Different types of param- large-scale atmospheric codes. Asymptotic predictions of eterizations are presented in combination with a history the linear theory are discussed and illustrated with com- matching algorithm putational examples. Remus G. Hanea Zbigniew P. Piotrowski TNO Built and Environment, National Center for Atmospheric Research [email protected] [email protected]

Piotr Smolarkiewicz CP3 NCAR Sensitivity Analysis and Parameter Estimation in MMM Groundwater Flows [email protected] In this work, we use Frechet derivatives of solutions of groundwater flow models with respect a hydraulic conduc- CP2 tivity parameter and demonstrate their applicability in es- Finding Normal Modes of Semi-Enclosed Bays Us- timating this parameter from flow data; We will discuss the ing the Statistical Modes of a Data Set of Modeled fact that the Frechet derivative operator is Hilbert-Schmidt Tsunami Wavefields and the implications for uncertainty quantification. We will use a power method and sensitivity equations to eval- Understanding the resonant modes of bays and harbours uate the most significant directions and compute reduced is important for tsunami hazard assessment and moni- representations of the operator for efficient gradient calcu- toring. Previous methods for determining normal modes lations. have adapted techniques developed for enclosed basins; but these generally rely on ad-hoc assumptions about the Vitor Leite Nunes boundary between basin and ocean. We demonstrate a Interdisciplinary Center for Applied Mathematics method for identifying the normal modes using Empirical Virginia Polytechnic Institute and State University Orthogonal Function (EOF) analysis of modeled tsunami [email protected] wavefields which does not have this limitation, and show examples for Poverty Bay and Monterey Bay. CP3 William L. Power History Matching of Production and 4D Seismic GNS Science Data for a Realistic Sagd Case [email protected] We describe an assisted history matching method applied to a realistic SAGD case. The objective is to constrain Elena Tolkova a reservoir model with both production and P impedance JISAO / NOAA Center for tsunami research variations, derived from the stratigraphic inversion of a 4D [email protected] seismic dataset recorded over three years of production. We built a workflow with geological modeling, upscaling, CP3 flow simulation and petroelastic modeling to compute the production and seismic responses. Then, an optimization A Joint Inversion Scheme for Contaminant Source process is run to minimize the data mismatch. Zone Reconstruction Elodie Tillier, Sebastien Da Veiga, Mickaele Le Ravalec, A parametric level set (PaLS) method is used to charac- Axelle Baroni, Vincent Clochard, Karine Labat, Olivier terize contaminant source zone geometry and entrapped Lerat saturation distribution from electrical resistance and hy- IFP Energies nouvelles drological (downstream concentration) data. The low or- [email protected], der representation provided by the PaLS approach allows [email protected], for tractable computation of all sensitivities based on exact [email protected], physical models for resistance tomography and multiphase [email protected], 62 GS11 Abstracts

[email protected], John B. Bell [email protected], CCSE [email protected] Lawrence Berkeley Laboratory [email protected]

CP4 Ann S. Almgren Near-Well Simulation in 3D Using Mpfa-Methods Lawrence Berkeley National Laboratory [email protected] Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. We investigate numerical schemes based on logarithmic grid refinement Marc Day around wells. In particular, multi-point-flux approxima- LBNL tion (MPFA) methods are investigated in three dimensions [email protected] (3D) on different types of hybrid grids for the single phase pressure equation. The numerical experiments are used to Michael Lijewski provide guidelines for selection of preferred grid and dis- Lawrence Berkeley National Laboratory cretization method for near-well simulation in 3D. [email protected]

Haakon Haegland CIPR, University of Bergen, Norway CP4 [email protected] Mathematical and Numerical Study of a Two- Phase Two-Component Porous Media Model CP4 We will present the mathematical existence of a degenerate Sensitivity for Coupled Systems of Flow and Trans- parabolic system modeling two phase (liquid and gaz) two port component (water and hydrogen) flow in porous media in the context of radioactive waste storage where the veloc- We discuss several approaches to sensitivity analysis for ity of the mass exchange between dissolved hydrogen and coupled systems modeling flow and transport in porous me- hydrogen in the gaz phase is supposed finite. We will also dia. The techniques include adjoint and global sensitivity present a numerical scheme to discretise this system and methods and the sensitivity equations. The applications we will present some properties for this numerical scheme. include a transport model coupled to the flow with inertia and a system of diffusion equations in heterogeneous multiscale formations. Sensitivity analysis aids in the choice Bilal Saad of a reduced model which may decrease the computational CEA complexity. [email protected]

Ken Kennedy Mazen Saad Oregon State University Ecole Centrale de Nantes [email protected] [email protected]

Malgorzata Peszynska Florian Caro Department of Mathematics CEA Oregon State University ﬂ[email protected] [email protected]

CP4 CP4 A Coupled Large-Scale Model for Hydromechanical Adaptive Mesh Refinement Algorithm for Simulat- Simulation of Co2 Geological Storage ing Two-Phase Compressible Flow in Porous Media A coupled hydro-mechanical modeling of CO2 injection We describe an adaptive mesh refinement (AMR) algo- into deep aquifers is proposed. Multiphase and multicom- rithm for simulating two-phase compressible flow in porous ponent fluid flow is considered in interaction with the rock media under isothermal condition. The governing equa- geomechanical behaviour. The numerical methods used to tions are decomposed based on the total velocity split- link a flow transport code and a mechanical code, in par- ting approach to obtain a parabolic equation for the pres- ticular fields transfer between non-coincident meshes and sure and a set of hyperbolic equations for the component time coupling algorithm, are then presented. Some results densities. This formulation forms the basis of a second- of large scale simulations especially some aspects of the order sequential algorithm in which the pressure equa- mechanical integrity of caprock are finally discussed. tion is solved implicitly and the component conservation equations are solved explicitly. The algorithm is then im- Pierre Sochala plemented within a parallel block-structured AMR frame- BRGM work, enabling us to perform efficient large-scale simula- [email protected] tions. To demonstrate features in the algorithm, we will examine simulation results for an idealized model of a gas Vivien Desveaux leaking from an underground LPG storage cavern. UniversitédeNantes2ruedelaHoussinière 44000 Nantes George Pau [email protected] LBNL [email protected] Jérémy Rohmer, Darius Seyedi BRGM 3 avenue claude guillemin GS11 Abstracts 63

45000 Orléans TBaumann [email protected], [email protected] Institute of Hydrology Technische Universitaet Muenchen [email protected] CP5 An Analytical Model for Transient Heat Flow in Shallow Geothermal Systems CP5 How Phase Transition Is Affected by Chemical Po- This contribution introduces a new analytical model ca- tential and Relative Concentration pable of simulating fully transient conductive-convective heat transfer processes in a shallow geothermal system con- When we consider the phase transition of liquid to gaseous sisting of a borehole heat exchanger embedded in a soil water, relative humidity is considered the primary driving mass. The spectral analysis method is utilized. It calcu- force. For adsorption/desorption, the relative concentra- lates the temperature distribution in all components using tion of the species is considered the primary driving force. the discrete Fourier transform, for the time domain, and Theoretical considerations via Hybrid Mixture theory indi- the Fourier-Bessel series, for the spatial domain. Numeri- cate that it is the difference between phase chemical poten- cal examples will be presented. See Al-Khoury, 2010, IJFF tials of the species which is the fundamental driving force. 20, issue 7. In this presenation we report preliminary theory on the relationship between chemical potential and the relative Rafid Al-Khoury concentrations. Civil Engineering and Geosciences Delft University of Technology Eric R. Sullivan, Lynn Bennethum, Lincoln Collins [email protected] University of Colorado Denver [email protected], [email protected], CP5 [email protected] Elastic Response of Granular Soils with Multiscale Substructure CP5 Effective medium theories for elastic and/or seismic re- Numerical Solution to a Nonlinear Transport sponse of granular soils have typically used theories such as Model for Swelling Porous Materials Hertz-Mindlin or Walton-type methods to determine overall behavior. For environmental applications, it may also We demonstrate the results of a novel numerical scheme be necessary to consider smaller scale granularity due to used to solve a coupled system of nonlinear transport mod- biomineralization. An important second scale of granu- els consisting of a Volterra partial integrodifferential equa- larity arises when various forms of calcium carbonate are tion of the second kind and a nonlinear diffusion equation. precipitated on the soil grains, and near the regions of con- A model application is a drug delivery device consisting of tact between soils grains. The strengthening effects can be a drug interlaced within a polymer matrix. Results will significant. be shown for concentration profiles and moisture content along with an interpretation of viscoelastic effects present James G. Berryman in the model. Lawrence Berkeley National Lab Earth Sciences Division Keith Wojciechowski [email protected] Department of Mathematical Sciences University of Colorado Denver [email protected] CP5 Characteristic Thermal Profiles in Open-Loop Geothermal Energy Harvesting CP5 Numerical Method for Poroelasticity Based on a In exploring deep geothermal energy (> 2000 m), heat Coupling of Nonconforming and Mixed Finite Ele- losses in the boreholes can be significant and are depen- ment Methods Using Rectangular Elements dent of the pumping rates, and sharp transitions in well diameters and in geology. Temperature drops of 20-30 % In this talk, we present a finite element formulation to ap- between the top of the deep aquifer and ground surface are proximate the coupled fluid and mechanics in deformable common. Quantifying these energy losses are fundamen- porous media. The method uses a nonconforming finite tal to determining the capabilities of the technology. We element for the displacement of the solid phase, and the formulate a mathematical model of the pipe-soil system in lowest-order Raviart-Thomas mixed finite element for the the limit where axial convective transport within the pipe pressure and the velocity of the fluid phase. To achieve balances radial diffusion in the surrounding medium. This the discrete Korn’s inequality, we add a penalty term to results in a coupled system of boundary-value problems for the variational formulation. We provide apriorierror es- steady-state solutions, and the rates of thermal losses in the timates. axial direction are found as a function of the different pipe radii and lengths, as well as the thermal properties of the Son-Young Yi surrounding medium. Design choices for the pipe staging The University of Texas at El Paso are suggested based on the local geology of the site. [email protected] Burt S. Tilley, Miguel A. Rasco Mathematical Sciences Department CP6 Worcester Polytechnic Institute Existence of a Weak Solution for the Fully Coupled [email protected], [email protected] 64 GS11 Abstracts

Navier-Stokes/Darcy-Transport Problem BOKU-University of Natural Resources and Applied Life Sciences, Vienna We study a surface/subsurface multiphysics problem [email protected] arising from the problem of groundwater contamination through rivers. Specifically, a convection-diffusion type transport equation is coupled with the Navier- CP6 Stokes/Darcy flow via velocity field and concentration. On Solution of Time-Dependent the interface, we accept balance of forces, continuity of Pde Through Component-Wise Approximation of the flux and the Beavers-Joseph-Saffman condition. We Matrix Functions analyze this problem by proving the existence of a weak solution by a method based on Galerkin approach in time. Krylov subspace spectral (KSS) methods have been demonstrated to be effective time-stepping methods for parabolic Aycil Cesmelioglu and hyperbolic variable-coefficient PDE. Their effective- IMA ness stems from the use of different approximations for each [email protected] Fourier component of the solution, based on techniques for approximating bilinear forms developed by Golub and Beatrice Riviere Meurant. In this talk, it is shown how this essential in- Rice University gredient of KSS methods can be adapted to finite element Houston, Texas, USA methods that are applied to PDE that arise in reservoir [email protected] simulation.

James V. Lambers CP6 University of Southern Mississippi Permeability of Fluid Flow Through Cilia Department of Mathematics [email protected] This work concentrates on finding the permeability for viscous flow though a structure of periodic cylinders as a function of cylinder density and cylinder angle. We use a full CP6 three-dimensional model of incompressible viscous fluid in Randomized Operator Fitting for Preconditioning combination with the Buckingham Pi Theorem to deter- the Wave Equation Hessian mine the relationships. Numerical results are obtained using Mixed Finite Element Method. The results are com- In this seminar, we consider the problem of approximating pared with Zick and Homsy (1982). Applications include the inverse of the wave-equation Hessian, also called nor- modeling the flow of mucus in lung tissue mal operator, in seismic imaging. We develop an expansion scheme for the pseudodifferential symbol of the inverse Kannanut Chamsri Hessian, and recover the coefficients via least-squares fit- University of Colorado Denver ting from a certain number of applications of the normal [email protected] operator on adequate randomized trial functions. We show how to construct these functions properly through analytical considerations and the Curvelet transform. Once an CP6 approximate inverse Hessian is available, application to an Modelling of Tunnel Inflow with Complicated Dis- image of the model can be done in very low complexity. cretisation We also present numerical experiments demonstrating the performance of the method. We solve a 3D groundwater flow problem, predicting the inflow into a deep tunnel to fit the field measurement. The Pierre-David Letourneau main problem is a combination of a kilometer scale of the Stanford University whole model and a scale of the tunnel 3.6m diameter. This [email protected] is done with sophisticated set mesh parameters, changing from 1m to 100m. We show comparisons with measured Laurent Demanet data and also discuss possible solutions without explicit Mathematics, MIT shape of the tunnel in the model geometry. [email protected] Milan Hokr, Ilona Skarydova Technical University of Liberec, FM NTI CP6 [email protected], [email protected] An Adaptive Approach for Simulation of Flow Ac- cumulation; a Mathematical Modification of Rmmf CP6 Model Smc Methods for the Calibration of Stochastic Simulation of flow accumulation with available GIS soft- Rainfall-Runoff Models ware to use in the Revised-Morgan Morgan-Finny model causes high overestimation of erosion at large scales (catch- The rainfall-runoff model considered in this talk is a con- ment or regional). The provided remedy was implementing ceptual stochastic model, formulated in contiuous-discrete harmonic and P-series in calculation of distributed runoff state space form. We use a maximum likelihood approach for simulating flow accumulation. Results showed that based on an EM algorithm. In this approach, the key ingre- error in Harmonic-series approach was considerably de- dient is the computation of smoothed additive functionals pendent on slope length, whereas in P-series formulation of hidden states (Olsson et al., 2008). Sequential Monte remained less than 10% for various slope lengths. The Carlo methods (SMC), also called particle methods, are accumulation of runoff along the slope was validated by used for smoothing in the state space model. measured discharge within Namchun watershed, Thailand, Franz Konecny which was acceptable according to Morgan 2005. The GS11 Abstracts 65

study revealed that through the new modiﬁcation, the and stability under high CFL numbers. RMMF model can be a useful empirical-physically-based model in erosion assessment at large scale. Susana Serna Department of Mathematics Khatereh Polous Universitat Autonoma de Barcelona ITC Institute, Twente University, The Netherlands [email protected] [email protected]

Amir Hooshmand CP7 Institute for Advanced Study Constrained Optimization Schemes for 1D Inverse Technical University of Munich, Germany Wave Propagation Problems [email protected] We compare three constrained optimization schemes for solving 1D inverse wave propagation problems posed as Yousef Hooshmand PDE-constrained optimization programs. Our goal is to Institute for Product Engineering identify the best scheme that incorporates inequality con- University of Duisburg-Essen, Germany straints over the model parameter, i.e. shear modulus, to [email protected] be used in conjunction with a robust algorithm that solves the inverse problem. We conduct a numerical experimen- CP7 tation for each method with synthetic problems, created based on velocity models derived from seismic measure- Short Wave Instabilities in Free Surface Shear ments, and report their performance. Flows Anibal Sosa In this study, We investigate the linear stability of inviscid The University of Texas at El Paso plane Poiseuille flow between two parallel free surfaces. We Computational Science Program show that there are short wave instabilities with eigenfunc- [email protected] tions localized near the free surface and derive the asymptotics of these modes. The stability of wall bounded inviscid shear flows has been studied for more than a cen- Leticia Velazquez tury. However, shear flows bounded by free surfaces are The University of Texas at El Paso also a solution of the Euler equations. Although there are Department of Mathematical Sciences entire books on stability of films and jets, these studies [email protected] have focussed on instabilities due to surface effects, such as surface tension and air drag, and they usually assume a Carsten Burstedde uniform velocity within the jet or film. They consider an The University of Texas at Austin axisymmetric jet bounded by a free surface with a Hagen- [email protected] Poiseuille profile of the velocity. They conclude that the nonuniform velocity in the jet has a stabilizing effect. This Miguel Argaez conclusion, however, is due to their failure to consider non- University of Texas at El paso axisymmetric modes. In recent work by M. Renardy, it was [email protected] shown that plane parallel shear flows bounded by two free surfaces have long wave instabilities for all velocity profiles Omar Ghattas that are not uniform. This is in marked contrast to the wall University of Texas at Austin bounded case, where criteria such as those of Rayleigh and [email protected] Fjortoft guarantee stability of a broad class of flows. In this work, we shall show that some flows, such as plane Poiseuille flow, also have short wave instabilities. Again, CP8 this is in marked contrast to the wall bounded case. In this A Sigma-Coordinate, Discontinuous Galerkin case, no smooth velocity profiles unstable to short waves Method for the Three-Dimensional Shallow Water are known, and for certain classes of flows there are even Equations results ruling out short wave instability. In this presentation, we describe the development, imple- Ahmed Kaffel mentation, and application of a novel sigma–coordinate virginia tech discontinuous Galerkin (DG) method for the three– kaff[email protected] dimensional shallow water equations. The h (mesh) and p (polynomial order) convergence properties of the method are demonstrated on a set of analytic test cases. The devel- CP7 opment of new efficient (in some cases optimal) cubature Analysis and Numerics of the Magnetohydrody- rules for integration over triangular prism elements is also namic Equations for Real Gases discussed. We present an analytical study of the wave structure of the Ethan Kubatko MHD equations for real gases based on the local decompo- Department of Civil and Environmental Engineering sition in characteristic wavefields. We propose a complete The Ohio State University system of eigenvectors that guarantees continuity with re- [email protected] spect to the conserved variables in the neighborhood of singular points. We formulate a high order characteristic- Clint Dawson based entropy-fix upwind numerical scheme based on the Institute for Computational Engineering and Sciences analytical study. Numerical examples show good accuracy University of Texas at Austin [email protected] 66 GS11 Abstracts

Ashley Maggi, Colton Conroy study using Sobol indices the sensitivity of model results The Ohio State University to the value and the spatial distribution of saturated hy- [email protected], [email protected] draulic conductivity along a slope.

Marie Rousseau CP8 Universit´eParis-Est,CERMICS-ENPC Large Time Step Finite Volume Evolution Galerkin BRGM Schemes for Shallow Water Flows [email protected]

We present two new large time step methods within the Olivier Cerdan framework of the well-balanced finite volume evolution BRGM Galerkin (FVEG) schemes. The methodology will be il- [email protected] lustrated for low Froude number shallow water flows with source terms modeling the bottom topography and Coriolis Alexandre Ern forces, but results can be generalized to more complex sys- Universite Paris-Est tems of balance laws. The FVEG methods couple a finite CERMICS, Ecole des Ponts volume formulation with approximate evolution operators. [email protected] The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken Olivier Le Matre into account explicitly. This is a novel feature of our FV Laboratoire d’Informatique pour la Mécanique et les method. As a result the FVEG schemes are typically 10 Sciences times more accurate than standard FV schemes. In order LIMSI-CNRS to approximate multiscale phenomena we have developed [email protected] two variants of large time step FVEG method: a semi- implicit time approximation and an explicit time approxi- Pierre Sochala mation using several evolution steps along bicharacteristic BRGM cones. Behaviour of new FVEG schemes will be illustrated [email protected] on a set of numerical experiments.

Maria Lukacova CP8 University of Mainz Effects of Shear Flow on KdV Balance, with Ap- Institute of Mathematics plications to Tsunami [email protected] Building upon recent work on the applicability of KdV to Anna Hundertmark, Florian Prill tsunami propagation, we discuss the effects of shear flow on Institute of Mathematics, University of Mainz the KdV balance. This leads in the shallow-water limit to [email protected], [email protected] the Burns condition which determines propagation speeds that arise in the KdV balance. For waves propagating counter to the shear, KdV dynamics arise earlier, while CP8 they arise later for waves propagating with the shear, the Numerical Modeling of Surface Flows Based on magnitude of this effect depending on surface shear veloc- Multi-Dimensional Models and Variational Data ity. Assimilation. Application to Flood Plain Flows Raphael Stuhlmeier In geophysical flows such as surface water flows, multi- Faculty of Mathematics, University of Vienna scales features and uncertainties of input parameters (eg [email protected] topography, parametrization of empirical laws) invite to derive multi-dimensional models (or multi-scale models like CP8 shallow-water / ALE free surface) while comparing the numerical results to observations. We present a global al- Semi-Implicit Finite Volume Schemes for Shallow gorithm based on optimal control and adjoint equations Free Surface Flows which makes fit the coupled multi-dimensional (or multi- We address the derivation of FV schemes for thin film flows scales) models with heterogeneous data (in-situ, remote- with low Froude number (eg surface water flows), and with sensed). potential wet-dry front. We present and analyze a new Jerome Monnier semi-implicit scheme, unconditionaly stable and robust, for Mathematics Institute of Toulouse unviscid shallow-water models. Numerical examples are [email protected] presented in a river hydraulics context, w/wo over-flowing (flood plain).

CP8 Jean-Paul Vila Mathematics Institute of Toulouse Study of Overland Flow with Uncertain Inﬁltration [email protected] Using Stochastic Tools.

Saturated hydraulic conductivity is a key parameter in CP9 overland flow models with infiltration, but several studies have shown the difficulty to correctly measure or estimate Stable Algorithms for a Two Domain Natural Con- this parameter. We therefore propose to consider this pa- vectionProblemandObservedModelUncertainty rameter as a stochastic input parameter. We use a Monte Numerical algorithms are studied for a Boussinesq model of Carlo method to quantify uncertainty propagation and to natural heat convection in two domains, motivated by the GS11 Abstracts 67

dynamic core of climate models. One algorithm is coupled CP9 across the ?uid-?uid interface. Another is decoupled using Modeling of Uncertainty for a Spatial Simulator a partitioned time stepping approach that retains uncon- Response ditional stability. An empirical study of model uncertainty is presented where stochastic noise is introduced into two Complex numerical models such as oil reservoir simula- nonlinear coupling terms that play an important role in tor involves lots of uncertain input parameters (geological, stability. fluid flow parameters...) and can yield spatial outputs like oil saturation maps. To compute sensitivity analysis and Jeffrey M. Connors uncertainties studies, experimental design and metamodels Lawrence Livermore National Laboratory are used. We propose an innovative strategy based upon Center for Applied Scientific Computing the wavelet decomposition of the output, the optimal se- [email protected] lection of wavelet coefficients and their metamodeling by the Gaussian processes. An application on an oil reservoir Benjamin Ganis illustrates the methodology. University of Texas at Austin Center for Subsurface Modeling Amandine Marrel, Mathieu Feraille [email protected] IFP Energies nouvelles [email protected], [email protected] CP9 Time-dependent Wellbore Index Pressure Calcula- tions CP9 Multiscale Wavelet-Analysis-Based Localization of We discuss a new post-processing technique for stan- Covariance Estimates in the Ensemble Kalman Fil- dard reservoir simulators to determine detailed information ter about the time-dependent pressure at a wellbore. This information is used in well test analysis. Standard simulators IntheensembleKalmanfilter,asequentialMonteCarlo use point or line source well models and do not resolve down method for Bayesian inversion, covariances are estimated to the tiny scale of the well radius. Our method involves from a small ensemble. There, sampling errors manifest just a local solve of the time dependent pressure equation in spurious, long-range correlations. In this work we dis- in the vicinity of the wellbore, using as boundary data in- cuss a new method to reduce the negative impact of such formation from the main reservoir simulation. We describe correlations. It is designed for inversion problems where the connection with the Peacemann wellbore index, discuss the forward model contains significant features on multi- the accuracy and show results from a number of test cases. ple scales, e.g. history matching of hydrocarbon reservoirs. Different scales are resolved by a multi-scale wavelet transform. Dugald Duncan, Nneoma Ogbonna Heriot-Watt University Oliver Pajonk [email protected], [email protected] Institute of Scientific Computing Technische Universität Braunschweig [email protected] CP9 On a Distribution of the Enkf Sampling Error Ralf Schulze-Riegert SPT Group GmbH Ensemble Kalman filter is a state space ensemble-based for- [email protected] mulation of the Kalman filter. It is based on a low-rank covariance approximation from a moderately sized ensemble. Hermann G. Matthies Sampling errors lead to artificial effects, such as spurious Institute of Scientific Computing correlations, deteriorating the estimates and the forecasts Technische Universität Braunschweig of the system states. We derive the distribution of the sam- [email protected] pling error for the EnKF after a single analysis step. The distribution depends on ensemble size, model dimension and observation locations. CP9 Andrey Kovalenko Stochastic Parameterizations of Highly Heteroge- Center for Integrated Petroleum Research neous Media University of Bergen We discuss new approaches to stochastic parameterizations [email protected] of flow in porous media based on Karhunen-Loeve, Haar, and other series expansions appropriate for highly hetero- Trond Mannseth geneous media. Of particular interest are parameteriza- Center for Intergrated Petrleum Research tions for discontinuous and multiscale porous media as well University of Bergen as interpretations of data simulated with geostatistics pack- [email protected] ages such as GSLIB. We use these parameterizations in finite element algorithms to compute moments of variables Geir Nvdal of interest such as pressures and fluxes. International Research Institute of Stavanger & Centre of Integrated Petroleum Research, UoB Veronika S. Vasylkivska, Malgorzata Peszynska, Mina [email protected] Ossiander Department of Mathematics Oregon State University [email protected], 68 GS11 Abstracts

[email protected], pling in Geophysical Systems [email protected] Numerous problems in the Earth sciences involve the dynamic interaction between solid bodies and viscous flow. CP10 While modelers are well equipped to deal with the end- Operator Splitting For Advection Diffusion Equa- member cases of predominantly liquid or solid systems, the tions with Discontinuous Coefficients intermediary regime remains challenging. We develop a new computational methodology for simulating solid-fluid We consider time dependent advection diffusion equations interactions based on distributed Lagrange multipliers and with discontinuous diffusion coefficient. Using an opera- apply our approach to investigate the competing effects of tor splitting methodology we develop a fictitious domain entrainment and sedimentation of crystals during magma method to numerically solve the time dependent diffusion cooling. equation. For the advection part we use a dispersion optimized nonstandard finite difference method that enables Jenny Suckale following the transport and tracking sharp fronts more ac- Massachusetts Institute of Technology curately. The problems addressed here are motivated by [email protected] applications combining the transport, growth and decay of biological/chemical species in heterogeneous landscapes. James Sethian University of California, Berkeley Vrushali A. Bokil Department of Mathematics Oregon State University [email protected] [email protected] Jiun-Der Yu CP10 Epson Research&Development Inc. [email protected] Direct Numerical Simulation of Inertial in Pourous Media Linda Elkins-Tanton At modest flow rates (Re > 100) through porous me- MIT dia and packed beds, fluid inertia can result in complex [email protected] steady and unsteady recirculation regions, dependent on the local pore geometry. As a result of fluid intertia, flow through porous media and packed beds can develop com- CP10 plex steady and unsteady recirculation regions at modest Simulation of Pore Scale Precipitation and Disso- flow rates (Re > 100). We investigate these inertial flow lution Using Adaptive, Finite Volume Methods regimes using (i) a body-fitted unstructured grid Navier- Stokes solver [Moin and Apte, AIAA J. 2006], and (ii) a Precipitation (or dissolution) of mineral grains modifies fictitious domain based finite-volume approach [Apte et al. the geometry of the pore space in subsurface sediment JCP 2009], wherein non-body conforming Cartesian grids with continuously evolving solid-liquid boundaries. In are used and the no-slip boundary conditions on the pore turn, changes in the pore space alter the groundwater flow boundaries are enforced implicitly through a rigidity con- through the sediment, which ultimately affects the contin- straint force. For the body-fitted unstructured grid ap- uum scale reaction rates that are relevant for field appli- proach, we present methods to parameterize and simplify cations such as carbon sequestration. Modeling provides a mesh generation for packed beds, with an eye toward ob- unique tool to understand and quantify the feedback pro- taining efficient mesh independence for Reynolds numbers cesses between mineral precipitation (or dissolution) and in the inertial and unsteady regimes. To handle the ge- flow at the pore scale. Higher-order algorithms based on ometric singularity at the sphere-sphere and sphere-wall adaptive mesh refinement and finite volume methods have contact points, we use a fillet bridge model, in which every been successfully applied to flow and reactive transport in pair of contacting entities are bridged by a fillet, eliminat- complex microscale geometries such as microarray chan- ing a small fluid region near the contact point. A second nels. Here, we couple a geochemical module that includes order accurate, parallel, incompressible flow solver is used aqueous complexation and mineral reactions to a new flow to simulate flow through three different sphere packings: and transport simulation capability based on adaptive, fi- a periodic simple cubic packing, a wall bounded hexag- nite volume methods. We have also extended this frame- onal close packing, and a randomly packed tube. Mesh work to track moving solid-fluid interfaces as a result of independence is assessed using several measures including mineral reactions. This approach is consistent with those Ergun pressure drop coefficients, viscous and pressure com- used for moving fluid-fluid interfaces, providing a robust ponents of drag force, kinetic energy, kinetic energy dissi- and algorithmically consistent methodology for multiphase pation and interstitial velocity profiles. Direct comparisons flow. We show that these advanced methods offer a promis- of the body-fitted and the fictitious domain approaches are ing alternative for reactive pore scale modeling through made to evaluate the accuracy of the latter approach for simulations of single pore throats as well as packed beds. simulation of flow through complex configurations observed David Trebotich, Sergi Molins, Carl Steefel in randomly packed beds. Lawrence Berkeley National Laboratory Sourabh V. Apte, Justin Finn [email protected], [email protected], [email protected] Oregon State University [email protected], fi[email protected] CP10 Title Not Available at Time of Publication CP10 Multiscale methods have received significant attention in Direct Numerical Simulations of Solid-Fluid Cou- recent years. Multiscale formulations, however, have not yet reached the robustness and applicability range nec- GS11 Abstracts 69

essary for general-purpose reservoir simulation practice. constraint on general computational grids with low-order Here, we address two aspects associated with highly het- finite elements. This is achieved by augmenting the un- erogeneous models that pose a serious challenge to existing derlying variational principle with appropriate constraints multiscale finite-volume formulations, namely, channel-like (which will be in the form of inequalities). The resulting features and strongly anisotropic transmissibility (tensor problem belongs to convex quadratic programming, which permeability, high aspect ratio). We describe a Two-stage is solved using active-set strategy. Representative numeri- Algebraic Multiscale Solver (TAMS) for the pressure linear cal examples are presented to show the overall performance system. One stage deals with a global coarse-grid prob- of these special shape functions, and their ability to re- lem, which is constructed using prolongation and restric- solve the heterogeneity of the medium using coarse com- tion operators. The prolongation operator is assembled putational grids. We also present numerical convergence from the multiscale basis functions. The restriction oper- studies of the proposed methodology with respect to re- ator is either the transpose (i.e., Galerkin coarsening), or finement of both coarse- and fine-scale meshes. This work a conservative scheme. The second stage uses a local pre- is in collaboration with Professor Albert Valocchi (UIUC) conditioner (e.g., Block Incomplete LU) on the fine-grid. and M. K. Mudunuru (Texas A&M University). TAMS is guaranteed to converge to the fine-grid solution with a computational cost superior to existing state-of-the- Kalyana Nakshatrala art approaches, such as Algebraic MultiGrid (AMG). Thus, Texas A&M University TAMS can be used as linear-solver for the pressure equa- [email protected] tion. TAMS also guarantees conservation after every iteration; so, TAMS can serve as an approximate pressure solver in a conventional simulator, where the results are CP11 used to perform transport computations. Reactive Transport Simulation with Embedded Discontinuity in Fractured Porous Media Hui Zhou Stanford Univ. Material discontinuities in fractured porous media strongly [email protected] influence single/multiphase fluid flow. When continuum methods are used to model transport across material interfaces, they smear out jump discontinuities of concentra- CP11 tion or saturation. To overcome this problem, we split the Multilevel Simulation and a-Posteriori Estimators finite-element models with complementary node-centred for Double-Porosity Models finite-volumes along the material interfaces, developing a transport scheme that represents the dependent variable Double porosity models are useful for modeling flow and discontinuities arising at these interfaces. We have found diffusion in highly heterogeneous media of binary charac- that using the discontinuous scheme is crucial to capture ter. The well-known Barenblatt and Warren-Root models the emerging patterns due to the interaction of heterogene- are actually asymptotic limits of models of tertiary struc- ity, and reactive transport. ture, and the latter can be seen as a special case of the former. We present numerical solutions on multilevel meshes Hamid M. Nick for these models and propose an appropriate a-posteriori Department of Earth Sciences - Geochemistry error estimator which is robust in the parameters and al- Utrecht University lows to compare the models. [email protected]

Viviane Klein Pierre Regnier Oregon State University Biogeochemical Modeling of the Earth System [email protected] Université Libre de Bruxelles [email protected] Malgorzata Peszynska Department of Mathematics Martin Thullner Oregon State University Department of Earth Sciences - Geochemistry [email protected] Utrecht University [email protected] CP11 Stephan K. Matthai Special Functions to Capture Spatial Heterogeneity Montan University of Leoben for Diffusion Equation with Decay Leoben, Austria In this talk we discuss on developing special shape func- [email protected] tions for diffusion with decay that capture underlying heterogeneity of the medium. We show that generating shape Florian Centler functions using homogeneous differential equation (which Department of Environmental Microbiology is the standard way of generating special functions un- Helmholtz Centre for Environmental Research - UFZ der the Multiscale Finite Element Method) will not sat- fl[email protected] isfy the partition of unity property for the chosen equation. Herein, we consider an alternate (non-homogeneous) boundary value problem for generating shape functions CP11 that ensures Kronecker-delta and partition of unity prop- Mixed Multiscale Basis Functions for Iterative Do- erties. In addition, if the medium is homogeneous, we remain Decomposition Procedures cover the standard shape functions for that particular finite element under the proposed method. Another novel We discuss the development of a multiscale method for feature of the proposed methodology is that the resulting the solution of the heterogeneous Poisson’s equation that solution satisfies maximum principles and the non-negative can take advantage of state-of-the-art CPU-GPU proces- 70 GS11 Abstracts

sors. We consider non-overlapping and overlapping do- ing order result in a coupled set of elliptic equations for main decomposition procedures for mixed finite element the unknown laminate spacing and the local pore pressure. discretizations of the elliptic equation with discontinuous Effective stress-strain relations are derived based on the lo- coefficients. Mixed multiscale basis functions with Robin- cal geometry and material properties of the laminates and type boundary conditions are proposed. Computational fluid. efficiency is achieved through a careful selection of sub- spaces of the space spanned by these basis functions for Burt S. Tilley,BVernescu approximating local problems. Mathematical Sciences Department Worcester Polytechnic Institute Alexandre Francisco [email protected], [email protected] Universidade Federal Fluminense [email protected]ff.br J. Plummer Civil and Environmental Eng. Dept. Victor E. Ginting Worcester Polytechnic Institute Department of Mathematics [email protected] University of Wyoming [email protected] CP12 Felipe Pereira Leveraging the General-Purpose Computation on Center for Fundamentals of Subsurface Flow Graphics Processing Units (gpgpu) Architecture University of Wyoming for Lidar Data Processing [email protected] Processing datasets associated with LiDAR mappings is prohibitive due to the large datasets and computational Joyce Rigelo nature of the processing. This is particularly problematic University of Wyoming when working to achieve interactive or real-time data ma- [email protected] nipulation. By leveraging GPGPUs and reevaluation of the computational algorithms used in the processing of large CP11 LiDAR datasets we are able to accelerate the datamining process. Our results reflect aspects of GPGPU environ- Effective Behavior of Flow and Transport Parame- ments that achieve significant speedups (and slowdowns) ters at Different Scales in Spatially Heterogeneous when ported to the GPGPU environment. Porous Media Without Scale Separation Paul Gray We investigate the effective behavior of hydraulic con- University of Northern Iowa ductivities and mixing coefficients in heterogeneous media Computer Science without scale separation. The covariance function of the [email protected] log hydraulic conductivity can be modeled by an algebraic function. The exponent of this power law is chosen that no finite integral length exists. Such functions can be written Dossay Oryspayev, Ramanathan Sugumaran as a superposition of Gaussian covariance functions with University of Northern Iowa finite correlation lengths. We give explicit expressions and [email protected], [email protected] coarse graining results for flow and transport parameters. Katharina Ross CP12 Institute of Geosciences A Comparison of Parallel Preconditioners for the University of Jena Mixed Finite Element Solution of Darcy’s Equation [email protected] Darcy flow in a heterogeneous medium can be accurately computed with mixed finite elements. Hybridization leads Sabine Attinger to a positive definite system, solved by an iterative method. Institute of Computational Computational The LifeV finite element library,developped by EPFL, EnvironmentaScience MOX and INRIA, relies on Trilinos for solving the lin- UFZ Leipzig ear system. Trilinos includes parallel iterative solvers, and [email protected] preconditioners based on one level Schwarz (IFPACK) and parallel multi-level methods (ML). We compare the effi- CP11 ciency and parallel scalability of these preconditioners for solving Darcy flow. On Flows Through Deformable Laminates Michel Kern Fluid flows through anisotropic media are found in a INRIA wide variety of geophysical and biological systems. The [email protected] macroscale behavior of these systems depend on the unknown microstructure, which depend on the local physical processes. As a first model, we consider the flow of an Alessio Fumagalli incompressible fluid that saturates an array of deformable MOX, Politecnico di Milano laminates with gravity acting in the spanwise direction. Italy The aspect ratio of the characteristic spacing between the [email protected] laminates is much smaller than the characteristic scale of the laminate length, and we use this aspect ratio to find CP12 effective equations for the components of the stress tensor of the effective material. Compatibility conditions at lead- Numerical Modeling of Flow Through Porous GS11 Abstracts 71

Structures and Vegetated Regions Universite Rennes 1 [email protected] Due to computational constraints, when modeling incompressible flow over and around porous structures or through heavily vegetated regions one must often use upscaling MS1 techniques to find parameterizations for resistance due to Large Eddy Simulation of Mixing in Stratified form drag. We analyze and perform theoretical and compu- Flows tational upscaling techniques for flows ranging from those with very small Reynolds numbers to those that are tur- Mixing is a challenging quantity to get right accurately, yet bulent through a variety of 2D and 3D domains. it is important for many oceanic processes and the general circulation. Performance of various eddy-viscosity and ap- Steven A. Mattis proximate deconvolution type subgrid-scale models (SGS) The Institute for Computational Engineering and Sciences in LES is evaluated in the lock-exchange problem, which University of Texas at Austin contains shear-driven mixing, internal waves, interactions [email protected] with boundaries and convective motions, while having a simple domain, initial and boundary conditions, and forc- Clint Dawson ing. The measure of the comparison taken as the back- Institute for Computational Engineering and Sciences ground potential energy and DNS results at 103 ≤ Re ≤ University of Texas at Austin 104 are used as benchmarks. By relying on the best- [email protected] performing SGS models, estimates of mixing at higher Re are provided. Chris Kees U.S. Army Engineer Research and Development Center Tamay Ozgokmen Coastal and Hydraulics Laboratory University of Miami/RSMAS [email protected] [email protected]

Matthew Farthing Traian Iliescu US Army Engineer Research and Development Centerq Interdisciplinary Center for Applied Mathematics [email protected] [email protected]

Paul F. Fischer CP12 University of California, Irvine and From a Coarse-Scale Flow Model to Fine-Scale Per- Weizmann Institute of Science, Israel meability Identification fi[email protected] We apply an inverse modeling approach to determine fine- scale permeabilities based on heads - flow rates pairs com- MS1 puted on the level of a coarse-scale model. This fits into A New Projection Method for Separating Surface a downscaling framework if we assume that coarse scale and Interior Modes in Oceanic Data permeabilities are actually determined within an upscaling scheme. In our approach a double constraint method A number of recent studies have demonstrated that al- is used, based on finite element discrete approximations. timetric observations of the ocean’s mesoscale eddy field The results obtained apply to models with anisotropy ef- reflect the combined influence of both surface buoyancy fects. anomalies and interior potential vorticity anomalies. The former are associated with surface-trapped modes, with Anna Trykozko an exponentially-decaying vertical structure, and the lat- University of Warsaw ter with the standard baroclinic modes, the oscillating [email protected] eigenfunctions of the quasigeostrophic potential vorticity stretching operator. In order to assess the relative importance of the two contributions to the signal, one MS1 wouldliketoprojecttheobservedfieldontoasetof On a LES-deconvolution Model for the Ocean with complete modes that separates the influence of each as- aFixedWind pect of the dynamics in a natural way. However, because the surface-trapped solutions are dependent on horizon- Kolmogorov’s theory predicts that simulating turbulent 9/4 tal wavenumber, they are not, in general, orthogonal to flows by using the Navier-Stokes Equations requires R the (wavenumber-independent) interior baroclinic modes, degrees of freedom, where R is the Reynolds number.This thus any combined projection will contain energetic over- number is too large to perform a Direct Numerical Simu- laps. Here we propose a generalization of potential vor- lation. This is why one aims at computing mean values of ticity that includes surface buoyancy anomalies (akin to the flows field. The case that we study is an oceanic basin Bretherton’s generalized form, but without the use of nu- with a fixed wind. We consider means obtained by convo- merically ill-defined delta-functions), and compute its ver- lutions like in usual Large Eddy Simulation models. We tical eigenfunctions for each horizontal wavenumber. These introduce the concept of deconvolution model that aims eigenfunctions provide a set of mutually-orthogonal modes at reconstructing the true flow field by regenerating high that reflect surface and interior components naturally. We frequency wave numbers when the numerical mesh has a compute these modes for a given stratification, and demon- fixed size. We summerize some mathematical results and strate their use by projecting out the energy of a set of finally show numerical simulations in an oceanic basin with high-resolution, eddying simulations. a given fixed wind, using the deconvolution concept. Shafer Smith Roger Lewandowski Center for Atmosphere Ocean Science IRMAR, UMR 6625 Courant Institute 72 GS11 Abstracts

[email protected] Andrew Majda Courant Institute NYU Jacques Vanneste [email protected] School of Mathematics University of Edinburgh [email protected] MS2 Stochastic Models for Tropical Convection: From Idealized Conceptual Models to GCM Simulations MS1 Suitable Boundary Conditions for the Shallow Wa- Large scale models that are used for longterm weather ter Equations in a Limited Domain. forecastandclimatepredictionarebasedonacoarsedis- cretization of the governing equations with a grid spacing In this lecture we will discuss two issues of general interest varying from 50 km to 200 km. For a such complex sys- in scientific computing, namely: - Numerical simulations tem –the Earth-ocean-atmosphere system, many important in a limited domain when the boundary conditions are not processes such clouds, radiation, air sea interaction, vege- well defined at the boundary, and, - The use of multilevel tation, and boundary layer turbulence, remain unresolved; methods for solving partial differential equations. Both they are represented by various recipes known as param- problems will be discussed in the context of the inviscid terizations. However, most of these parametrizations such shallow water equations. as those pertaining to clouds and atmospheric convection are based on equilibrium closures that are hardly tested Roger M. Temam and in most cases underestimate the dynamics due to very Inst. f. Scientific Comput. and Appl. Math. intermittent local interactions at small scales. In this talk Indiana University we will discuss a hierarchy of stochastic models that rep- [email protected] resent various unresolved physical processes, and their effect on the large-scale resolved variables, ranging from con- Arthur Bousquet, Ming-Cheng Shiue vective inhibition, using an Ising-type spin flip model, to Indiana University multi-state Markov chains for organized tropical convec- [email protected], [email protected] tion consisting of three cloud types, congestus, deep, and stratiform. The models are first test on simple toy models where their intrinsic features are explored and their pa- MS2 rameters calibrated then more recently implemented in the An Asymptotic Description of the Interaction context of more comprehensive atmospheric general cir- fo Waves on the ITCZ with Midlatitude Quasi- culation models that are used for operational long term geostrophic Dynamics weather and climate predictions.

In a ground breaking paper, Majda & Klein introduced Boualem Khouider two new dynamical regimes describing the tropical tropo- University of Victoria sphere. The first regime, IPESD provides a framework for Department of Mathematics the recent multiscale models of the Madden-Julian oscil- [email protected] lation. The second regime, the mesoscale equatorial weak temperature gradient (MEWTG), describes a circulation forced by latent heating due to moist convection. The MS2 weak temperature gradient feature of this regime implies A Potential Vorticity Dynamics for Rotating Shal- that diabatic heating balances vertical velocity on equa- low Water on the Sphere torial mesoscales, O(500km), and within timescales of less than one day. Majda recognized that this new multiscale The evolution of weather systems in the midlatitude at- MEWTG is a closed model by going to higher order in mosphere is well-explained by the theory of quasigeostro- the asymptotics. The resulting model contains the origi- phy (QG), in which slow, synoptic-scale airflows are de- nal MEWTG equations modulated by a large scale, zon- scribed through the advection of potential vorticity (PV). ally propagating gravity wave. The temperature and wind The mathematics of QG is often justified by a limit of small properties of the large scale wave are independent of both Rossby number. However, this assumed limit is made in- the zonal and meridional mesoscales and are, thereby, con- valid across the equator by the vanishing of the Coriolis sistent with the weak temperature gradient nature of the effects. A globally-valid analog of QG (sPV), that is based tropics. The mean zonal winds described by the multiscale upon the dynamics of PV, is developed for rotating shal- MEWTG equations become unbounded at large latitudes low water on the sphere. Specifically, a PV-streamfunction away from the equatorial belt. Unless specific restrictions relationship is defined which determines the flow velocities are made on the mean of the diabatic heating, the the- for the entire sphere. At midlatitudes, the fluid dynam- ory also yields solutions with non-zero meridional velocities ics are asymptotically equivalent to the beta-plane theory far from the equatorial belt; i.e. an open Hadley circula- of QG, in the usual small Rossby number sense. In the tion. Furthermore, meridional geostrophic balance is not equatorial regions, wave propagation at short-scales mim- described by this theory, yet this is known to be the main ics the dispersion relation for equatorial beta waves. Global balance for subtropical and midlatitude winds. We derive Rossby waves, as described in recent works by Verkley matching condition to the subtropics which closes the mul- (2007) and Schubert (2008), are also included within the tiscale MEWTG theory and connects the equatorial flows sPV framework. As a benchmark test of the dynamics, the with midlatitude dynamics. propagation of waves in the sPV model are shown to be an excellent approximation to computations of the equa- Joseph A. Biello torial crossing of topographic waves by Grose & Hoskins University of California, Davis (1979). Despite that this sPV model is not obtained in the Department of Mathematics usual manner of small Rossby number asymptotic analysis, [email protected] the propagation of mesoscale waves across the equatorial region retains QG-like accuracy. The mathematical con- GS11 Abstracts 73

sistency of these sPV dynamics with the rotating shallow in Oregon. Finally, Gaussian beam migration of seismic water primitive equations is demonstrated from the per- data from the recent Hi-CLIMB experiment in Tibet is spective of ray theory. Extensions to baroclinic instability used to image the Tibetan lithosphere. The results from and the possibility of PV coupling to Kelvin waves are dis- Gaussian beam imaging are found to compare favorably cussed. with imaging results obtained using ray/Born inversion.

David J. Muraki Robert Nowack Department of Mathematics Purdue University Simon Fraser University [email protected] [email protected] MS3 MS2 Gaussian Beam Methods A Simple Model for Atmospheric Circulations Driven by Convection Gaussian beams and their superpositions are approximate high frequency solutions to linear hyperbolic PDEs. In this This talk proposes a mathematical theory explaining the talk, I will give a brief review of Gaussian beams and their sharp transition between tropics and extra-tropics in terms superpositions and discuss some of the mathematical tools of the diurnal cycle of thermal forcing by the sun. This that are necessary to prove that they are valid asymptotic transition, at a latitude of 30 degrees, coincides with the solutions. From a simulation point of view, I will address outer edge of the Hadley cells, and is marked by a steep the question of how to decompose high frequency initial jump in the height of the troposphere, from around fifteen and boundary data into a superposition of Gaussian beams. kilometers in the tropics to about nine in the mid and high latitudes. The tropics, equatorwards of 30 degrees, are characterized by easterly surface winds -the Trades- and a Nicolay Tanushev strong diurnal signal in the wind, pressure and tempera- Department of Mathematics ture, often marked by regular daily storms in the rainy sea- The University of Texas at Austin son. Polewards of 30 degrees, the winds are westerly, and [email protected] the weather systems have longer spatio-temporal scales. This change of behavior can be explained in terms of diurnal waves, created by thermal forcing and trapped equa- MS3 torwards of 30 degrees by the Coriolis effect [?]. These The Basics of Constructing Frames Entirely out of waves organize the convective activity, leading to more ac- Complex Gaussians and Applications to the Wave tive mixing and vertical transport in the tropics. This can Equation be illustrated in simple mathematical models, presently We focus on the construction of a frame of complex Gaus- ranging from forced linear oscillators to nonlinear conserva- L2 Rn tion laws with entraining shock waves, accounting for the sians for the space of ( ) functions. When propa- entrainment into the troposphere of air from the surface gated along bicharacteristics for the wave equation, the boundary layer. frame can be used to build a parametrix with suitable error terms. When the coefficients of the wave equation have Esteban G. Tabak more regularity, propagated frame functions become Gaus- Courant Institute sian beams. This work is theoretical in nature and relates New York Universityb to the errors in Gaussian beam solutions. [email protected] Alden Waters UCLA MS3 [email protected] Seismic Imaging of Teleseismic Waves using Gaus- sian Beams MS3 The earthquake seismology community now regularly uses Frozen Gaussian Approximation for High Fre- seismic waves from distant sources to illuminate structures quency Wave Propagation beneath seismic arrays in so-called passive imaging experiments. Similarly, oil reservoirs for petroleum applications The frozen Gaussian approximation provides a highly effi- can be imaged with seismic waves incident from below cient computational method for high frequency wave prop- using sources in boreholes. Gaussian beams can be ap- agation. It makes use of fixed-width Gaussian functions pliedforpassiveimagingbasedonanover-completeframe- on phase plane to approximate the solution. The moti- based Gaussian beam representation of the seismic wave- vation comes from Herman-Kluk propagator developed in field. Paraxial Gaussian beams are then utilized for the chemistry literature. The method works in both scenario propagation of the seismic waves back into the medium. of caustics and spreading. Lagrangian and Eulerian algo- The approach provides stable imaging of seismic data in rithms will be introduced in this talk. Rigorous analysis smoothly varying background media where caustics and result on the convergence of this method will be also pre- triplicated arrivals can exist. Gaussian beam imaging is sented. found to be very flexible with respect to different experi- Xu Yang,JianfengLu mental geometries and can be configured to allow for dif- Courant Institute of Mathematical Sciences ferent types of converted or reflected waves. A synthetic New York University example is first given for a collisional zone structure with [email protected], [email protected] an incident P-wave from below where several different scattered wave types are used to image the structure. Seismic data from the 1993 Cascadia experiment are then used to MS4 image the subduction zone beneath the Pacific Northwest Hybrid Simulations of Reactive Transport in 74 GS11 Abstracts

Porous Media HTMC coupling will be presented. Using Monte Carlo simulations, we present the impact of parameter uncertainties Darcy-scale models of flow and transport in porous media of the geological characterization on the response of the often fail to describe experimentally observed phenomena, HTMC model. while their pore-scale counterparts are accurate but can be computationally prohibitive. Most numerical multi-scale Souheil M. Ezzedine models, which seek to combine these two descriptions, re- LLNL quire empirical closures and/or assumptions on the behav- [email protected] ior of pore-scale quantities at the continuum (Darcy) scale. We present a general formulation of an iterative hybrid numerical method that links these two scales without re- MS4 sorting to such approximations. The algorithm treats the Hydromechanical Simulation of Triggered Earth- fluxes exchanged at the internal boundaries between the quakes and Mine Dewatering pore- and continuum-scale domains as unknown, and allows for iteratively determined boundary conditions to be Two hydromechanical simulations are presented. (1) In applied at the pore-scale in order to guarantee their con- south Iceland two magnitude Ms 6.6 earthquakes in June tinuity. While the algorithm proposed is general, we use 2000 were separated by an 81-hour time delay and 18-km it to model Taylor dispersion in a fracture with chemically distance. The models test the hypothesis that the pairing reactive walls. Results show significant improvement upon is the result of a two-step triggering process. (2) In the standard continuum-scale formulations. former Homestake gold mine in Lead, S.D., smulations were able to explain the co-existence of shallow and deep flow Ilenia Battiato systems, which are characterized by significantly different Max Planck Institute for Dynamics and Self-Organization hydromechanical properties. [email protected] Herbert Wang Daniel M. Tartakovsky University of Wisconsin University of California, San Diego [email protected] [email protected] K. L. Feigl, T Ali Alexandre Tartakovsky U. of Wisconsin-Madison Pacific Northwest National Laboratory [email protected], [email protected] [email protected] L.C. Murdoch Clemson Univ MS4 [email protected] Influence of THMC Couplings on Thermal Recov- ery from EGS Systems MS5 We explore the evolution of thermal output from EGS Adaptive Pattern Research for Parallel Block Ap- reservoirs where coupled THMC effects influence the evolu- proximate Inverses tion of permeability structure and respond to the presence of heterogeneity at a variety of length-scales. Heterogene- An adaptive algorithm is presented to generate automat- ity results from the presence and initial length, orientation ically the non-zero pattern of the Block FSAI (BFSAI) and strength of fractures present within the reservoir and preconditioner. It is demonstrated that in SPD problems the response is exacerbated by the strong coupling between BFSAI minimizes an upper bound of the Kaporin number THMC processes. of the preconditioned matrix. The mathematical structure of this bound suggests an efficient parallel strategy to im- Joshua Taron prove a given non-zero pattern of BFSAI, providing a novel UFZ Adaptive BFSAI (ABF) preconditioner. Numerical exper- [email protected] iments performed on large FE matrices provide evidence of ABF effectiveness. Derek Elsworth Penn State University Carlo Janna [email protected] DMMMSA - University of Padova [email protected] Ghazal Izadi, Baisheng Zheng Energy and Mineral Engineering Massimiliano Ferronato Penn State University University of Padova [email protected], [email protected] DMMMSA [email protected]

MS4 MS5 Uncertainty Quantification in Stochastic Discrete Fracture Network THMC Model Block Preconditioners for Fully Implicit Atmo- spheric Climate Simulations Fractures and fracture networks are the principle pathways for migration of water and heat in enhanced geothermal We discuss the development of block preconditioners in systems, oil and gas reservoirs migration, carbon diox- an effort to reduce computational costs associated with ide leakage from carbon sequestration field, and radioac- fully implicit time integration of atmospheric climate mod- tive and toxic industrial wastes from underground storage els within CAM-HOMME. We construct a fully implicit repositories. A stochastic discrete fracture network and a framework based on the shallow water equations and view GS11 Abstracts 75

the subsidiary linear system as a block matrix. Formal LU duce flow within the framework of hybrid mixture. decomposition is performed and block preconditioners are derived based on approximations to the upper triangular Lynn S. Bennethum block. University of Colorado Denver [email protected] P. Aaron Lott Lawrence Livermore National Laboratory [email protected] MS6 A Two-Scale Computational Model of pH-Sensitive Swelling Porous Media MS5 Preconditioning for Flow and for Flow Control In this talk we present the pore-scale modeling of a porous medium composed of electrically charged macromolecules I will describe some solution techniques for flow compu- saturated by an electrolyte solution with four ionic mono- tations and for optimization problems for the control of valent species (Na+,CL-,H+,OH-). Ion exchange reactions flows. In particular, I will describe preconditioned iterative give rise to a pH-dependent surface charge which is mod- solution methods for incompressible viscous flow (Stokes eled by a nonlinear Neumann boundary condition for the and Navier-Stokes problems) and for problems of PDE- Poisson-Boltzmann governing the local electric potential. constrained optimization where incompressible flow equa- By coupling the governing equations in the fluid domain tions provide the constraints. These approaches are appli- with the elasticity problem for the solid particles the ho- cable to finite element and other discretization methods. mogenization procedure is applied to upscale the model to the macroscale. Among the homogenized results a new Andrew J Wathen constituive law is derived for the disjoining pressure de- Oxford University pendent on pH. Numerical simulations of a free swelling Numerical Analysis Group experiment are performed and results compared with ex- [email protected] perimental observations. Marcio A. Murad MS5 National Laboratory of Scientific Computation An Accelerated Fixed-Point Iteration for Solution LNCC/MCT of Variably Saturated Flow [email protected]

We investigate effectiveness of an acceleration method ap- Ranena Ponce plied to the modified Picard iteration for simulations of Dept Engineering Mechanics PUC/RJ variably saturated flow. We solve nonlinear systems using [email protected] both unaccelerated and accelerated modified Picard iteration as well as Newton’s method. Since Picard iterations can be slow to converge, the advantage of acceleration is to Sidarta Lima provide faster convergence while maintaining advantages of Federal University Rural of Rio de the Picard method over the Newton method. Results indi- Janeiro cate that the accelerated method provides a robust solver [email protected] with significant potential computational advantages. Homer F. Walker MS6 Worcester Polytechnic Institute The Impact of Pore Deformation on Sorption and [email protected] Capillary Condensation in Mesoporous Solids We report recent theoretical developments in the study of Carol S. Woodward gas-liquid transitions of fluids confined to deformable meso- Lawrence Livermore National Laboratory porous materials. Due to a synergistic coupling the phase Center for Applied Scientific Computing behavior of the confined soft matter phase is significantly [email protected] affected by the deformation of the confining material which in turn is deformed as a result of phase changes occur- Ulrike Yang ring in the confined phase. If the confined fluid is gas-like Lawrence Livermore National Laboratory its wetting characteristics affect the deformation isotherm [email protected] such that the pore may expand or contract as more gas is adsorbed prior to capillary condensation. Directly at capillary condensation the pore abruptly shrinks on account MS6 of fluid-substrate attraction. If the density of the confined Macroscale Potentials for Charged Swelling Porous liquid-like phase is then enhanced further the pore expands Media again. This expansion allows one to determine nanome- chanical properties of the confining solid directly from the In this talk we discuss the macroscopic potentials that deformation isotherm. In the future it might be possible induce bulk fluid flow or diffusive flow through swelling to fabricate sensors that allow one to measure mechani- porous materials. Swelling porous media such as expan- cally changes in thermodynamic properties of confined soft sive soils, food stuff, biotissue, and swelling polymers have matter phases. complex microstructure such as a possibly charged solid surface and a large liquid-solid interface causing the solid Martin Schoen and liquid to be highly interactive. Here we discuss the Stranski Laboratorium fur Physikalische und Theor. macroscopic pressures and chemical potentials that pro- Chemie Technische Universitat Berlin martin.schoen@fluids.tu-berlin.de 76 GS11 Abstracts

MS6 Technische Universiteit Eindhoven, Netherlands Food Engineering Applications of Continuum Me- [email protected] chanics During fluid transport processes such as drying, sorption MS7 and frying, physical and chemical changes take place in the Upscaling of Adsorptive Transport Under Unsatu- food biopolymers. Hybrid mixture theory based multiscale rated Condition equations were developed that allow incorporating these changes into transport models. Multiscale transport and In general, solute transport mechanisms under saturated thermomechanical equations were solved to predict fluid conditions have been studied in detail. However, under un- transport (vapor, water, oil) and viscoelastic stresses in saturated conditions, these mechanisms need to be under- foods. Comparisons were made to the macro and micro- stood in greater detail. In such cases, dispersion coefficient scale experiments. The optimized operating parameters varies with Darcy velocity and saturation, and principal in- resulting in improved food quality were obtained. teractions usually occur at the solid-water interfaces (SWI) and air-water interfaces (AWI), thus greatly influenced by Pawan S. Takhar water content. In this study, we have investigated upscal- Animal and Food Sciences ing of adsorptive transport process under unsaturated con- Texas Tech University ditions. [email protected] Amir Raoof University of Utrecht, Netherlands MS7 [email protected] Upscaling Kinetics and Geometrical Heterogeneity for Flow and Transport Models Majid Hassanizadeh University of Utrecht The transport of dissolved species in porous media is a [email protected] major concern for the environment, for waste storage management, agriculture or carboxyde underground storage. Anomalous diffusion is frequently observed within the con- MS7 text of natural porous media, especially in the under- Upscaling in-situ Combustion Processes for Heavy ground. We aim to focus on different meanings of the word Oil Recovery When Kinetics and Phase Behavior ”anomalous”. We revisit the classical problem of disper- Wreak Havoc sion of a point discharge of tracer in laminar pipe Poiseuille flow. For Péclet numbers corresponding to Taylor’s disper- In-situ combustion is an attractive enhanced recovery sion regime, we derive rigorously an effective model for the method for heavy oil reservoirs: a small fraction of the oil enhanced diffusion. It is justified by error estimates. We is burned in-situ, which creates a steam drive and mobilizes explicit the retardation and memory effects of the adsorp- the oil. Traditional reservoir simulators are not capable of tion/desorption reactions on the dispersive characteristics resolving the thin reaction fronts, because these are orders and show their importance. The chemistry influences di- of magnitude smaller than the typical reservoir scale. In- rectly the characteristic diffusion width and the effective stead, we propose an upscaled model that effectively rep- convection. Then we show how tracer dispersion can be resents the heat generation and combustion products at divided into three regimes. For small times, diffusion dom- realistic grid cell sizes. inates advection yielding a symmetric Gaussian dispersion cloud. At large times, the flow is in the Taylor regime. M Gerritsen However, in an intermediate regime, the longitudinal diffu- Stanford sion is anomalous. We emphasize that the previous effect [email protected] is completely different from the nonfickian effects often observed before the diffusive asymptotic. An example involv- Zhouyuan Zhu, Alexandre Lapene ing fractional derivatives is rigorously constructed through Energy Resources Engineering, Stanford. random walks. [email protected], [email protected]

Catherine Choquet University of Marseille MS8 [email protected] Reduced-Order Models for Boussinesq Flows

We consider POD-Galerkin models for Boussinesq flows. MS7 Reduced-bases are computed by post-processing multiple Upscaling of Reactive Flows Involving Free Bound- CFD simulations computed using different boundary con- aries dition inputs. The resulting model allows for time-varying boundary conditions and seeks to accurately predict the We consider the transport of solute particles in a reac- temperature in a comfort zone in a thermally stratified tive flow under dominant transport conditions for the vari- room. These models are developed to model thermal trans- able geometry in the case of a thin strip. We derive the port in buildings and design the control systems (con- upscaled model(1-D) from the 2-D model using perturba- trollers as well as sensor/actuator placement). tion methods and compare the 1-D model with direct 2-D computations numerically. Further, we use rigorous ho- Jeff Borggaard mogenization techniques for a specific choice of reaction Virginia Tech rate, namely crystal precipitation and dissolution in peri- Department of Mathematics odic porous medium (fixed geometry case). [email protected]

Kundan Kumar GS11 Abstracts 77

MS8 Mihai Anitescu New Methods for Estimating Poleward Eddy Heat Argonne National Laboratory Transport using Satellite Altimetry Mathematics and Computer Science Division [email protected] Current-generation altimetry products are too coarse to resolve most of the turbulent spectrum of the ocean and drastically underestimate eddy fluxes such as the poleward MS9 heat transport. We show that, by extracting aliased high- Data Assimilation System Diagnosis and Tuning of wavenumber information from the low-wavenumber band, Error Covariance Parameters one can derive “superresolved’ velocity fields from sparse satellite observations. When used in combination with an The specification of accurate statistical information on the adaptive stochastic model for the unresolved scales, these errors in the prior state estimate and observational data techniques produce significantly better estimates of pole- is unanimously recognized as a major practical difficulty ward eddy heat transport. in geophysical data assimilation. A mathematical formalism to adjoint sensitivity analysis for diagnostics and tun- Shane R. Keating ing of the error covariance input parameters is provided in New York University the context of variational data assimilation. Applications Courant Institute of Mathematical Sciences to atmospheric modeling are presented from the proof-of- [email protected] concept stage to the current status of implementation at numerical weather prediction centers.

MS8 Dacian N. Daescu The Two-dimensional Boussinesq System - Analyt- Portland State University ical and Computational Study Department of Mathematics and Statistics [email protected] Abstract not available at time of publication. Adam Larios MS9 Department of Mathematics Computational Performance of a Parallel Matrix- UC Irvine free Implementation of the Ensemble Kalman Fil- [email protected] ter The Ensemble Kalman Filter (EnKF) has become an im- MS8 portant data assimilation tool for numerical models in geo- Poisson Solvers in Thin Domains sciences. For large data sets a potential bottleneck in EnKF is the computation of the Kalman gain matrix. In Abstract not available at time of publication. this talk we discuss a matrix-free parallel implementation of EnKF where the form of the matrices is exploited using Alberto Scotti a Sherman-Morrison-Woodbury inversion algorithm. This UNC Chapel Hill approach scales linearly with the number of observations. [email protected] Performance results with a shallow-water model are presented.

MS9 Humberto C. Godinez,DavidMoulton Quantifying Uncertainty in Wind Power Predic- Los Alamos National Laboratory tions for Stochastic Unit Commitment Optimiza- Applied Mathematics and Plasma Physics tion [email protected], [email protected] We discuss uncertainty quantification in wind power forecasts using numerical weather prediction (NWP) models MS9 with applications in proactive management of energy sys- Comparison of Ensemble Data Assimilation Meth- tems. Weather is one of the major drivers of energy gen- ods in the Presence of a Nonlinear Observation Op- eration and consumption, especially with the adoption of erator such renewable resources as wind. Our strategy consists in using numerical dynamical models to forecast ambient con- A new comparison of three frequently used sequential ditions and propagate uncertainties from initial conditions data assimilation methods illuminating their strengths and to produce accurate confidence intervals. We analyze the weaknesses in presence of linear and nonlinear observa- impact of assimilating satellite radiance in our forecasts. tion operators is presented. The ensemble Kalman filter We present an integrative unit commitment or energy sys- (EnKF), the particle filter (PF) and the Maximum Likeli- tem scheduling problem that uses weather forecasts with hood Ensemble Filter (MLEF) methods were implemented uncertainty, and validate our results using real observa- and spectral shallow water equations model in spherical ge- tions. ometry model was employed using Rossby-Haurwitz Wave no 4 as initial conditions. Numerical tests reveal that all Emil M. Constantinescu three methods perform satisfactory for linear observation Argonne National Laboratory operator 15 days model integration, whereas EnKF, with Mathematics and Computer Science Division the nonlinear observation operator failed. The particle fil- [email protected] ter and the hybrid filter (MLEF) both performed satisfac- torily with highly nonlinear observation operators . Victor Zavala Argonne National Laboratory Milija Zupanski [email protected] Cooperative Institute for Research in the Atmosphere Colorado State University 78 GS11 Abstracts

[email protected] eikonal equation iteratively. The initial prior may come from the Gaussian beam approximation computed by dy- IonelM.Navon namic ray tracing. The result embraces complete details Florida State University of the velocity model and therefore can help enhancing ac- Department of Scientific Computing curacy of Gaussian-beam migration and other applications [email protected] of Gaussian beams in seismology. Siwei Li, Sergey Fomel Mohamed Jardak University of Texas at Austin CSIT, Florida State University [email protected], [email protected] [email protected] Alexander Vladimirsky MS10 Dept. of Mathematics Amplitude Calculations for 3-D Gaussian Beam Cornell University Migration using Complex-valued Traveltimes [email protected] The use of Gaussian beams to represent Green’s functions in 3-D Kirchhoff migration algorithms adds four additional MS10 integrals to the processing. Ross Hill reduced the four inte- Recovery of High Frequency Wave Fields grals to two via the method of steepest descent for integrals with complex exponents. He presented the travel time ad- Gaussian beams are asymptotically valid high frequency justment, but not the amplitude adjustment necessary for solutions to hyperbolic partial differential equations, con- a “true amplitude’ approximation in the Kirchhoff sense. centrated on a single curve through the physical domain. We provide that adjustment here, using a recently devel- They can also be extended to some dispersive wave equa- oped iterated method of steepest descent. tions, such as the Schroedinger equation. Superpositions of Gaussian beams provide a powerful tool to generate more Norman Bleistein general high frequency solutions that are not necessarily Colorado School of Mines concentrated on a single curve. We are concerned with [email protected] the accuracy of Gaussian beam superpositions in terms of the wavelength, which was thought a rather difficult prob- Samuel H. Gray lem decades ago. We present a systematic construction CGGVeritas of Gaussian beam superpositions for all strictly hyperbolic Calgary, Canada and Schroedinger equations subject to highly oscillatory [email protected] initial data, and obtain the optimal error estimates in the appropriate norm dictated by the well-posedness estimate. The obtained results are valid for any number of spatial MS10 dimensions and are unaffected by the presence of caustics. Seismic Imaging with Gaussian Wave Packets This talk presents key ideas and techniques involved in this newly developed recovery theory of high frequency wave Fast algorithm for a reverse-time migration of seismic data fields, with materials drawn from recent works with J. Ral- can be designed using a flow-out of Gaussian wave packets ston (UCLA), and with N. Tanushev (UT-Austin) and O. (GWPs). It consist of three main steps: data decompo- Runborg (KTH). sition into GWPs; their flow-out into subsurface; imaging condition (cross-correlation of ’source’ and ’receiver’ fields). Hailiang Liu We achieve sparse data representation with GWPs us- Iowa State University ing iterative non-linear algorithm based on l1-optimization USA ideas. Rigid GWP flow-out along rays is used for down- [email protected] ward data continuation. Analytic formulas can be used for cross-correlating GWPs after their flow-out (fast im- MS11 plementation of the imaging condition). Multilevel Model Reduction Approaches for Flows Anton A. Duchkov in Multiscale Porous Media IPGG [email protected] In this talk, I will describe multilevel multiscale methods for flows in highly heterogeneous media with high contrast. In particular, I will describe multilevel construction of basis Fredrik Andersson functions and how they can be used in preconditioning of Lund University flow equations. [email protected] Juan Galvis Texas AM MS10 [email protected] Improving Wave-equation Fidelity of Gaussian Beams by Solving the Complex Eikonal Equation MS11 Gaussian beams are a well-known wavefield approximation. A Data-driven Stochastic Multiscale Method for A more accurate representation can be obtained by solving Model Reduction and Uncertainty Quantification the complex eikonal equation. We propose a constructive algorithm for solving the complex eikonal equation. By We introduce a data-driven stochastic multiscale method re-writing the complex traveltime as background real and to solve stochastic PDEs. One important feature of this imaginary parts and their respective perturbations, we ar- methods is to construct a multiscale stochastic basis from rive at an update scheme that aims at solving the complex GS11 Abstracts 79

limited samples of the stochastic solutions obtained by wise conservative velocity fields and accurate prediction of Monte Carlo methods. This multiscale method effectively sharp temperature convective fronts. reduces the dimensionality of the stochastic PDEs. As a consequence, we reduce the high dimensional stochastic Nicola Castelletto problem to a relatively small number of coupled determin- DMMMSA istic PDEs. Some numerical results will be presented to University of Padova demonstrate the effectiveness of the method. [email protected]

Thomas Hou Massimiliano Ferronato, Giuseppe Gambolati Applied Mathematics University of Padova California Technology Institute DMMMSA [email protected] [email protected], [email protected]

MS11 MS12 Use of Reduced-order Models for Improved Data Coupled Poromechanics of Faulted Reservoirs Assimilation within an EnKF Context The coupling between pore pressure and mechanical de- Reduced order modeling using trajectory piecewise lin- formation is essential to understand the initiation of fault earization (TPWL) has been shown to achieve dramatic slip and the evolution of fault hydraulic properties. This (2-3 order of magnitude) speedup for production optimiza- coupling is likely a critical determinant of when and where tion problems. In this work, we extend TPWL methodol- earthquakes are triggered, but the mechanisms controlling ogy to history matching problems. The TPWL represen- the influence of the pore pressure field on the onset of slip tation is then incorporated into an Ensemble Kalman Fil- are currently poorly understood. Here, we present a cou- ter (EnKF) method. TPWL and EnKF combine well, as pled model of flow and mechanics of faulted geologic reser- the EnKF ensemble provides a reasonably large and varied voirs. Faults are represented as 2D entities embedded in training set for TPWL. Further, because of the sequential a 3D domain, which exhibit irreversible behavior in their nature of EnKF, where forecasting is performed over short friction and dilatancy poromechanical response. We em- time periods, the use of linearized models is reasonable. ploy an unconditionally-stable iteratively coupled scheme The performance of the new methodology on 2D and 3D to solve the coupled flow-mechanics equations, which we example cases is demonstrated. implement in an open source tectonic deformation simulator. Pallav Sarma Chevron Energy Technology Company Birendra Jha San Ramon CA MIT [email protected] Civil and Environmental Engineering [email protected] MS11 Bradford Hager Toward Effective Multiscale Parameterization of MIT Reservoir Models Earth, Atmospheric and Planetary Sciences A survey of emerging approaches toward reliable reservoir [email protected] performance Uncertainty quantification and history matching often require a large number of reservoir simulations Ruben Juanes that is often infeasible in practice. At the core of the chal- MIT lenge is the curse of dimensionality. In this talk, we ex- Civil and Environmental Engineering amine the premises of the existing modeling approach and [email protected] review recent advances in reservoir characterization, geologic modeling, and understanding of impact of geologic features on fluid flow. These advances point to potential MS12 ways of effective, multiscale parametrization of reservoir Coupling Geomechanics and Multiphase Flow in models. Porous Media

Xiao-Hui Wu We discuss Biot models that treat the coupling of mul- ExxonMobil Upstream Research Company tiphase flow and elasticity in different subdomains. Ex- [email protected] tensions that include compositional flow are also considered. Here we employ locally conservative algorithms such as mixed finite element methods for flow and Galerkin for MS12 mechanics. Theoretical error estimates for certain model Thermo-hydro-mechanical Modeling in Porous Me- problems will be given as well as computational results. dia: A Coupled Mixed and Galerkin Finite Element Formulation Mary F. Wheeler Center for Subsurface Modeling The efficient solution to the coupled system of PDEs gov- University of Texas at Austin erning the mass and the energy balance in deformable [email protected] porous media requires advanced numerical algorithms. A combination of Mixed and Galerkin Finite Elements along with a staggered method are employed, addressing iter- MS12 atively flow-deformation by a coupled approach and heat Scalable Newton-Krylov Solvers for Coupled Hy- transport via a splitting technique, at each time step. Such formulation warrants stable numerical solutions, element- 80 GS11 Abstracts

dromechanical Systems University of Padova DMMMSA In this work, we consider efficient solution methods for [email protected] mixed finite element models of fluid flow through deformable porous media. In many geotechnical and geo- Carlo Janna physical applications, the behavior of a solid/fluid mixture DMMMSA - University of Padova is highly-nonlinear, introducing additional challenges for [email protected] tightly-coupled solution algorithms. In our talk we focus on the implementation of implicit Newton-Krylov methods for coupled hydromechanical problems. The main difficulty Giuseppe Gambolati is to design effective preconditioners that achieve good al- University of Padova gorithmic scaling on today’s high performance computing DMMMSA platforms. We highlight an approach in which precondi- [email protected] tioners are constructed from block factorizations of the coupled systems. The resulting methodology allows one MS13 to extend single-physics preconditioners in a natural way to multiphysics applications, allowing for significant code Preconditioning Surface and Subsurface Flow Cou- reuse and an object-oriented framework. We test the per- pling for Arbitrary Geometries on a Structured formance of the proposed techniques on several numerical Grid examples drawn from geotechnical and reservoir engineer- Due to complex dynamics inherent in the physical mod- ing applications. els, numerical formulation of subsurface and overland flow Ronaldo Borja coupling can be challenging to solve. ParFlow is a sub- Stanford University surface flow code that couples with overland flow via an [email protected] overland boundary condition prescribed at the top surface. This talk will present a preconditioning approach to discrete systems arising from implicit coupling of these flow Joshua White regimes in ParFlow. Numerical results will explore the ef- Lawrence Livermore National Laboratory fectiveness of the preconditioner and its cost. [email protected] Daniel Osei-Kuffuor Univer. of Minnesota MS13 [email protected] Iterative Solution Methods for Stokesian Dynamics

Stokesian dynamics is a computational technique for simu- Reed M. Maxwell lating the motions of particles suspended or dispersed in a Department of Geology and Geologic Engineering fluid medium and interacting through hydrodynamic and Colorado School of Mines non-hydrodynamic forces. Particle velocities are computed [email protected] from the forces by solving with a resistance matrix which is a function of particle positions and orientations only. The Steve G. Smith, Andy Tompson, Carol S. Woodward resistance matrix is composed of a slowly-changing, dense, Lawrence Livermore National Lab long-range component, plus a fast-changing, sparse, indefi- [email protected], [email protected], nite, short-range component. We discuss iterative solution [email protected] methods for scaling up Stokesian dynamics to very-large problem sizes by exploiting this structure of the resistance matrix, as well as the design of preconditioners suitable MS13 for upcoming high-performance computing architectures. Quasi-Newton Preconditioner Updates for Two- Joint work with Tadashi Ando and Jeffrey Skolnick. phase Flow Simulations

Edmond Chow We study Broyden-type rank-one updates of an initial School of Computational Science and Engineering preconditioner for solving the sequence of linear systems Georgia Institute of Technology arising from Newton-like linearizations of FEM-discretized [email protected] two-phase flow problems. Starting from the incomplete LU decomposition of the initial Jacobian matrix, we apply this approach to build a sequence of preconditioners. Numerical MS13 experiments show a reduction in the number of iterations Constraint Preconditioners for Ill-conditioned needed to achieve convergence in the linear solver and in Consolidation Problems the cost of computing the preconditioner. Block constraint preconditioners prove very efficient for Luca Bergamaschi the solution of the indefinite linear systems arising in FE Universita di Padova consolidation problems. Their implementation on parallel Italy computers, however, is not straightforward. We present a [email protected] novel Parallel Inexact Constraint Preconditioner (ParICP) which is based on Block FSAI, a recent and promising de- Mario Putti velopment in the field of approximate inverses. ParICP is Dept. Mathematical Methods and Models for Applied a scalable and efficient implementation of constraint pre- Sciences conditioning for high performance computing, proving very University of Padua robust especially in ill-conditioned problems. [email protected]

Massimiliano Ferronato GS11 Abstracts 81

MS14 tical Mechanics except the upscaling tool via central limit Evaporative Deposition Patterns of Bacteria and theorems (CLT) use second moments. When Levy motions Microspheres from a Sessile Drop: Potential for are applied to velocity or position processes CLT plays sig- Characterizing Particle Adhesiveness nificant roles in modeling transport in porous media. In this talk, I will present the results in the CLT approach for Evaporative deposition of colloidal particles (bacteria and microbial motility in porous media. microspheres) on mica from a sessile drop is investigated as a simple way to control particle deposition as well as inves- Moongyu Park tigate fundamental particle-surface forces. We show that University of Alabama at Huntsville it is possible to continuously vary the deposition pattern Department of Mathematics from ring deposits to cellular pattern deposits by incre- [email protected] mental changes in surface wettability which we achieve by timed exposure of the mica surface to the atmosphere. MS15 Joan Curry Homogenization of the Linearized Ionic Transport Soil, Water and Environmental Science Equations in Rigid Periodic Porous Media University of Arizona [email protected] We undertake the rigorous homogenization of a system of PDEs describing the transport of a N-component electrolyte in a dilute solvent through a rigid porous medium. MS14 Smallness of the electric field and hydrodynamic force, al- Heterogeneous Reactions with Memory and Links lows us using O’Brien’s linearized equations as the start- to Multirate Mass Transfer Models of Convolution ing model. We establish convergence of the homogeniza- Type tion procedure and prove that Onsager’s effective tensor is symmetric positive definite. (Joint work with G. Allaire The convolution form used to express mass transfer be- (Paris) and A. Piatnitski (Narvik)) tween mobile and immobile aqueous domains, and often associated with multirate mass transfer representations of Andro Mikelic matrix diffusion processes, is generalized to the case of un- Institut Camille Jordan, Departement de Mathématiques equal forward and reverse rates for each of the multiple UniversitéLyon1 rates of the multirate mass transfer, and is shown to rep- [email protected] resent also linear but non-Markovian reactions that kinet- ically partition mass between mobile and immobile phases with rate of return to mobile phase dependent on contigu- MS15 ous time spent in immobile phase. In the case where a Homogenization of a Sulfate Corrosion Problem: multirate model refers to multiple sites with distributed Modelling and Analysis mobilization or release rates but single-valued immobilization rate, an equivalent formulation is found using single We model and then analyse a reaction-diffusion (RD) sce- site mobilization-immobilization with non-Markovian mo- nario describing the agressive corrosion with sulfates of the biliation rate dependent on contiguous time spent immo- sewer pipes made of concrete. Besides being partly dissipa- bilized. tive, our RD system includes two interface-reaction mechanisms: (1) the Henry’s law and (2) a non-linear chemical Tim Ginn reaction capturing the action of the most aggressive species SO2− University of California at Davis – 4 – on the boundary of the pore walls. After dis- [email protected] cussing basic aspects of the pore-model analysis, we focus on the rigorous derivation of a set of macroscopic equations. As periodic homogenization limiting procedure, we MS14 use the two-scale convergence approach combined with the Fractional Brownian Motion Run with a Non-linear periodic unfolding. The main difficulty lies in passing to Clock the (homogenization) limit in the nonlinear reaction terms defined on the oscillatory micro-interfaces. We derive both We construct a family of stochastic processes with nonsta- the weak and strong formulation of the limiting RD system. tionary, correlated increments which allow a priori indepen- We conclude the talk by pointing out correctors, which de- dent selections of both fractal dimension and mean-square fine the quality of our averaging procedure. displacement. The family is essentially fractional Brown- ian motion (fBm) run with a non-linear clock (fBm-nlc). Adrian Muntean The fractal dimension of fBm-nlc is shown to be the same Department of Mathematics and Computer Science as that of the underlying fBm process. We also compute TU Eindhoven the p- variation and discuss the problems in using this to [email protected] differentiate between diffusive processes. Tasnim Fatima Dan O’Malley Department of Mathematics and Computer Science Purdue University TU Eindhoven, NL [email protected] [email protected]

MS14 MS15 Upscaling Chaotic Dynamics in Porous Media via Colloid and Fluid Dynamics in Porous Media - Central Limit Theorems Modelling, Analysis and Numerics

There are several upscaling (renormalization) techniques We consider a non-stationary electro-hydrodynamic sys- for transport in porous media. All approaches in Statis- 82 GS11 Abstracts

tem at the pore scale. After applying homogenization Texas Tech University technique to this system of partial differential equations Department of Mathematics and Statistics we discuss the resulting equivalent macroscopic model de- [email protected] scription. These theoretical results are complemented by numerical simulations. As special application we thereby Eugenio Aulisa focus on colloidal transport within a porous medium, which Department of Mathematics and Statistics. fundamentally influences contaminant transport. Exten- Texas Tech University sions of the model regarding changes of the underlying mi- [email protected] crostructure due to interaction with the porous matrix will also be considered. MS16 Nadja Ray On Non-Darcy Flows in the Porous Media University of Erlangen-Nuremberg [email protected] Non-Darcy flow is usually treated by approximate analytical and numerical techniques in petroleum engineering. Florian Frank Recent applications in gas reservoirs, hydraulic fractures, Friedrich-Schiller University of Jena and naturally fractured porous media, however, require [email protected] more detailed treatments. Of particular interest are the pressure- and rate-transient responses of wells under the influence of non-Darcy flow. This talk will summarize the MS15 standard treatment of non-Darcy flow in petroleum engi- Moving Boundary Problems in Porous Media neering and discuss the approximate application of deconvolution for non-Darcy flow. We discuss processes in porous media with moving boundaries at the pore-scale such as deposition, biofilm growth Erdal Ozkan and crystal dissolution and precipitation. All these pro- Colorado school of mines petroleum engineering cesses may change the pore geometry. We use the pore- [email protected] scale free boundary problem to derive upscaled effective equations on the Darcy scale via a formal homogenization procedure. Numerical simulations show that solutions of MS16 the upscaled model match the averaged solutions of the Modeling Flow with Inertia at Porescale and pore-scale model very well. Mesoscale: Implications for Transport

T. L. van Noorden We discuss computations of flow at pore-scale and Eindhoven University of Technology mesoscale via discretizations of Navier-Stokes and non- [email protected] Darcy models. We upscale from pore-scale for linear laminar and inertia regimes of Reynolds numbers and compare with experimental data. We address the issues of grid- MS16 convergence and appropriate scaling needed when REV A Predictive Pore-Scale Model for Non-Darcy Flow and grain size change, as in homogenization. Most recent in Porous Media results concern the influence of inertia models on the parameters of transport coupled to the flow at pore-scale and Non-Darcy flow is porous media often observed in domains mesoscale. where relatively high velocities occur. In these regions an empirical model, Forchheimers equation, is used. In this Anna Trykozko study, we use the method of homogenization to develop a University of Warsaw filtration law in porous media that includes the effects of [email protected] inertia at finite Reynolds numbers. A major contribution of this study is that the coefficients of the polynomial law can Malgo Peszynska be derived a priori, by solving sequential Stokes problems. Department of Mathematics Oregon State University [email protected] Matthew Balhoff ICES The University of Texas at Austin Ken Kennedy balhoff@ices.utexas.edu Oregon State University [email protected]

MS16 MS17 Modeling of Well Productivity Index for Nonlinear Flows and Applications in Reservoir Engineering UTBEST3D – A Coastal Ocean Modeling System Based on a Discontinuous Galerkin Method Motivated by the concept of the well Productivity Index (PI) we study a functional for general non-linear Forch- We describe the application of a Local Discontinuous heimer equation. The impact of the nonlinearity on the Galerkin method to the three-dimensional hydrostatic sys- value of the PI is analyzed. Exact formula for the “skin tem in primitive variables for coastal and ocean modeling. factor’ in radial case is derived. Dynamics of the PI for the Starting from a simple ’proof-of-concept’ code UTBEST3D class of boundary conditions is studied. Developed frame- grew into a modular, object-oriented, highly scalable par- work is applied to obtain non-linear analog of Peaceman allelized package that can be used to simulate barotropic formula for the well-block pressure in unstructured grid. and baroclinic turbulent ﬂows for a wide range of physical Lidia Bloshanskaya GS11 Abstracts 83

conditions and forcings. to Gulf of Mexico simulations using the Hybrid Coordi- nate Ocean Model. Examples of uncertainty outputs will Vadym Aizinger be be presented, and the potential and limitations of the Max Planck Institute for Meteorology methodology will be presented. [email protected] Mohamed Iskandarani Clint Dawson Rosenstiel School of Marine and Atmospheric Sciences Institute for Computational Engineering and Sciences University of Miami University of Texas at Austin [email protected] [email protected] Ashwanth Srinivasan University of Miami MS17 [email protected] Issues in Coastal Ocean Modeling Carlisle Thacker In this talk we will give an overview of current issues in National Oceanic and Atmospheric Administration coastal ocean modeling that will be discussed by various [email protected] speakers in this minisymposium. We will also discuss recent research on hurricane storm surge modeling and the application of discontinuous Galerkin methods to modeling Omar M. Knio flow and transport processes in the near shore. Dept. of Mech. Eng. Johns Hopkins University Clint Dawson [email protected] Institute for Computational Engineering and Sciences University of Texas at Austin [email protected] MS18 Variational Data Assimilation for Fine-scale CO2 Source/Sink Estimation MS17 A Triangular Discontinuous Galerkin Coastal Measurements of atmospheric CO2 concentration are be- Ocean Model (dgcom) coming available at increasingly dense spatial and temporal resolution, most notably from satellites such as GOSAT, We will report on current and future developments of DG- the OCO reflight mission, and other planned missions. If COM which is a research code for simulating tsunamis and successful, these data could permit estimation of sources storm surges. In this talk we will report on the inclusion and sinks of CO2 at scales of 100-200 km or better, at sub- of high-order time-integrators including their implementa- synoptic time resolutions. While these data will initially tion with boundary conditions (no-flux, non-reflecting, and permit only net CO2 sources to be estimated, separation wetting and drying conditions). Finally, we will describe of the anthropogenic and natural components may also be- our plans to include adaptivity into the triangular code come easier using measurements of other species, such as for tracking storm-surges. Time permitting, we will de- C14, NOx, etc. Estimating surface CO2 fluxes at atmo- scribe the DG non-hydrostatic atmospheric model that is spheric model grid resolution imposes computational de- also under development that will be used to generate the mands that are being met with methods that achieve their wind stresses to be used in storm-surge simulations. The efficiency by abandoning the calculation of the full-rank overlap between the two models will be discussed as well covariance of the estimate. Here we present one of these as the MPI implementation of the DG amtospheric model methods, variational data assimilation, as applied to the and strategies for coupling the two models. surface source/sink problem. We will discuss the physical aspects of the problem, including the linearity of atmo- Shivasubramania Gopalakrishnan spheric transport (no internal chemical sinks) for CO2, as Department of Applied Mathematics well as the time scales of atmospheric mixing, and their im- Naval Postgraduate School plications for any estimation system. We will outline the [email protected] the method, including a description of the control variable strategy used. We will discuss the calculation of the low- Francis X. Giraldo rank covariance estimate, computed here using the BFGS Naval Postgraduate School method. And we will give some representative results from [email protected] simulation studies. David F. Baker MS17 Cooperative Institute for Research in the Atmosphere Quantifying Uncertainty in HYCOM simulation of [email protected] the Gulf of Mexico Oceanic simulations have numerous input parameters that MS18 are either unknowns, obtained from calibration, or known A Geostatistical Ensemble Square-Root Filter for only approximately. These include, for example, initial Estimating Surface Fluxes of CO2 and boundary conditions, as well as parameter embedded within subgrid scale parametrization. These uncertainties In recent years, one of the important challenges that has lead naturally to uncertainties in the output parameters; emerged in CO2 source/sink estimation is the increase parametric studies must then be performed to explore the in computational cost associated with solving the atmo- dependency of the solution on these parameters. Here we spheric inverse problem. Solving problems in batch mode is explore one approach to uncertainty quantification using becoming more and more computationally infeasible given polynomial chaos expansions, and apply the methodology the increasing spatial and temporal resolution of satellite data and ground based CO2 concentration measurements. 84 GS11 Abstracts

The alternative to these batch approaches are data as- MS19 similation (DA) techniques that efficiently solve the in- Mesh-independent Finite Element Methods for verse problem by making certain numerical approxima- Earthquake Simulation tions. However, a fundamental question that has remained unanswered is the impact on estimation precision and ac- Earthquake simulation is complicated by the complex na- curacy by implementing the numerical DA tools relative to ture of faults which rupture. Faithful representation of the batch inversions. In this work, we will present the first re- fault network geometry and solution robustness to varia- sults from a geostatistical ensemble square root filter that is tion of this geometry have proven difficult problems for used to estimate CO2 surface fluxes over North America us- standard finite element methods, which require simulation ing ground-based continuous measurements for 2008. The meshes to conform to the faults. Here we present a mesh- geostatistical ensemble square root filter is a novel method independent method, in which faults are included indepen- that is being developed to take advantage of both the ver- dently of the simulation mesh. We demonstrate the versa- satility of a geostatistical inverse modeling framework, and tility of the method in earthquake and crustal deformation of the computational efficiency of the ensemble approach. simulations. This presentation will not only focus on the methodological framework driving the geostatistical ensemble square root Ethan T. Coon filter but also on comparing the results from the filter with Los Alamos National Laboratory a batch solution for the same problem. The sensitivity of [email protected] both estimates and their uncertainties due to a shift from geostatistical batch inversion to a geostatistical ensemble Bruce Shaw technique will be analyzed. Further discussions will centre Columbia University around the properties of the filter (for example, impact of [email protected] ensemble size, representation of error covariances and their propagation, adaptive inflation etc.) and the overall frame- Marc Speigelman work required to reduce the computational cost associated Lamont Doherty Earth Observatory with CO2 source/sink estimation while providing a best es- [email protected] timate and estimated uncertainty equivalent to traditional batch inversions. MS19 Abhishek Chatterjee, Vineet Yadav, Kim Mueller, Sharon Large-scale Earthquake Simulations and the Pre- Gourdji, Anna Michalak diction of Strong Ground Motion University of Michigan [email protected], [email protected], Accurate, scalable numerical simulations of earthquake [email protected], [email protected], ruptures and the concomitant excitation and propagation [email protected] of stress waves in realistic three-dimensional geologic models are important to our understanding of the physics of earthquakes and the prediction of strong ground motion. MS18 We give an overview of some insights that have accrued Quantification of Uncertainty for the Vulcan from recent large-scale simulations. These have revealed Project High Resolution Fossil Fuel CO2 Emissions unexpected interactions between the source and the geo- Data Product logic structure that have been further illuminated by adjoint simulations. Abstract not available at time of publication. Steven Day Kevin Gurney Dept of Geological Sciences Arizona State University San Diego State university [email protected] [email protected]

MS18 Kim Olsen Ensemble Kalman Filters Applied to CO2 Source Dept of Geological Sciences Inversion San Diego State University [email protected] We present a numerical study using a hybrid Ensemble Kalman Filtering (EnKF) algorithm to invert for CO2 Yifeng Cui sources. The underlying transport model is a convection- San Diego Supercomputer Center diffusion model in which the source terms are represented [email protected] by the pixels of a satellite image of the US at night. The intensity of the lights represents the magnitude of the emissions. We investigate the use of this model as prior infor- MS19 mation in the EnKF based inversion. Adaptive Mesh Refinement for Earthquake Rup- ture Simulations Bart van Bloeman Waanders, Sean McKenna Sandia National Laboratories Strong shaking from large earthquakes extends tens to hun- [email protected], [email protected] dreds kilometers from faults of comparable size, but numerically resolving laboratory-constrained frictional pro- Jaideep Ray cesses requires millimeter to centimeter grid spacings. Con- Sandia National Laboratories, Livermore, CA strained by current computational resources, the standard [email protected] modeling approach is to use approximately constant grid spacings with artificially increased frictional length scales. We present an alternative approach that uses adaptive GS11 Abstracts 85

mesh refinement to exploit the fact that fine-scale reso- gin by introducing a surrogate dual porosity, dual perme- lution needs are localized around the propagating rupture ability model for tracer flow in this type of system. To front. quantify the uncertainty, the ideal situation is to inte- grate available static and dynamic data into this surrogate Jeremy E. Kozdon model. This is accomplished within a Bayesian framework Stanford University using Markov Chain Monte Carlo methodology. A num- Geophysics ber of numerical examples are presented to illustrate the [email protected] performance of the method.

Eric M. Dunham Victor E. Ginting Department of Geophysics Department of Mathematics Stanford University University of Wyoming [email protected] [email protected]

MS19 MS20 Simulations of Long-term Slip of Earthquake- A New Problem Adapted Hierarchical Model Re- producing Faults: Importance of Incorporating duction Technique Based on Reduced Basis Meth- Full Inertial Effects during Seismic Slip ods and Dimensional Splitting We study mechanics and physics of earthquakes using a We present a new dimension reduction technique [M. unique modeling approach that reproduces both earth- Ohlberger and K. Smetana, 2010]. In comparison to the quakes and slow slip, with full inclusion of inertial effects Boussinesq approach we do not neglect the dependency on during simulated earthquakes. Here, we compare this ap- the vertical direction but enhance the solution for the hor- proach to a popular simplified, so-called quasi-dynamic, izontal direction with appropriately chosen basis functions method, in which inertial effects are incorporated through living on the vertical one. This is done by a combination a radiation damping approximation. We find that the two of the frameworks of hierarchical model reduction [S. Per- methods can produce qualitatively different earthquakes otto, A. Ern, and A. Veneziani, 2010] and the reduced basis and long-term fault behavior. Our eventual goal is to de- methods [B. Haasdonk, M. Dihlmann and M. Ohlberger, termine the range of applicability for the quasi-dynamic 2010]. We derive a new a posteriori error estimate and approaches. demonstrate in numerical experiments that few basis functions suffice to get good approximations. Nadia Lapusta, Marion Thomas, Hiro Noda, Jean-Philippe Avouac Kathrin Smetana California Institute of Technology Institute for Computational and Applied Mathematics, [email protected], [email protected], Westfaelische Wilhelms-University Muenster [email protected], [email protected] [email protected]

Mario Ohlberger MS20 Universität Münster An Energy-conserving Discontinuous Multiscale Institut für Numerische und Angewandte Mathematik Finite Element Method for the Wave Equation in [email protected] Heterogeneous Media

In this talk, we present a new multiscale finite element MS21 algorithm for simulating acoustic wave propagation in het- A Practical Modeling Approach to Evaluate Long- erogeneous media. This method solves the wave equation term CO2 Storage in Real Geological Systems on a coarse grid using multiscale basis functions and a coupling mechanism to relate information between fine and Large-scale models of CO2 injection into geological forma- coarse grids. Our method is based on a mixed formu- tions must capture the relevant geological and geophysical lation of the wave equation and staggered discontinuous processes that affect the migration and ultimate fate of in- basis functions. Thus, our multiscale methods have the jected CO2. These processes span many spatial and tempo- following nice properties. (1) The total wave energy is con- ral scales, and traditional numerical methods cannot solve served, (2) Mass matrix is diagonal on a coarse grid and these large, complex systems in a practical way. A new energy-preserving, and (3) Multiscale basis functions can modeling approach solves coarse-scale vertically-integrated accurately capture the subgrid behavior. Some numerical governing equations that are coupled with subgrid models results will be shown. This is a joint work with Yalchin to capture important small-scale processes in an efficient Efendiev and Richard Gibson. and accurate way. Eric Chung Sarah Gasda The Chinese University of Hong Kong University of North Carolina at Chapel Hill Department of Mathematics [email protected] [email protected] Jan M. Nordbotten Department of Mathematics MS20 University of Bergen A Bayesian Uncertainty Quantification of Frac- [email protected] tured Reservoirs using Surrogate Flow Model

The modeling of fractured reservoirs typically involves sep- Michael A. Celia aration of the matrix and fracture parameters, and we be- Princeton University Dept of Civil Engineering 86 GS11 Abstracts

[email protected] analysis and migration.

Jeffrey C. Shragge,DavidLumley MS21 University of Western Australia The Effect of Capillary Forces on Two-phase Flow jeff[email protected], [email protected]

We derive a two-phase gravity current model from fractional flow theory under the assumption large aspect ratio MS21 and vertical gravity-capillary equilibrium. The saturation The Rock Physico-chemical Basis for Time-lapse profile in combination with the relative permeability deter- Seismic Reservoir Monitoring of CO2 Injection mines the dynamics of the two-phase current. The model significantly improves estimates of the vertical sweep, the 4D laboratory experiments, high-resolution imaging, and magnitude of residual trapping, and the propagation speed computational rock physics are used to monitor the effect of the current. This model provides physical insight and of physicochemical processes occurring upon injection of an efficient formulation for large scale geological carbon CO2 within sandstone and carbonate rocks. The goal is to dioxide storage. understand the effect of salt precipitation and dissolution on transport and seismic properties and verify the need for Marc A. Hesse extending tools currently available in rock physics to in- University of Texas fer subsurface conditions where the coupling between pore Department of Geological Sciences fluids and rock matrices is not purely mechanical. Results [email protected] show that the seismic response of CO2-brine-rock systems is far from being a pure fluid-substitution problem. Madeleine Golding Cambridge University Tiziana Vanorio [email protected] Department of Geophysics Stanford University [email protected] Jerome Neufeld Cambridge University Department of Applied Mathematics and Theoretical Elizabeth Diaz Physics Ingrain Inc. [email protected] [email protected] Amos Nur MS21 Stanford University Stochastic Inversion of Seismic and Electromag- Ingrain Inc. netic Data for Co2 Saturation Prediction [email protected]

Stochastic inversion of seismic (AVA) and electromagnetic (CSEM) data are used to predict CO2 saturation. A 2D MS22 synthetic model constructed for hydrocarbon exploration Mixed Hybrid and Linear Conforming Finite Ele- has been adapted to fill the reservoirs with CO2. Synthetic ments for the Simulation of Reactive Multicompo- seismic and CSEM data are used to test the resolution of nent Transport in Porous Media CO2 saturation predictions under a range of experimental variables. The choice of rock physics model, the proximity Mixed hybrid FE are applied to reactive transport in of wells used for rock physics, noise levels and choice of porous media and compared to linear conforming FE with geophysical forward models all effect the quality of the CO2 respect to the numerical diffusion they introduce and their saturation prediction. behavior in the case of discontinuous coefficient functions. A general discretization of the nonlinear transport-reaction G. Michael Hoversten equations with RT0,BDM1 and RT1 elements is shown. Chevron Energy Technology Company We present numerical tests giving evidence that mixed [email protected] schemes may be preferable for this application where the primary unknown is not a vector variable. Jinsong Chen Lawrence Berkeley National Laboratory Fabian Brunner [email protected] University of Erlangen [email protected]

MS21 MS22 Time-lapse Wave-equation Imaging of CO2 Geose- questration A More Robust MHFE Scheme for Solute Trans- port in Porous Media Time-lapse seismic monitoring of CO2 geosequestration is emerging as an important geophysical research field. We present a new, more robust mass conservative finite Most 4D seismic inversions for estimating elastic property element scheme for reactive solute transport in porous change are linearized about baseline elastic models. Large- media. The transport is modelled by a convection- scale CO2 injection, though, can introduce large property diffusion-reaction equation, including equilibrium or non- perturbations that lead to complex wavefield coda and a equilibrium sorption. The numerical scheme is based on strongly non-linear inversion problem. We demonstrate mixed hybrid finite elements (MHFE) and it is more effi- that overcoming this non-linearity requires a time-lapse cient for high Péclet numbers as the classical one [1]. The seismic inversion procedure that includes 4D depth velocity lowest order Raviart-Thomas elements are used. We also present an upwind variant of it, which should be consid- GS11 Abstracts 87

ered for strong convection dominated problems. Various Zdenek Strakos numerical tests, including the case of heterogeneous soil Department of numerical mathematics, Charles University are shown. Prague, Czech Republic [email protected]ff.cuni.cz REFERENCES F.A. Radu, N. Suciu, J. Hoffmann, A. Vogel, O. Kolditz, Martin Vohralik C-H. Park and S. Attinger. Accuracy of numerical simula- Université Pierre et Marie Curie tions of contaminant transport in heterogeneous aquifers: Paris, France a comparative study. Advances in Water Resources, 2010, [email protected] doi:10.1016/j.advwatres.2010.09.012.

Florin A. Radu MS23 UFZ-Helmholtz Center for Environmental Research, Continuous and Discontinuous Data Assimilation Leipzig Methods for Estimating a Heterogeneous Conduc- Germany tivity Field by Assimilating Transient Solute Trans- ﬂ[email protected] port Data

An ensemble Kalman Filter (EnKF) is developed to iden- MS22 tify a hydraulic conductivity distribution in a heteroge- Convergence and Interpolation of Numerical Raw neous medium by assimilating solute concentration mea- Field Methods on General Grids surements of solute transport in the field with a steady state flow. A synthetic case with the mixed Neumann/ We discuss conditions and limitations for convergence of Dirichlet boundary conditions is designed to investigate the some multi-point flux approximation (MPFA) methods on capacity and effectiveness of the proposed continuous and polyhedral meshes in the presence of a discontinuous per- discontinuous data assimilation methods to identify a con- meability field. In a more general setting we look at what ductivity distribution. The developed method is demon- the difference between raw field methods (like the MPFA strated in 2-D transient solute transport. The study results and mimetic FD methods) and full field methods (like the indicate that the EnKF method will significantly improve mixed finite element method) implies and the importance the estimation of the hydraulic conductivity field by as- of interpolation. Our discussion is supplemented with some similating continuous or discontinuous solute concentration illustrative numerical examples measurements. In comparison with the continuous data assimilation method, the discontinuous data assimilation Runhild A. Klausen method can better identify the heterogeneous conductivity University of Oslo field, especially in the downstream flow field Norway [email protected] Bill Hu Earth, Ocean and Atmospheric Sciences Annette Stephansen Florida State University CIPR / University of Bergen [email protected] [email protected] MS23 MS22 Some Recent Advances in the Scaling of Earth and Guaranteed and Robust a Posteriori Stopping Cri- Environmental Variables teria for Iterative Linearizations and Linear Solvers It has been demonstrated theoretically and numerically We present a posteriori error estimates of the linearization by the author that data sampled from fractional Gaus- error in approximation of nonlinear problems and of the sian/Lévy noise (fGn/fLn) exhibit apparent/spurious mul- algebraic error in the solution of linear systems and derive tifractality. Here we generalize Neuman’s development in stopping criteria for (non)linear iterations. Our estimates a way that (a) rigorously subordinates (truncated) fLn to control the overall error. They are also locally efficient (truncated) fGn, (b) extends the analysis to a wider class and thus allow to predict the error spatial distribution and of subordinated self-affine processes and (c) explains why to refine the mesh adaptively. We present strategies for the distribution of corresponding data tends to evolve from achieving a user-specified accuracy at minimal cost and heavy tailed at small lags (separation distances or scales) illustrative numerical experiments. to Gaussian at larger lags. Linda El Alaoui Shlomo Neuman LAGA, Université Paris 13 University of Arizona Villetaneuse, France Department of Hydrology and Water Resources [email protected] [email protected]

Alexandre Ern MS23 Universite Paris-Est CERMICS, Ecole des Ponts Uncertainty Quantification in Subsurface Modeling [email protected] We consider a a set of parabolic partial differential equations with uncertain coefficients that describe flow and Pavel Jiranek transport in heterogeneous porous media. To quantify CERFACS predictive uncertainty in such systems, we treat uncertain Toulouse, France coefficients as random fields with known statistics, which [email protected] renders the corresponding governing nonlinear differential 88 GS11 Abstracts

equations stochastic. We derive a deterministic equation ﬂow in the fracture. for the probability density function (PDF) of the system state. By going beyond computing system state’s mean Fernando Morales, Ralph Showalter and variance, which is the standard practice in many un- Department of Mathematics certainty quantiﬁcation studies, the PDF equations enable Oregon State University one to compute probabilities of rare events (distribution [email protected], tails), which are required in modern probabilistic risk anal- [email protected] yses. Daniel M. Tartakovsky MS24 University of California, San Diego Schur Complement Preconditioning for Flow Sim- [email protected] ulation in 3D Discrete Fracture Networks

Marco Dentz The simulation of flow in discrete fractured media requires IDAEA to solve very large linear systems. Those systems are sparse Spanish National Research Council (CSIC) and with a specific shape due to the underlying physical [email protected] problem. In order to take advantage of this specific structure, a preconditioned conjugate gradient method based on the Schur complement is used. Several preconditioning MS23 approaches are tested. We present simulations results in Iterative Coupling for Treating Compositional sequential as well as in parallel. Flow and Geomechanics Baptiste Poirriez We formulate a scheme for coupling an equation of state INRIA Rennes (EOS) compositional flow model with elasticity. We dis- University of Rennes 1 cuss iterative coupling, discretizations, solvers, and parallel [email protected] scaling issues. Jocelyn Erhel, Geraldine Pichot Mary F. Wheeler INRIA Rennes Bretagne Atlantique Center for Subsurface Modeling France University of Texas at Austin [email protected], [email protected] [email protected] MS24 MS24 Modeling Fluid Flow Along Faults Interface Conditions for Fluid Flow in Porous Me- dia withReduced Order and Non Matching Frac- We study an approach to model fluid flow along fault tures compatible with the standard oil industry flow simulators where faults are represented by interfaces across which the For large scale computations of flows in porous media with grid does not match. The fault zone is represented by two complex fracture networks the conformity of the mesh can sets of faces, each set matching its neighbouring matrix represent a severe constraint. We propose a method that cells, and flow is modeled by a surface model. We present allows for non-matching grids, thus very advantageous if results ranging from academic cases to one phase flow in the position of the fractures is uncertain and multiple sim- basin modeling where sliding along faults occurs. ulations are required. We consider mixed hybridized finite elements for the discretization of the bulk flow and the Isabelle Faille, Marie-Christine Cacas reduced problem in the fractures and provide the correct IFP Energies Nouvelles interface conditions. France [email protected], Alessio Fumagalli [email protected] MOX, Politecnico di Milano Italy Thierry Gallouet [email protected] UniversitédeProvence [email protected] Anna Scotti Politecnico di Milano Pascal Havé, Roland Masson, Xavier Tunc,Fran¸coise [email protected] Willien IFP Energies Nouvelles Carlo D’Angelo France MOX - Department of Mathematics [email protected], Politecnico di Milano [email protected], [email protected] [email protected], [email protected] MS24 Darcy-Stokes Fracture Flow MS25 On Stability of the Fluid Structure Interaction in The asymptotic analysis of Darcy flow in a region coupled Porous Media fo Non-linear Potential Flows to Stokes flow in a very thin fracture is revisited. The appropriately scaled model leads to a limiting problem con- In this work we consider the dynamical response of a non- sisting of Darcy flow in the region coupled to Brinkmann linear plate with viscous damping interacting with a non- GS11 Abstracts 89

linear potential flow. The system is modeled using non- Forchheimer Relationship linear momentum equations for the axial and transverse displacements coupled with fluid flow subjected to Forch- Detailed simulations of single-phase flow in the imaged- heimer type flow. In particular we show that for a class based realistic porous media are carried out using Lattice of boundary conditions given inlet velocity flow for liquid, Boltzmann Method (LBM) over a wide range of Reynolds dynamic of the process is stable with respect to boundary number. Inertial effects manifest themselves as the devia- input Data. tion from Darcys law on the macroscopic scales. Transition from viscous forces dominated flow regime to inertia dom- Eugenio Aulisa inated flow can be systematically predicted as well as the Department of Mathematics and Statistics. parameters such as permeability and Forchheimer coeffi- Texas Tech University cient can be calculated from three-dimensional flow simu- [email protected] lations.

Luan Hoang Mayank Tyagi Texas Tech University LSU Department of Mathematics and Statistics [email protected] [email protected] MS26 Yasemen Kaya Grid Resolution Requirements and Computational Department of Mathematics Overhead in Nonhydrostatic Coastal Ocean Mod- Texas Tech University eling [email protected] Computation of the nonhydrostatic pressure may be required in coastal ocean models if the relevant horizontal MS25 scales of motion are on the same order as the vertical scales. Multi-scale Modeling of Brinkman’s Filtration in I will present a method to determine how much grid reso- Layered Porous Media lution is required to resolve nonhydrostatic processes. Al- though solution of the nonhydrostatic pressure can be ex- We applied the theory of homogenization to the case of pensive, I will show that weakly nonhydrostatic processes Brinkman filtration of viscous incompressible fluid through can incur minimal overhead with the use of appropriate heterogeneous porous medium, whose material structure preconditioners. was characterized by periodicity over several length scales. We derived governing equations for all scales and obtained Oliver Fringer general relationships between the pressure and the velocity Environmental Fluid Mechanics Laboratory of fluid. The derivation of effective coefficients was reduced Stanford University to the solution of periodic problems in cells, which were [email protected] solved numerically.

Viktoria Savatorova MS26 Physics Department, Modeling Storm Surges with the Multilayer Shal- National Research Nuclear University low Water Equations [email protected] Storm surges created by tropical storms pose significant flooding risks to coastal populations. Many current models MS25 of surge use the single layer shallow water equations, which On a Power Series Solution to the Boussinesq Equa- capture much of the physics while allowing rapid compu- tion tation over vast regions. We are examining the potential advantages of using the multilayer shallow water equations The Boussinesq equation describes water flows in uncon- together with adaptive mesh refinement to efficiently cap- fined groundwater aquifers under the Dupuit assumption ture additional storm surge physics. that the equipotential lines are vertical, making flow horizontal. It is a nonlinear diffusion equation with diffusivity Kyle T. Mandli depending linearly on water head. We also analyze a gener- University of Washington alized Boussinesq equation, where the diffusivity is a power Dept. of Applied Mathematics law function of water head. For certain classes of initial and [email protected] boundary conditions approximate analytical solutions can be constructed using the scaling properties of the equation. Randall J. LeVeque Applied Mathematics Aleksey S. Telyakovskiy University of Washington (Seattle) Department of Mathematics and Statistics [email protected]; [email protected]; rjl@washingt University of Nevada [email protected] MS26 Title Not Available at Time of Publication MS25 Abstract not available at time of publication. Pore-scale Fluid Dynamical Perspective of Non- Darcy Effects in the Inertial Flows Through Re- Joannes Westerink alistic Porous Media: A First Principle Analysis of Department of Civil Engineering and Geological Sciences University of Notre Dame [email protected] 90 GS11 Abstracts

MS26 Center for Subsurface Modeling Challenges in 3D Cross-Scale Modeling University of Texas at Austin [email protected] Originally developed as a 3D baroclinic circulation model for the Columbia River estuary-plume-shelf system, SELFE (Semi-implicit Eulerian-Lagrangian Finite El- MS27 ement) has evolved into a comprehensive, open-source Pressure Preconditioning Using Proper Orthogo- community-supported modeling system. Grounded on un- nal Decomposition structured grids, the model is designed for the effective simulation of 3D baroclinic/barotropic flows across river- We developed and implemented a new physics-based pre- to-ocean scales. It uses an efficient semi-implicit finite- conditioning method for solving the pressure equation in element Eulerian-Lagrangian method to solve the Navier- large-scale reservoir simulation as an alternative to the Stokes equations (in either hydrostatic or non-hydrostatic popular Algebraic Multi Grid (AMG) method. The new form), written in MPI FORTRAN90 to realistically ad- method uses a small set of pre-computed pressure solutions dress a wide range of physical processes and of atmospheric, to transform the pressure equation into a lower-order rep- ocean and river forcings. The combination of unstructured resentation using Proper Orthogonal Decomposition. In grids, implicit time stepping and an Eulerian-Lagrangian test cases we reduced the linear solver time by about 50% Method in SELFE leads to superior flexibility, accuracy, compared to AMG preconditioning. efficiency and robustness. We present new developments of the SELFE modeling system in the areas of 3D baro- Jan Dirk Jansen clinic circulations, tsunami and storm surge inundation (in- Technische Universiteit Delft cluding wave-current interaction). The cross-scale nature Shell International E&P of the SELFE modeling system (from minutes to decade, [email protected] and from meters to hundreds of kilometers) also presents great computational/algorithmic challenges (e.g. wetting MS27 and drying; multi-physics in a single modeling framework etc) that beckon applied mathematicians to address. AlocalPOD-BasedMulticaleMixedFEMfor Model Reduction of Multiphase Compressible Flow Yinglong J. Zhang CMOP, OHSU We develop a local basis model-order reduction technique [email protected] for approximation of flux/pressure fields based on local proper orthogonal decompositions (PODs) consistently glued together using the Multiscale Mixed FEM (MsM- MS27 FEM) framework on a coarse grid. Based on snapshots Overview of Upscaling, Multiscale and Reduced- from one or more simulation run, we perform SVDs for the order Modeling Techniques for Subsurface Flow flux distribution over coarse grid interfaces and use the singular vectors corresponding the largest singular values as A wide variety of upscaling (numerical homogenization), boundary conditions for the multiscale flux basis functions. multiscale modeling, and reduced-order modeling proce- The span of these basis functions matches (to prescribed dures have been developed for subsurface flow simulation. accuracy) the span of the snapshots over coarse grid faces. We will briefly discuss these general approaches, highlight- Accordingly, the complementary span (whats left) can be ing key similarities and differences. Then, a trajectory approximated by local PODs on each coarse block giving piecewise linearization approach will be described. This a second set of local/sparse basis functions. The reduced technique, which entails linearization around saved states system unknowns corresponding to the second set of basis and a POD-based projection into a low-dimensional sub- functions can be eliminated to keep the system size low. space, is applied for subsurface flow modeling. Some exist- To assess the accuracy, we apply the methodology to a re- ing challenges will also be discussed. alistic test problem (two-phase compressible flow including gravity) with several wells and compare to results obtained Lou Durlofsky from full order simulations. Both changing well configura- Energy Resources Engineering Department tions and changing well placements (with local update of Stanford University bases) are considered. In addition, comparison to standard [email protected] POD is considered. Stein Krogstad MS27 SINTEF ICT Parameterized Model-Order Reduction for Large- [email protected] Scale Reservoir Models In this presentation, we investigate the use of the para- MS28 metric model order reduction(PMOR) techniques applied CO2 Geological Storage and Groundwater Re- to porous media flow simulation in a system-theoretical sources: Model Applications framework. PMOR entails the generation of reduced-order models which retains the functional dependency on spe- This paper provides an overview of research issues and cific parameters of the original large-scale system. Usually, modeling applications related to understanding potential an ensemble of models is used to assess uncertainty in the impacts of geologic carbon sequestration on groundwater reservoir simulation. In order to overcome the computa- resources. Issues addressed by multi-phase modeling and tional effort in this scenario, reduced-order models that reactive transport simulations include (1) the possibility of take into account this entire ensemble are necessary to ob- water quality changes due to leakage of CO2 (together with tain. co-migrating contaminants) into fresh water aquifers, and (2) the potential of regional-scale hydrogeologic perturba- Eduardo Gildin tion caused by the injection of CO2 and the subsequent GS11 Abstracts 91

displacement of native brine. [email protected]

Jens T. Birkholzer Steven L. Bryant Lawrence Berkeley National Laboratory Petroleum and Geosystems Engineering Department (LBNL) University of Texas at Austin [email protected] steven [email protected]

Quanlin Zhou, Liange Zheng, Nicolas Spycher Kamy Sepehrnoori Lawrence Berkeley National Laboratory (LBNL) Department of Petroleum and Geosystems Engineering [email protected], [email protected], [email protected] [email protected]

MS28 MS28 Variations of CO2/Water Interfacial Tension and Multiscale Numerical and Physical Modeling of Impact on CO2 Trapping Capacity Geologic Carbon Sequestration We have implemented an empirical correlation for wa- Geologic carbon sequestration is impacted by several pro- ter/CO2 interfacial tension (IFT) in the compositional flow cesses including multiphase flow with density and thermal and reactive module of IPARS parallel reservoir simulator. effects, dissolution of fluid phases, and reactions with reser- The IFT correlation is a function of pressure, salinity, and voir solids. These are largely controlled by pore-scale (mi- temperature. The relative permeabilities are generalized to cron to mm-scale) features of the fluid interfaces and solid account for combined effects of viscous, buoyancy, and cap- material surfaces, while quantitative predictions are needed illary forces. Several prototype aquifer models are studied at much larger length scales. We will present a suite of nu- to determine the impact of injection rates and IFT varia- merical and physical models defined at the pore scale and tions on CO2 migration and trapping. their application to field-scale simulations.

Mojdeh Delshad Timothy D. Scheibe Department of Petroleum and Geosystems Engineering Hydrology Technical Group The University of Texas at Austin Paciﬁc Northwest National Laboratory [email protected] [email protected]

Xianhui Kong Alexandre Tartakovsky, Mart Oostrom, Mark D. White Center for Subsurface Modeling Pacific Northwest National Laboratory The University of Texas at Austin [email protected], [email protected], [email protected] [email protected] Mary F. Wheeler Center for Subsurface Modeling MS29 University of Texas at Austin Finite Volume Approximation for Two-phase Flows [email protected] with Discontinuous Capillary Pressure We are interested in a PDE system describing an incom- MS28 pressible immiscible two-phase flow in a porous medium Title Not Available at Time of Publication made of two different rocks. Since the capillary pressure function depends on the rock type, the capillary pressure Abstract not available at timr of publication. field can be discontinuous at the interface between the rocks. We give a sense to the transmission conditions at Margot Gerritsen the interface, and then, we propose a Finite Volume scheme Dept of Petroleum Engineering allowing to deal with such discontinuities, and prove its Stanford University convergence towards a weak solution to the problem. [email protected] Konstantin Brenner Université Paris Sud (Orsay) MS28 [email protected] Analysis of Capillary Structures in Heterogeneous Formations Clement Cances Local capillary trapping is a potentially important mech- Université Pierre et Marie Curie , Paris, France [email protected] anism for immobilization of CO2. It occurs at small scales (compared to field scale) as CO2 rises under gravity through heterogeneous formations. The overall objective Danielle Hilhorst is to analyze the structures that could form local capillary Université Paris Sud (Orsay) traps in typical storage formations. We generate geosta- danielle hilhorst ¡[email protected] tistical realizations of permeability from variogram models populated with key petrophysical properties and analyze spatial properties of them to determine the potential for MS29 local capillary trapping. A New Corrected Operator Splitting Method Com- bining Streamline Approach for Two-phase Flow Ehsan Saadatpoor with Gravity Department of Petroleum and Geosystems Engineering The University of Texas at Austin Gravity is important for dynamics which often cannot be 92 GS11 Abstracts

neglected but poses significant challenges for the numeri- MS29 cal approximation of PDEs. Thus, this talk focuses on a Convergence Analysis of a Vertex-centered Finite new corrected operator splitting (COS) method for higher- Volume Scheme for a Copper Heap Leaching Model dimensional two-phase flow problems with gravity, and the COS method is devised by handling the gravity term based This work is motivated by a combined mixed finite element on streamline tracing for a front velocity field generated (MFE) - finite volume (FV) scheme of a two phase flow from flux splitting. Different numerical examples are sim- model for the heap leaching of copper ores modeled by a ulated and explained. degenerate parabolic equation

Yufei Cao ∂tu −∇·(∇β(u)+F (u)) = r(u), in QT ≡ (0,T) × Ω. IWS, University of Stuttgart, Germany [email protected] Initially we have u(0) = u0 in Ω, whereas u =0on∂Ω. In the above 0

Mauricio Sepulveda MS29 Universidad de Concepcion The Application of Homogenization Theory to [email protected] Study the Stability of Density-driven Flows in Het- erogeneous Formations MS30 Density-driven flows cut across many practical applications Porous Media Research at Purdue: Past and Fu- like normal and nuclear waste repository management, the ture protection of coastal groundwater aquifers from salty sea- water intrusion, the harnessing of geothermal resources and My group has focused on four basic porous media prob- the exploration of petroleum. A typical feature of such sys- lems over the years, i) swelling porous media (mixture the- tems is that they can become unstable and exhibit the fin- ory and homogenization), ii) nano films (computational gering phenomenon. A salient challenge to-date has been chemistry), iii) diffusion/dispersion in heterogeneous me- the absence of a stability criterion capable of predicting the dia (stochastic perturbation, CLTs, and statistical mechan- onset of fingering. In this work we apply homogenization ics) and iv)nutrient transport to growing roots (non-linear theory techniques developed in [Held et al. 2005] to derive moving BCs for diffusion problems). Each of these topics the small- and large-scale transport equations [Musuuza will be briefly discussed in the context of my students and et al., (2009)]. The small-scale equation is used to derive post docs efforts. A brief look toward the future will be a stability criterion in terms of the density, dispersivities presented. [Musuuza et al., (2010)] and heterogeneity properties. The criterion is tested on those variables and produced reason- John H. Cushman able predictions for the onset of convection. The large-scale Department of Mathematics equation is used to study mixing behaviour by evaluating Purdue University the macrodispersion tensor elements. The system stabil- [email protected] ity could be inferred from the temporal evolution of the longitudinal coefficient. MS30 Jude L. Musuuza Polar Field Theories: Small Scale to Large Scale University of Jena Applications [email protected] Micromorphic fluids contain a particulate substructure Florin A. Radu which affects the movement of the fluid. This structure UFZ-Helmholtz Center for Environmental Research, can be incorporated into the fluid flow model. This talk Leipzig will present two models using these fluids including small Germany and large scale examples. Current work initiated by Dr. fl[email protected] Cushman and associates related to large scale continental deformation will be discussed. The continental plates are Sabine Attinger being viewed as micropolar bodies with substructures that Institute of Computational Computational can rotate in addition to the translational movement. EnvironmentaScience Natalie Kleinfelter Domelle UFZ Leipzig Mathematics Department [email protected] Saint Marys College [email protected] GS11 Abstracts 93

John H. Cushman France Department of Mathematics jerome.jaff[email protected] Purdue University [email protected] Mokhles Mnejja Ecole Polytechnique de Tunisie Tunisia MS30 [email protected] Modeling Coupled Hydrological and Chemical Pro- cesses in Unsaturated Fractured Porous Media Jean E. Roberts Environmental remediation often leads to geochemical INRIA Paris-Rocquencourt transformations, such as precipitation and dissolution of France minerals and evolution of gases and bio-films. These trans- [email protected] formations may in turn modify the hydraulic properties of the system. If significant changes take place in either the MS31 flow paths or the hydraulic properties, they may have an impact on the geochemical transport processes. We show Homogenization Approach to the Quasistatic Cou- how transient changes in hydrological properties caused by pling Poroelastic/ Elastic Media coupling of hydrological and chemical processes often lead In this contribution, investigations are focused on the cou- to local flow channeling and saturation increases in unsat- pling of the single phase subsurface flow with poroelastic- urated fractured porous media. ity. Most of the multiscale approaches to Biot’s equation Sumit Mukhopadhyay concentrate on the dynamic case, where memory effects appear. Here we are interested in the quasistatic case and Earth Sciences Division/Hydrogeology obtain rigorously the Biot consolidation theory equations. Lawrence Berkeley National Laboratory Furthermore, we find the interface conditions between two [email protected] different flow regimes. Andro Mikelic MS30 Institut Camille Jordan, Departement de Mathématiques Computation of Flow and Transport in Large and UniversitéLyon1 Sparse Fracture Networks [email protected] The discrete fracture network (DFN) approach to compute flow in large two-dimensional fracture networks is an accu- Mary F. Wheeler rate but computationally intensive methodology. Contin- Center for Subsurface Modeling uum based methods allow for simulation of processes not University of Texas at Austin presently achievable using DFN approach but can suffer [email protected] from lack of accuracy especially in prediction of transport behavior and in cases with sparse fracture networks. Tech- MS31 niques to improve the computational efficiency of DFN method and predictive accuracy of a continuum method An Efficient MPFA Approach to Discrete Fracture are presented. Matrix (DFM) Flow Models Rishi Parashar A control volume discretization along with a Multi-Point- Division of Hydrologic Sciences Flux Approximation (MPFA) is considered for a Discrete Desert Research Institute, Reno, NV Fracture Matrix (DFM) flow model. Inspired by a recently [email protected] introduced approach based on Two-Point-Flux Approxima- tion (TPFA), elements in the intersection of fractures are eliminated by a star-delta transformation; hence, avoiding MS31 associated time-step restriction and numerical instabilities. Two-phase Flow in Porous Media with Discrete Numerical results demonstrate the flexibility and robust- Fractures ness of the new approach. In this talk we present a discrete fracture model for flow of Tor Harald Sandve a two-phase fluid in a porous medium. Fractures are rep- University of Bergen resented as interfaces and fluid exchange between the frac- Norway tures and surrounding medium is permitted. Thus there is [email protected] a coupling of n-dimensional flow with (n − 1)-dimensional flow. The global pressure formulation is used and the frac- Inga Berre ture domain is assumed to be of a rock type different from University of Bergen that of the surrounding medium; i.e. the relative perme- Christian Michelsen Research ability and capillary pressure curves for the fracture do- [email protected] main are different from those for the surrounding rock matrix. Thus continuity of the saturation can not be assumed Jan Martin Nordbotten in the derivation of the model. The model is implemented University of Bergen with a mixed finite element method being used in both Princeton University the matrix and the fracture but with non matching grids. [email protected] Numerical results will be shown.

Jérôme Jaffré MS31 INRIA Paris-Rocquencourt An XFEM Approach for the Simulation of Frac- 94 GS11 Abstracts

tured Porous-Media Systems ation Development of an Offline Water Quality Model Fractured porous-media systems are simulated, where the characteristic flow behaviour depends on the fractures and Puget Sound, (or Salish Sea) a fjordal estuary in Washing- the matrix. The global solution is obtained by splitting ton, has experienced water quality degradation in the form the system into a structured rock-matrix grid and an ar- of harmful algal blooms and hypoxia in recent decades. bitrarily orientated fracture network of codimension one. Given climate change and sea level rise possibilities, there No matching conditions for the two grids are required. A is considerable interest in understanding the current and consistent weak coupling scheme is developed that is based future effects of anthropogenic activities such as coastal on an XFEM approach. development and nutrient loading on circulation and water quality. An unstructured grid multi-scale model of Puget Nicolas Schwenck Sound with a grid size capable of resolving small channels University of Stuttgart near river mouths to coastal open waters and accommo- [email protected] dating complex shoreline geometry, waterways, and islands was set up using finite volume coastal ocean model (FV- Bernd Flemisch COM). To facilitate long-term water quality simulations University of Stuttgart, Germany independent of hydrodynamics, a companion offline water bernd.fl[email protected] linkage code has been developed using FVCOM discretization of the study domain using biogeochemical kinetics Barbara Wohlmuth from CE-QUAL-ICM model. A total of 19 state variables University of Stuttgart are considered including two species of algae, dissolved and [email protected] particulate carbon, and nutrients, as part of the carbon cycle to calculate algal production and decay, and the impact Rainer Helmig on dissolved oxygen. Preliminary model application is pre- IWS, University of Stuttgart, Germany sented in the form of a sensitivity analysis to evaluate the Institut fur Wasserbau effect of alterations to nutrient loads, hydrologic loads, and [email protected] sea level rise on circulation, and dissolved oxygen and algae growth. The effect of hydraulic modifications such as the presence of a floating bridge on flushing time and wa- MS32 ter quality are also examined. The overall objective is to Performance of the Integrally-Coupled, identify whether human sources of nutrients in and around Unstructured-Mesh SWAN+ADCIRC(DG) Model Puget Sound significantly impact ecosystem and if so how much nutrient reduction is necessary to improve ecological The coupling of wave and circulation models is neces- health in sensitive areas. sary to generate waves and surge in deep water, propagate them onto the continental shelf, and dissipate them Tarang Khangaonkar, in complex nearshore systems. In this work, the authors Pacific Northwest Laboratory couple the SWAN and ADCIRC(DG) models and investi- [email protected] gate their performance during a hindcast of Hurricane Ike (2005). The computed circulation is compared between Taeyun Kim,ZhaoqingYang ADCIRC(CG) and ADCIRC(DG), and its differing effects Pacific Northwest National Laboratory on the computed wave solution are examined. [email protected], [email protected]

Joel C. Dietrich Department of Civil Engineering and Geological Sciences MS32 University of Notre Dame Title Not Available at Time of Publication [email protected] Abstract not available at time of publication.

Clint Dawson, Jessica Meixner Ethan Kubatko Institute for Computational Engineering and Sciences Department of Civil and Environmental Engineering University of Texas at Austin The Ohio State University [email protected], [email protected] [email protected] Joannes Westerink, Andrew Kennedy Department of Civil Engineering and Geological Sciences MS32 University of Notre Dame Storm Surge/Inundation Model Inter-Comparisons [email protected], [email protected] via a Super-Regional Test Bed on the U.S. Atlantic and Gulf of Mexico Coasts Rick Luettich University of North Carolina - Moorehead City Abstract not available at time of publication. rick [email protected] Rick Luettich University of North Carolina - Moorehead City Marcel Zijlema, Leo Holthuijsen rick [email protected] Department of Civil Engineering and Geosciences Delft University of Technology [email protected], [email protected] MS33 Designing a Top-down Inversion System Accurate MS32 Enough for Operational Use Response of Puget Sound to Anthropogenic Alter- With California law limiting greenhouse gas emissions GS11 Abstracts 95

(AB32), policy makers will need emission estimates that sitive to treatment of spatial and temporal correlations. In- are much more accurate than are usually achieved by top- creasingly dense observations allow these correlations to be down methods. One particular challenge is that the math- evaluated with more confidence. We present assessments of ematical inversion techniques usually used assume that er- the spatial and temporal correlations in model-data differ- rors in the model and observations are unbiased. How- ences in atmospheric mixing ratios and surface fluxes. We ever, we find that biases have a major impact on retrieved evaluate the importance of quantification of these correla- emissions. We also show how observation networks can be tions in flux estimates and uncertainty assessments, using optimized with respect to multiple constraints. data from North America and from the Midcontinent In- tensive. Philip Cameron-Smith Lawrence Livermore National Laboratories Ken Davis [email protected] Penn State University [email protected] Donald Lucas, Daniel Bergmann Lawrence Livermore National Laboratory Timothy Hilton [email protected], [email protected] The Pennsylvania State University [email protected]

MS33 Thomas Lauvaux What Can We Learn About Fossil Fuel Emissions [email protected] Across North America from a Geostatistical Atmo- the pennsylvania state university spheric CO2 Inversion Using Ground-Based Con- tinuous Measurement Data? Martha Butler, Liza Diaz, Klaus Keller, Natasha Miles, Estimating anthropogenic CO2 emissions from variabil- Scott Richardson ity in atmospheric CO2 concentrations requires separat- The Pennsylvania State University ing out the anthropogenic from the strongly varying bio- [email protected], [email protected], spheric signal. Without the use of expensive C14 mea- [email protected], [email protected], surements, atmospheric CO2 inversions can still provide [email protected] some insight into the quality of inventory-based emission estimates. This talk will present results from a geosta- Arlyn Andrews tistical inversion over North America for 2004 and 2008 NOAA ESRL using continuous ground-based measurement data and a [email protected] Lagrangian atmospheric transport model. This method is unique among inversion setups as it provides the opportu- Nathan Urban nity to a) infer a set of total flux estimates that are com- Princeton University pletely independent of any process-based model output, [email protected] while b) gaining insight into the underlying processes, e.g. by correlating individual sectors from a fossil fuel inventory database with estimated fluxes. The method can also be MS33 used to identify how consistent fossil fuel inventories are Multiscale Spatial Models for Representing CO2 with the atmospheric measurements at larger regions such Emissions as state boundaries. Results also show how the expand- ing continental measurement network helps to further con- While multi-Gaussian models have been successfully used strain and isolate the fossil fuel emission signal across the to represent biospheric CO2 emissions in inversion studies, continent, providing hope for future inversions that will use it is less clear what models may apply for anthropogenic satellite-based data for large regional anthropogenic CO2 emissions. In this talk, we will explore various models budgeting. that employ easily observed covariates like GDP, population density etc to capture spatially variable anthropogenic Sharon Gourdji, Kim Mueller, Vineet Yadav, Abhishek CO2 emission. The dimensionality of the model will be of Chatterjee, Deborah Huntzinger particular interest. The models will be tested using data University of Michigan from fossil-fuel emissions databases for North America. [email protected], [email protected], [email protected], [email protected], Jaideep Ray [email protected] Sandia National Laboratories, Livermore, CA [email protected] Arlyn Andrews NOAA ESRL Sean McKenna [email protected] Sandia National Laboratories Albuquerque, NM Anna Michalak [email protected] University of Michigan [email protected] Bart G. Van Bloemen Waanders Sandia National Laboratories [email protected] MS33 Impacts of Spatial and Temporal Correlations in Regional Atmospheric Inverse Estimates of Green- MS34 house Gas Fluxes Advances in Tsunami Wave Propagation and Inun- High-resolution inversions of greenhouse gas fluxes are sen- 96 GS11 Abstracts

dation Modeling with Adaptive Triangular Meshes Shiva Gopalakrishnan Department of Applied Mathematics Adaptive triangular meshes have proven their suitability Naval Postgraduate School for representing complex bathymetry/topography features [email protected] as well as multi-scale phenomena and interaction. An adaptive tsunami propagation and inundation model using Dimitrios Alevras Galerkin-type numerical approximations has been devel- Hellenic Hydographic Organization oped and validated. In this presentation we introduce the Athens, Greece numerical method and show results of diverse simulations. [email protected] It turns out that the adaptive mesh refinement improves computation time without sacrificing accuracy. MS34 Joern Behrens KlimaCampus, University of Hamburg Computational Challenges in Real-time Tsunami [email protected] Forecasting The next generation tsunami forecast provides estimates MS34 of all critical tsunami parameters (amplitudes, inundation distances, current velocities etc.) based on direct tsunami An Adaptive Approach for the Propagation- observation and model predictions. There are significant Inundation Tsunami Problem challenges in meeting Tsunami Warning Centers opera- When dealing with geophysical problems we encounter tional requirements - speed, accuracy, and user interfaces multi-scale physical phenomena. A very actual exam- that provide guidance that is easy to interpret. Tsunami ple is the tsunami case where a hundred of kilometers modeling methods have matured into a robust technol- characteristic-length waves travel trough the ocean to in- ogy that has proven to be capable of accurate simulations teract with meter-lengths scale coastal topography in the of past tsunamis. However, implementing this technol- process of inundation. One possible approach to solve the ogy into real-time tsunami forecast and warning operations full problem is to discretize the physical domain with the presents significant computational obstacles, including ac- smaller scale resulting in a very inefficient computation due cess to large model database, real-time data assimilation, to the over-resolved tsunami waves. Another possibility real-time model runs etc. The methodology, tools, test re- is to subdivide the physical domain in several single-scale sults, operational implementation and computational chal- problems, solve the equations on each of them from the lenges of the tsunami forecast system are discussed. coarser to the finer scale and connect them using bound- Vasily Titov ary conditions. The problem with this approach is that we obtain a one-way communication pattern, from coarse NOAA/Pacific Marine Environmental Laboratory to fine mesh, which can lead to inaccurate local solutions. 7600 Sand Point Way NE, Bldg.3, Seattle, WA We are working on solving the complete problem following 98115-6349 an adaptive approach. For spatial variability we adjust the [email protected] mesh resolution using unstructured meshes while for time variability we use a local time step approach. We combine MS34 these techniques with an high-order accurate finite volume numerical method. Nonlinearity, Dispersion and Friction in Tsunami Modeling Cristóbal E. Castro KlimaCampus, University of Hamburg Abstract not available at time of publication. [email protected] Ahmet Yalciner METU Department of Civil Engineering MS34 Ocean Engineering Research Center, 06531 Ankara Turkey Tsunami Simulations with DGCOM: A High-order [email protected] Triangular Discontinuous Galerkin Coastal Ocean Model MS35 We describe the development of a triangular high-order Upscaling of Fine Scale Geological Models for Non- discontinuous Galerkin coastal ocean model that is being Linear Flow Simulations developed for modeling tsunamis. The model had previously been used to study the 2004 Indian Ocean tsunami The generalized Forchheimer law is considered for incom- but that version did not have wetting and drying al- pressible and slightly compressible flow filtration in porous gorithms. With wetting and drying algorithms now in media. The resulting system can be rewritten in term of place, we can study the effects of this phenomenon on the non-linear equations for the pressure only, characterized by strengths of the tsunami waves and their impact on the the permeability tensor depending on the pressure gradient shore lines. We will describe our wetting and drying al- norm. In this work we explore the possibility of extending gorithms and discuss extensions to high-order methods as some of the local and extended local linear Darcy upscal- well as describe other types of high-order boundary condi- ing models to the non-linear Forchheimer law. Coarse scale tions (such as non-reflecting types). Finally, we will dis- simulation results are presented. cuss the time-integration strategy being developed for this model including explicit, semi-implicit, and fully-implicit Akif Ibragimov, Eugenio Aulisa time-integrators. Department of Mathematics and Statistics. Texas Tech University Francis X. Giraldo [email protected], [email protected] Naval Postgraduate School [email protected] GS11 Abstracts 97

MS35 criteria are also numerically examined. Uncertainty Quantification for Subsurface Flow Problems using Coarse-scale Models Seong H. Lee Chevron ETC Uncertainty quantification for subsurface flow often re- [email protected] quires flow simulation on multiple geological models. We present an upscaling approach that entails statistical as- Hadi Hajibeygi signment of upscaled functions, and rapidly generates those Institute of Fluid Dynamics functions for multiple models. The goal is to reproduce the ETH Zurich ensemble statistics (e.g., P50, P10 and P90) of the fine- [email protected] scale flow. This differs from most existing upscaling techniques, in which the intent is to reproduce the fine-scale Ivan Lunati solutions on a realization-by-realization basis. University of Lausanne [email protected] Yuguang Chen Chevron Energy Technology Company [email protected] MS36 Modelling of Biofilm Growth and its Influence on MS35 CO2 and Water (two-phase) Flow in Porous Media An Eulerian Joint Velocity-concentration PDF With the aim of aiding experimental design and for feasi- Method for Solute Dispersion in Highly Hetero- bility studies, a numerical model is developed capable of geneous Porous Media simulating the precipitation of calcite in sand or rock samples due to the activity of ureolytic bacteria. The model, In risk analysis applications involving solute dispersion in which is defined on the Darcy scale, accounts for the accu- heterogeneous formations, the knowledge of the concentra- mulation of biofilms, their influence on pH, and the sub- tion probability density function (PDF) at different spa- sequent changes in the properties of the porous medium. tial locations and times is crucial. A new joint velocity- concentration PDF method is proposed that is applicable for highly heterogeneous porous media. The corresponding Rainer Helmig PDF transport equation accounts for advective transport, IWS, University of Stuttgart, Germany pore-scale dispersion, molecular diffusion, and chemical re- Institut fur Wasserbau actions. It is solved numerically using an efficient particle- [email protected] based approach.

Daniel W. Meyer MS36 Institute of Fluid Dynamics GasInvasioninSoftSediments [email protected] We investigate the displacement of one fluid by another in Patrick Jenny a deformable medium with pore-scale disorder. We develop Institute of Fluid Dynamics a model that captures the dynamic pressure redistribution ETH-Zentrum at the invasion front, and the feeback between fluid inva- [email protected] sion and microstructure rearrangement. Our results suggest how to collapse the transition between invasion per- Hamdi Tchelepi colation and viscous fingering in the presence of quenched Petroleum Engineering Department disorder. We predict the emergence of a fracturing pattern Stanford University for sufficiently deformable media, in agreement with obser- [email protected] vations of drainage in granular material, and we identify a dimensionless number that appears to govern the crossover from fingering to fracturing. MS35 Adaptive Error Control in the Multiscale Finite Ran Holtzman, Ruben Juanes Volume Method for Multiphase Flow in Porous MIT Media Civil and Environmental Engineering [email protected], [email protected] The iterative MSFV method is extended to include the sequential fully implicit simulation of time dependent problems that involves a system of pressure-saturation equa- MS36 tions. To control numerical errors in simulation results, Sniffing for Leakage: Trace Gas Sensors and Car- an error estimate, based on the residual of the MSFV ap- bon Sequestration proximate pressure field, is introduced. In the initial time step in simulation, iteration is employed until a specified Trace gas sensors are based on optothermal detection and accuracy in pressure solution is achieved. This initial so- use a modulated laser source and a quartz tuning fork am- lution is then utilized to improve the localization assump- plifier to detect small amounts of gases for disease diag- tion of basis functions at later time steps. Additional it- nosis via breath analysis and monitoring of atmospheric erations in pressure solution are employed only when the pollutants and greenhouse gases. We introduce the first pressure residual becomes larger than a specified thresh- mathematical model of a resonant optothermoacoustic sen- old value. A priori error estimate and control based on sor. The model is solved via the finite element method and pressure-equation residuals are derived to guarantee the couples heat transfer and thermoelastic deformation to de- desired numerical accuracy in saturation solution. Effi- ciency of the adaptive iteration strategy and error control 98 GS11 Abstracts

termine the strength of the generated signal. Equipe SAGE INRIA Rennes Bretagne Atlantique Susan E. Minkoff [email protected] University of Maryland, Baltimore County Dept of Mathematics and Statistics Jocelyne Erhel sminkoff@umbc.edu INRIA-Rennes, France Campus de Beaulieu Noemi Petra [email protected] Institute for Computational Engineering and Sciences University of Texas at Austin Jean-Raynald de Dreuzy [email protected] Geosciences Rennes, UMR6118 CNRS Université de Rennes 1 John W. Zweck [email protected] University of Maryland Baltimore County Mathematics and Statistics Michel Kern [email protected] INRIA [email protected] Anatoliy Kosterev, James Doty Department of Electrical and Computer Engineering Rice University MS37 [email protected], [email protected] Flow and Mechanics in Discrete Fracture-matrix Rock Systems: Hydromechanical Behavior Utiliz- ing an Extended Finite Element Method MS36 Role of Guest Molecule Exchange Kinetics on the This study aims to develop a fully coupled hydromechani- Injectivity of Liquid CO2 into Gas Hydrate Bearing cal model which can more easily treat complex fracture ge- Formations ometries. Our proposed method is based on the extended finite element method (XFEM) to represent fractures as Geologic accumulations of natural gas hydrates hold vast lower dimensional elements for mechanics and solve a cou- organic carbon reserves, potentially meeting global energy pled problem in a monolithic manner. It can improve fea- needs for decades. The principal challenge for this uncon- sibility for meshing and nonlinear analysis. Our numerical ventional energy resources is to develop production tech- study shows the proposed method can produce very similar nologies that minimize energy costs and environmental im- results to the interface element approach. pacts. The CO2-CH4 guest molecule exchange technology hold promise in this regard. Previous numerical simula- Norihiro Watanabe tions using an equilibrium approach predict pore plugging Department of Environmental Informatics upon injecting of CO2. This numerical study considers the Helmholtz Centre for Environmental Research - UFZ impact of exchange kinetics on formation injectivity. [email protected]

Mark D. White Wenqing Wang Paciﬁc Northwest National Laboratory Department of Environmental Informatics [email protected] Helmholtz Centre for Environmental Research [email protected] MS37 Simulation of Transport in 2D Heterogeneous Joshua Taron Porous Media via a Random Walk Particle Track- UFZ ing method [email protected]

We study the transport of an inert species in a 2D het- Olaf Kolditz erogeneous porous medium via a Random Walk Particle Helmholtz Centre for Environmental Research Tracking (RWPT) method. The main objective is to derive [email protected] the macroscopic properties of the transport by the means of Monte-Carlo simulations in large domains. Conditions to reach asymptotic macro-dispersion coefficients will be MS37 given. We will also present our on-going research about PDF Methods for Uncertainty Quantification. the RWPT method in presence of discontinuities within the domain. We obtain the probability density function (PDF) of the distribution of a passive scalar that diffuses in a random Géraldine Pichot velocity field. We derive an explicit map between the veloc- Equipe SAGE ity distribution and the scalar PDF, and determine exact INRIA Rennes Bretagne Atlantique solutions for the PDF of the normalized scalar. This allows [email protected] for the explicit quantification of the impact of diffusion on the evolution of the scalar PDF without recurrence to a Anthony Beaudoin closure approximation in terms of a mixing model. Institut Pprime UniversitédePoitiers Daniel M. Tartakovksy [email protected] University of California, San Diego [email protected] Nadir Soualem Marco Dentz GS11 Abstracts 99

IDAEA Method in CO2 Storage Spanish National Research Council (CSIC) [email protected] Deep saline aquifers hold great capacity for CO2 geosequestration but also have great uncertainty. Streamline Simulations are ideal for fast simulation, as complex 3D MS37 systems are divided into 1D problems. We combine com- Numerical Issues of Two-phase Flows in Heteroge- pressibility and a new phase behaviour algorithm in our neous Media with Full Permeability Tensor simulator, which improves convergence without additional computational cost. Simulations on 10 geological realisa- We consider the water flooding stage of oil recovery when tions following a Huff-and-Puff injection scheme (Otway water is injected into injection wells and pushes oil toward Project) are compared with an industrial simulator with the production wells. We discuss two numerical issues results of 80% of CO2 rendered immobile. of modeling two-phase immiscible flow in heterogeneous porous media with jumping anisotropic permeability ten- Lorena Lazaro Vallejo, Tara LaForce sor. The first issue is the effect of the discrete flux approx- Imperial College London imation on the front behavior and the water breakthrough [email protected], [email protected] time. The second issue is the choice of the efficient solver for algebraic systems produced by the simulator. MS38 Yuri Vassilevski Microporosity Characterization and Representa- Institute of Numerical Mathematics tive 3D Modeling of Tight Gas Sandstones Russian Academy of Sciences [email protected] Accurate representation of geometry has the first order influence on multiphase fluid flow in porous media on all Ivan Kapyrin relevant scales. Existing pore scale network flow models that successfully model granular materials and sandstones Russian Academy of Sciences < . [email protected] of porosity =01 do not capture capillary-pressure behavior characteristic of many tight gas sandstones. We present an image based characterization of microporosity, crucial Kirill Nikitin, Aleksander Danilov for tight porous media, as well as how to incorporate it into Institute of Numerical Mathematics a3Dmodel. Russian Academy of Sciences [email protected], [email protected] Masa Prodanovic University of Texas at Austin Department of Petroleum and Geosystems Engineering MS38 [email protected] Tetrahedral Mesh Generation for Reservoir Simu- lations; Barriers and Opportunities Peter Eichhubl The challenges and opportunities of using tetrahedral University of Texas at Austin meshes as reservoir simulation grids is investigated. In [email protected] contrast to the current industry practices of using corner point grids, tetrahedral meshes are capable of representing Steven Bryant multi-scale geological features efficiently in a completely Department of Petroleum and Geosystems Engineering automated way. The use of these grids opens many oppor- Institute for Computational and Engineering Sciences tunities for building a reservoir simulator that uses mixed steven [email protected] higher order numerical schemes on the tetrahedral grids and the dual control volumes. Edward Wanat, J. Steven Davis ExxonMobil Upstream Research Company Ahmed H. ElSheikh, Jefferson Gomes, Matthew Jackson [email protected], Department of Earth Science and Engineering [email protected] Imperial College London, South Kensington Campus [email protected], [email protected], [email protected] MS38 Mortar Coupling of Pore-scale Models to Reservoir Tara LaForce Simulators; a True Multiscale Approach Imperial College London [email protected] Pore-scale models are useful tools for estimating macroscopic parameters (e.g., permeability), but direct upscal- Gerard Gorman ing could result in misleading values, partly because em- Department of Earth Science and Engineering ployed boundary conditions ignore the impact of surround- Imperial College London, South Kensington Campus ing media. Here, we develop a novel multiscale simulator, [email protected] where pore-scale models are coupled directly with continuum scale models. Continuity of pressures and fluxes are enforced at shared boundaries using finite element mortars. Chris Pain Moreover, we develop priori upscaling techniques that al- Imperial College low for fast coupling between pore-scale models. [email protected] Tie Sun University of Texas at Austin MS38 [email protected] Impact of Geological Uncertainty and Simulation 100 GS11 Abstracts

Matthew Balhoff separable scales. The University of Texas at Austin Department of Petroleum and Geosystems Engineering Ilya D. Mishev balhoff@mail.utexas.edu ExxonMobil Upstream Research Company Department Technical Software Development Yashar Mehmani [email protected] The University of Texas at Austin [email protected] Lijiang Jiang IMA, University of Minnesota [email protected] MS39 Multiscale Mortar Methods for Flow in Heteroge- neous Porous Media MS39 Multiscale Mortar Multipoint Flux Mixed Finite We consider a second order elliptic problem with a het- Element Methods for Flow in Porous Media erogeneous coefficient written in mixed form. We view the domain decomposition method as a multiscale method with We develop a multiscale mortar multipoint flux mixed finite restricted degrees of freedom on the interfaces. We devise element method for flow in porous media. The equations an effective but purely local multiscale method that in- in the coarse elements are discretized on a fine grid scale corporates information from homogenization theory. We by a multipoint flux mixed finite element method that re- also use this decomposition method approach to devise ef- duces to cell-centered finite differences on irregular grids. fective preconditioners that incorporate exact coarse-scale The subdomain grids do not have to match across the in- information to iteratively solve the full fine-scale problem. terfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of Todd Arbogast the mortar space, we derive optimal order convergence on Dept of Math; C1200 the fine scale for both the multiscale pressure and velocity, University of Texas, Austin as well as the coarse scale mortar pressure. The algebraic [email protected] system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that Hailong Xiao is solved using a multiscale flux basis. Numerical exper- ICES iments are presented to confirm the theory and illustrate The University of Texas at Austin the efficiency and flexibility of the method. [email protected] Mary F. Wheeler Center for Subsurface Modeling MS39 University of Texas at Austin Multiscale Mixed FEM for Compressible Flow [email protected]

Multiscale methods have been shown to be a robust and Guangri Xue accurate alternative to traditional upscaling methods for Institute for Computational Engineering and Sciences incompressible ﬂow. We discuss the extension of a multi- University of Texas at Austin scale mixed method to compressible ﬂow, using more than [email protected] one basis function for each coarse face and a residual formulation with a domain-decomposition corrector. Ivan Yotov Univeristy of Pittsburgh Knut-Andreas Lie Department of Mathematics SINTEF ICT, Dept. Applied Mathematics [email protected] [email protected]

MS40 MS39 The Open Porous Media Initiative Mixed Multiscale Finite Volume Methods for Mod- eling of Fluid Flow in Porous Media The Open Porous Media Initiative aims to produce a wide range of simulators for porous media applications. Prin- We develop a framework for constructing mixed multiscale cipal goals include the ability to model relevant industrial finite volume methods for flows in porous media. Some scenarios, easy extensibility, high performance and ease of of the methods developed using the framework are already use. The software uses the DUNE framework, yet effort is known; others are new. New insight is gained for the known made to ensure the reusability of the code within other con- methods and extra flexibility is provided by the new meth- texts. Initial work at SINTEF and IRIS has concentrated ods. This method uses novel multiscale velocity basis func- on simulation of petroleum reserviors. We present an ini- tions that are suited for using global information, which is tial black-oil reservoir simulator and review its capabilites. often needed to improve the accuracy of the multiscale simulations in the case of continuum scales with strong non- local features. The method efficiently captures the small Kristin Flornes effects on a coarse grid. We analyze the new mixed MsFV IRIS, Bergen, Norway and apply it to solve two-phase flow equations in heteroge- [email protected] neous porous media. Numerical examples demonstrate the accuracy and efficiency of the proposed method for mod- Atgeirr Rasmussen eling the flows in porous media with non-separable and SINTEF, Oslo, Norway [email protected] GS11 Abstracts 101

MS40 opments focus, on one hand, on new numerical scheme (ki- Our Software Commons and Where We Can Make netic schemes), and on the other hand, on the validity ex- It Lead Us tension of the classical SWE system for the 1D model by adding speciﬁc source terms. Industrial applications will The global geoscience community is building a new, open, illustrate these developments. software toolbox. Instead of parochial, esoteric, highly- customized and under-maintained applications, we are see- Riadh Ata ing the development of user-friendly platforms, maintained EDF R&D by diverse and geographically widespread groups of aca- [email protected] demics and professionals. The opportunities are growing for collaborative innovation, spontaneous investigation, Nicole Goutal and just plain old fun. To realize this Arcadian dream, the EDF R&D & Saint-Venant Hydraulic Lab. community must learn to value openness, nurture the skills [email protected] to contribute, and embrace new business models. jacques sainte-marie Matt Hall INRIA & Saint-Venant Hydraulic Lab. ConocoPhillips [email protected] [email protected]

MS41 MS40 Immersed Boundary Method for Flood Simulation The Distributed and Unified Numerics Environ- ment DUNE and its Application to Porous Media Failure of dams and levees may lead to catastrophic floods with DuMuX that would cause loss-of-life and damage to urban and rural areas. In this talk we describe a two-dimensional flood The first part presents DUNE, the Distributed and Uni- model based on a first order explicit scheme in which an fied Numerics Environment, a modular toolbox for solv- immersed boundary technique is used to simulate linear ing partial differential equations (PDEs) with grid-based terrain features that cannot be captured by the resolution methods. The underlying idea of DUNE is to create slim of the structured computational grid. The cut-cell bound- interfaces allowing an efficient use of legacy and/or new li- x ary method is also used for providing coupled 1D-2D sim- braries. The second part provides an overview of DuMu , ulation capability. a DUNE-based module for multi-{phase, component, scale, physics, ...} flow and transport in porous media. Mustafa Altinakar, Marcus McGrath NCCHE - University of Mississippi Steffen Müthing [email protected], Institute of Parallel and Distributed Systems [email protected] University of Stuttgart steff[email protected] Edie Miglio Bernd Flemisch Politecnico di Milano (Italy) University of Stuttgart, Germany MOX, Dept. of Mathematics bernd.fl[email protected] [email protected]

MS41 MS40 MATLAB Reservoir Simulation Toolbox High-resolution Modeling of Urban Dam-break Flooding The MATLAB Reservoir Simulation Toolbox provides a Here, we present a modeling study of the Baldwin Hills comprehensive set of routines for developing and interac- dam-break flood (Los-Angeles 1963), whereby inundation tively studying simulation methods for porous media flow is resolved at a spatial and temporal scale of ca. 3 m and on unstructured grids. Emphasising flexibility and gener- 0.1 s, respectively. The ability of the model to correctly ality with respect to grid formats, particularly supporting predict flood extent and streamflow is reported, model sen- hierarchical grids in multiscale methods, MRST promotes sitivities are examined, and the potential to predict damage research and computational experiments on realistic mod- zones is discussed. The results of this study point to a new els. Moreover, being open-source results and frameworks paradigm for urban dam-break flood impact analyses. are accessible to anyone who wishes to reproduce or extend the existing work. brett Sanders Bard Skaflestad Univerity of California, Irvine SINTEF, Oslo, Norway [email protected] bard.skafl[email protected] Jochen Shubert The University of Nottingham MS41 [email protected] Free Surface Flows Modeling of Real Problems: The Electricit-De-France Point of View humberto Gallegos Univerity of California, Irvine Modeling free surface flows is one of the most challeng- [email protected] ing areas for EDF. For its own applications, EDF devel- ops 1D and 2D numerical tools (Telemac and Mascaret) based on the shallow-water equations (SWE). Last devel- 102 GS11 Abstracts

MS41 Department of Mathematics Improvement of the Flood Simulation with MAS- [email protected] CARET using Data Assimilation A data assimilation procedure was implemented on top of MS42 the mono-dimensional hydraulics model MASCARET. The Simulating Multivariate Particle Populations by procedure is two-fold: the BLUE algorithm is used to as- the Quadrature Method of Moments (QMOM) similate river water level observations to correct the upstream flow forcing and also to instantaneously correct the The method of moments (MOM) offers a statistically based water level and discharge. It was shown over a significant approach that tracks only the moments of a multivariate number of flood events for the Adour catchment that the particle population. This makes the method highly effi- two-step data-assimilation procedure improves the simula- cient. The introduction of quadrature in the QMOM gives tion in re-analysis and forecast modes both closure of the moment evolution equations and excellent approximation to distribution properties (physical, Sophie ricci, olivier Thual optical, etc.) in terms of moments. As one example of the CERFACS approach we use particle-resolved simulations of Riemer et [email protected], [email protected] al. [JGR, 2009] to benchmark QMOM accuracy during a bi-variate simulation of the mixing states of soot and sulfate particles undergoing coagulation. This important “ag- MS42 ing” mechanism determines aerosol optical properties and Simulations of a Field of Precipitating Trade-wind cloud condensation nuclei (CCN) concentrations in the at- Cumuli using a Particle-based and Probabilistic mosphere. Several different quadrature schemes are tested. Microphysics Model Coupled with LES: Modeling Gauss and Gauss-Radau quadratures appear to give nested Results and Validation against in-cloud Aircraft lower and upper bounds, respectively, to aerosol mixing Observations rate.SimilaritiesbetweentheQMOMandKalmanfilter- ing will also be discussed. We present results of LES modeling of a field of shallow convective maritime clouds using the so-called RICO set- Robert McGraw up (van Zanten et. al, submitted to J. Adv. Model. Atmospheric Sciences Division Earth Syst., 2010). We use the Super Droplet Method Brookhaven National Lab (Shima et al., Quart. J. Roy. Meteor. Soc., 2009) for [email protected] coupling the non-hydrostatic LES CReSS (Tsuboki and Sakakibara, Quart. J. Roy. Meteor. Soc., 2006) with particle- based simulation resolving explicitly such cloud- MS42 microphysical processes as CCN activation, condensational Parallel Particle Methods for Aerosol Simulation and collisional growth growth of cloud droplets and gravi- tational sedimentation including drizzle and rain precipita- Particle-resolved stochastic models offer unprecedented tion. Model results are compared with simulations employ- levels of detail for aerosol dynamics, but at the ex- ing bulk treatment of cloud microphysics as well as with pense of increased computational cost. To enable fast aircraft observations of cloud-droplet size spectrum during particle-resolved simulation we present several paralleliza- the RICO experiment (Arabas et al., Geophys. Res. Lett., tion strategies, including local mixing-based algorithms 2009). and global particle-request methods, and compare their performance and scaling. All of the parallel algorithms Sylwester J. Arabas considered are approximate, but we prove convergence to Institute of Geophysics the centralized case in appropriate limits. University of Warsaw, Poland [email protected] Matthew West Mechanical Science and Engineering Shin-ichiro Shima University of Illinois at Urbana-Champaign The Earth Simulator Center (ESC), Japan Agency for [email protected] Marine- Earth Science and Technology (JAMSTEC), Yokohama, MS43 JAPAN s [email protected] A Space-Filling-Curve Approach for Parallel Adap- tive Mesh Refinement in Tsunami Simulaton

MS42 Efficient parallel adaptive refinement (AMR), to capture land-ocean boundaries and to dynamically refine along Multiscaling and Approximations for Coagulation propagating wave-fronts, is a performance-critical compo- Processes in High Dimension nent of Tsunami simulation. We present a respective ap- Computing the time evolution of the multi-dimensional size proach for parallel AMR and respective solvers for systems distribution of atmospheric aerosol particles involves many of PDE that is based on recursively structured adaptive tri- computational subcomponents, and one of the more com- angular grids and corresponding element orders using Sier- putationally intense of these is computing the effect of co- pinki space-filling curves. The approach allows for perfor- agulations amongst particles. In this talk, we will discuss mance optimisation w.r.t multiple aspects: minimal mem- several methods of speeding up particle methods by ex- ory requirement, inherently cache efficient processing, as ploiting the multiple timescales in many coagulation sce- well as fast load balancing. Test results are presented for a narios. simple discontinuous Galerkin solver for the shallow water equations. Lee DeVille University of Illinois Michael Bader, Kaveh Rahnema University of Stuttgart GS11 Abstracts 103

Institute of Parallel and Distributed Systems Am Handelshafen 12, 27570 Bremerhaven, Germany [email protected], [email protected] [email protected] Annika Fuchs Csaba Vigh Alfred-Wegener-Institute for Polar and Marine Institut für Informatik [email protected] TU München, Germany [email protected] MS44 New Mathematical Models and Numerical Simula- MS43 tions of Multiphase Flows in Porous Media Includ- Seismic Inversion using Discontinuous Galerkin ing Phase Transitions and Chemical Reactions Methods Abstract not available at time of publication. We present a spectral-element-based Discontinuous Galerkin method to Karl Heinz Hoffmann discretize full wave form seismic inverse problems. The in- Physics Institute verse problem is formulated in a Bayesian framework, and a Technical University of Chemni discretize-then-optimize approach is used to derive the gra- hoff[email protected] dient and Hessian-vector product. A result on the equiva- lence between discretize-then-optimize and optimize-then- discretize will be presented. Finally, primarily results on MS44 full wave Bayesian inversion on massive parallel computers Time-relaxation Methods for Degenerate Trans- demonstrate the capabilities of our approach. port Problems Tan Bui-Thanh, Carsten Burstedde In this talk, we discuss the application of time-relaxation The University of Texas at Austin methods for degenerate transport problem. The work is [email protected], [email protected] motivated by regions in the subsurface where the governing equations change type from hyperbolic to parabolic. This Omar Ghattas, Georg Stadler, Lucas Wilcox occurs, for instance, when fronts move through the un- University of Texas at Austin saturated zone or when material parameters change. Our [email protected], [email protected], findings indicate that can improve results obtained from a [email protected] finite difference or continuous FEM scheme by applying a simple elliptic operator. We give theoretical and numerical evidence to support the use of these operators in legacy MS43 codes. Tsunami Edge Waves and Complex Earthquake Lea Jenkins Rupture Department of Mathematical Sciences Edge waves are a particular type of coastal wave trapped by Clemson University refraction that propagate parallel to the coastline. In com- [email protected] bination with scattering and resonance, edge waves create a complex waveform in which the offshore amplitude, runup, MS44 and timing of the largest wave are difficult to predict using standard numerical methods. Instead, edge waves from A Physics-based Sparsified Solver for Reservoir continental-shelf tsunamis, such as the 2010 Chile event, Simulation areexaminedfromananalyticperspectiveandinrelation In the present work we propose a percolation-based sparsi- to complex rupture models. fication algorithm to solve pressure-based systems arising Eric L. Geist in porous media flow applications. The main idea of this US Geological Survey physics-based strategy is to capture the connectivity lay- [email protected] out or solution paths describing the overall flow process on highly heterogeneous media. The proposed approach has the potential to mitigate the overhead associated with MS43 preconditioner construction and application. Results are Efficient Local Resorting Techniques with Space illustrated on a wide set of field cases arising in black-oil Filling Curves Applied to a Parallel Tsunami Sim- and compositional simulations. ulation Model Hector Klie The OpenMP-parallel model TsunAWI for the simulation ConocoPhillips Company of tsunami propagation and inundation discretizes the shal- [email protected] NC low water equations on an unstructured P1−P1 finite element grid. The data access to the variables on the unstruc- MS44 tured grid is crucial for the computational performance. A reordering of the unknowns at elements, nodes, and edges A Dirichlet-to-Neumann Multigrid Algorithm for along a space filling curve is presented that guarantees data Locally Conservative Methods locality on all levels of the memory hierarchy, thus reducing Discontinuous Galerkin methods and mixed finite element cash misses and false sharing. methods have grown in popularity in recent years with Natalja Rakowsky recent work showing that both methods give rise to lo- Alfred-Wegener-Institute for Polar and Marine Research cally conservative fluxes. In this talk we introduce a novel, physics-based geometric multigrid framework that incorpo- 104 GS11 Abstracts

rates both mixed and DG with optimal convergence prop- material parameters. In this situation dispersive mass-flux erties even in the case of multinumerics and unstructured is often more significant than diffusive processes. We use grids. Theoretical results for symmetric operators will be the empirically extended ideal gas equation to calculate the presented along with numerical results for the both sym- density for mixtures. Gas injection to reservoirs can cause metric and nonsymmetric problems. re-pressurization effects and reservoir temperature can fall significantly according to the Joule - Thomson cooling ef- Tim M. Wildey fect. The energy conservation equation is solved to account The University of Texas at Austin for heat loss due to gas expansion and viscous heat dissipa- Austin, USA tion. In two-phase flow systems density dependent effects [email protected] have to be considered in addition.

Mary F. Wheeler Norbert Böttcher Center for Subsurface Modeling TU Dresden University of Texas at Austin [email protected] [email protected] Ashok Singh UFZ MS45 [email protected] Complex Evolution of Transport Properties in CO2 Infiltrated Coal: Observations and Models Chan-Hee Park KIGAM We explore the evolution of permeability in coal with [email protected] swelling-induced sorption of single and multi-component gases such as CO2, CH4, N2 relative to non-sorbing He. We explore important differences in the sense and timing of Wenqing Wang permeability evolution in porous coals, ubiquitously frac- Department of Environmental Informatics tured coals and in coals containing a distribution of flaws. Helmholtz Centre for Environmental Research We extend these models to follow permeability evolution [email protected] in coals infiltrated by binary mixtures through the application of distributed parameter models. Joshua Taron, Uwe Görke UFZ Derek Elsworth [email protected], [email protected] Penn State University [email protected] Olaf Kolditz Helmholtz Centre for Environmental Research Shugang Wang, Ghazal Izadi, Hemant Kumar [email protected] Energy and Mineral Engineering Penn State University [email protected], [email protected], [email protected] MS45 Multiscale Modeling in the Context of CO2 Storage Jishan Liu, Zhongwei Chen Mechanical Engineering The disparity between laboratory scales and the scale University of Western Australia needed for CO2 storage to be meaningful, makes upscal- [email protected], [email protected] ing and simulation central research components. Here, we look at how coupled physical phenomena impact models at different scales. In particular, we emphasize how the repre- Jonathan Mathews sentation of physical processes changes on different scales Energy and Mineral Engineering within a coupled model. Penn State University [email protected] Jan M. Nordbotten Department of Mathematics Denis Pone University of Bergen ConocoPhillips [email protected] [email protected] MS45 MS45 Modeling the Complex Evolution of Fractured Non-isothermal Flows in Porous Media for CO2 Se- Geothermal Reservoirs questration Applications We develop models for the evolution of fractured geother- Non-isothermal flows in porous media for CO2 sequestra- mal reservoirs where mechanical and chemical responses tion applications Norbert Bttcher, Ashok Singh, Chan-Hee are innately linked. The linkage between mechanics and Park, Wenqing Wang, Joshua Taron, Uwe Grke and Olaf chemistry is shown to progress at a variety of different Kolditz Abstract: This paper deals with non-isothermal timescales depending on diffusional control of the pro- flow effects during carbon dioxide sequestration. We con- cesses. Effective stress effects are immediate, followed by sider two scenarios: (i) the miscible displacement of com- short-term thermal drawdown and the development of hy- pressible natural gases through a layer of the depleted gas droshears. The final stage of evolution involves chemical reservoir by injection of carbon dioxide and (ii) CO2 se- influences and their effect of the hydraulic performance of questration in deep saline aquifers. We consider the real the reservoir. behavior of gaseous mixtures and immiscible fluids through using energy and distance parameters in the calculation of Joshua Taron GS11 Abstracts 105

UFZ localized in space, and this in turn requires very accurate [email protected] simulation codes, as well as an accurate coupling algorithm. The Newton-Krylov method is a globally coupled approach Derek Elsworth that is both robust and accurate. We apply the method, to Penn State University a system including mineral reactions and gas dissolution, [email protected] that is relevant to CO2 storage. Blandine Gueslin Baisheng Zheng, Ghazal Izadi CRI Paris Rocquencourt Energy and Mineral Engineering INRIA France Penn State University [email protected] [email protected], [email protected] Michel Kern MS46 INRIA Anomalous Transport in Heterogeneous Media: [email protected] Broad Heterogeneity Distributions Versus Strong Heterogeneity Correlations MS47 We study mechanisms that can lead to anomalous trans- An Experimental Approach using Stereo Mi- port in quenched random media. Broad disorder point dis- croscope and X-ray Microtomography to Study tributions and strong disorder correlations cause anoma- Changes in Wettability due to Microbial Enhanced lous transport and can lead to the same anomalous scal- Oil Recovery at the Pore-scale inglawsforthecenteredmeanandmeansquaredparticle displacements. The respective mechanisms, however, are The effect of inherent wettability on recovery was studied fundamentally different. This difference is reflected in the within 2D micromodels imaged with stereomicroscopy and spatial particle densities and first passage time distribu- 3D columns imaged with x-ray microtomography. Water- tions, which provide indicators for identifying the origins wet to oil-wet surface ratios were produced in ratios: 1:5, of anomalous transport. 5:5, and 5:1 by treating a fraction of the pore space with octodecylthrichlorosilane, such that the spatial coordinates Marco Dentz of surface wettability are defined. Interfacial curvature, oil IDAEA blob morphology, and additional oil recovered are reported Spanish National Research Council (CSIC) for each mixed-wet system, prior to and after MEOR. [email protected] Dorthe Wildenschild, Ryan T. Armstrong Oregon State University Diogo Bolster [email protected], [email protected] University of Notre Dame [email protected] MS47 MS46 A Heterogeneous Multiscale Method (HMM) for Two-phase Flow in Porous Media Multiscale Finite Elements Methods for High Con- trast Diffusion Problems We present a formulation of heterogeneous multiscale method (HMM) for two phase flow in porous media. Stan- We discuss multiscale finite element methods for elliptic dard macroscopic (Darcy’s Law) equations are augmented problems with high contrast coefficients, arising in flow in with a network flow model on pore (micro) scale. Network a heterogeneous porous medium. For a restricted class of flow model captures flow pathway details true to the porous model problems our method has optimal convergence, in- medium geometry. We exemplify macro-micro iteration for dependent of the geometry and contrast of the PDE coef- two-phase flow in 1D and 2D, as well as using a conceptual ficient. We also present an adaptive variant of the method model of hydraulic fracture propagation. which can be applied to rather general flow problems with similar convergence properties. Experiments on a wide Chia-Chieh Chu range of model problems are presented. University of Texas at Austin [email protected] Ivan G. Graham University of Bath [email protected] Bjorn Engquist UT Austin [email protected] Ray Millward Dept of Mathematical Sciences University of Bath Masa Prodanovic [email protected] University of Texas at Austin Department of Petroleum and Geosystems Engineering [email protected] MS46 Numerical Simulation of Reactive Transport: Ap- Yen-HsiR.Tsai plication to CO2 Storage in Heterogeneous Media University of Texas at Austin, USA [email protected] Coupling transport with geochemistry adds chemical heterogeneity as a new difficulty to the simulation of flow and transport in porous media. Reactive phenomena, such as MS47 precipitation or dissolution of minerals, are usually highly Thermodynamic Equi- 106 GS11 Abstracts

librium In Multiphase Porous Media: Examining Manav Tyagi Equilibria Across Spatial Scales ETH Zurich Institute for Fluid Dynamics Macroscopic formulations for multiphase flow in porous [email protected] media rely on thermodynamics to provide a closure relationship for the capillary pressure. Obtaining a valid macroscopic formulation is contingent on specification of MS48 macroscopic thermodynamics that are defined in a way Numerical Upscaling of Flows in Highly Heteroge- that is consistent with microscopic thermodynamics. This neous Porous Media talk will address the challenges associated with developing a macroscopic definition for capillary pressure by consid- The generalized Stokes equations (called also Brinkman ering equilibration of multiphase systems over a range of equations), spatial scales and their relationship to more general multiphase flow processes. Simulations performed using the −μ u ∇p μκ−1u f, ∇·u in , lattice Boltzmann method will be used to illustrate the dif- Δ + + = =0 Ω ficulties associated with macroscopic averages of capillary pressure and to suggest an appropriate course of action. where μ is the viscosity and κ is the permeability, are used for modeling flows in highly porous media. Motivated by James E. McClure industrial applications of such materials we have developed Department of Environmental Sciences and Engineering a numerical method for comupting flows in heterogeneous University of North Carolina at Chapel Hill highly porous media with complicated internal structure of [email protected] the permeability. We will present a two-scale finite element approximation of Brinkman equations. The method uses Casey Miller two main ingredients: (I) discontinuous Galerkin finite el- University of North Carolina ement method for Stokes equations, proposed and studied casey [email protected] by J. Wang and X. Ye (2007, SINUM, v. 45) and (II) subgrid approximation developed by T. Arbogast for Darcy William G. Gray equations (2004, SINUM, v. 42). A number of numerical University of North Carolina - Chapel Hill examples will be presented to demonstrate the performance [email protected] of the subgrid method and an iterative method based it. Raytcho Lazarov MS47 Math Department/Inst. for scientific Computattion Dynamic Capillary Effects in Unsaturated Flow Texas A&M University Through Deformable Porous Media [email protected]

In recent years, non-equilibrium capillary effects in multi- Joerg Willems phase flow in porous media have been investigated by many RICAM and the University of Linz authors based on experimental work or numerical simula- [email protected] tions. However, all the previous work has been done for the flow in rigid porous media. In this work, we investigate the dynamic capillary effects in deformable porous media using MS48 numerical modeling. We consider 1D consolidation model Multilevel Multiscale Mimetic (M3)Methodfor incorporating the dynamic capillary pressure term, and we Subsurface Transport Problems in Heterogeneous illustrate and discuss the numerical results. Media

Son-Young Yi In our work we develop a multiscale method for modeling The University of Texas at El Paso subsurface contaminant transport within the framework es- [email protected] tablished by the Multilevel Multiscale Mimetic method. In this method a multilevel hierarchy of coarse-scale systems is constructed through a recursive coarsening procedure. MS48 The procedure involves an exact and approximate step and Stochastic Modeling of Complex Multi-phase Flows is locally conservative at all levels. Mimetic Finite Differ- to Link Pore and Darcy Scale Dynamics ence (MFD) method is a basis of this hierarchy. The presence of convection terms along with anisotropic diffusion To simulate complex non-equilibrium multi-phase flow in terms introduce additional challenges for multiscale meth- porous media a Lagrangian modeling framework was de- ods. Possible solutions for different regimes and unsolved vised, which employes computational particles as statistical issues will be presented in this talk. representatives of individual fluid elements. This approach allows to describe certain phenomena in a completely new Konstantin Lipnikov, Daniil Svyatskiy and more natural way. The main advantage, however, is Los Alamos National Laboratory its ability to represent complex joint distributions and to [email protected], [email protected] account for effects of unresolved features, e.g. the evolution of gravity fingers can be described without resolving David Moulton them. Los Alamos National Laboratory Patrick Jenny Applied Mathematics and Plasma Physics Institute of Fluid Dynamics [email protected] ETH-Zentrum [email protected] MS48 Mortar Multiscale Methods for Stokes-Darcy GS11 Abstracts 107

Flows in Irregular Domains visualization.

We study multiscale numerical approximations for the cou- Randall J. LeVeque pled Stokes-Darcy flow system. The equations in the coarse Applied Mathematics Darcy elements (or subdomains) are discretized on a fine University of Washington (Seattle) grid scale by a multipoint flux mixed finite element method [email protected]; [email protected]; rjl@washingt that reduces to cell-centered finite differences on irregular grids. The Stokes subdomains can be discretized by any Marsha Berger stable Stokes elements, including discontinuous Galerkin. Courant Institute of Mathematical Sciences The subdomain grids do not have to match across the inter- New York University faces. Continuity conditions between coarse elements are [email protected] imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of David L. George the mortar space, we derive optimal order convergence on Department of Applied Mathematics the fine scale for the multiscale pressure and velocity. The University of Washington algebraic system is reduced via a non-overlapping domain [email protected] decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illus- Kyle T. Mandli trate the efficiency and flexibility of the method. University of Washington Dept. of Applied Mathematics Ivan Yotov [email protected] Univeristy of Pittsburgh Department of Mathematics [email protected] MS49 DOLFWAVE: a FEniCS Application for Water Danail Vassilev Waves Simulation University of Pittsburgh In this talk, we present DOLFWAVE, i.e., an applica- [email protected] tion for solving surface water waves problems. A class of improved fourth-order Boussinesq-type models to simu- MS49 late the propagation and generation of dispersive waves is derived. To approximate their solutions a continu- Building a Reproducible Research Community: ous/discontinuous Galerkin finite element method with in- Experience of the Madagascar Open-source Project ner penalty terms is proposed. Dissipative effects and wave Madagascar (http://www.ahay.org)isanopen-software generation due to a time dependent varying sea bed are in- project, which has been in existence for nearly 5 years and cluded. To demonstrate the applicability of the numerical has accumulated nearly 100 reproducible research publica- scheme, several test cases are considered. tions, mostly in applied geophysics and reflection seismol- Nuno Lopes ogy. Madagascar is released under the GPL license and Centro de Matemática e Aplicaões Fundamentais, Lisboa developed by a community of two dozen developers spread [email protected] around the world between industry and academia. I will describe the main design principles and the experience of implementing and maintaining a reproducible research dis- Pedro Pereira cipline, which implies integrating computational results, in- Instituto Superior de Engenharia de Lisboa cluding input data and open software code, with scientific [email protected] publications. Reproducible research enables higher levels of scientific scrutiny and collaboration but requires a com- L. Trabucho munity support to provide a continuous maintenance of Faculdade de Ciencias e Tecnologia, reproducible results. Universidade Nova de Lisboa [email protected] Sergey Fomel University of Texas at Austin [email protected] MS49 The Central Role of Geophysics in the Repro- ducible Research Movement MS49 The GeoClaw Software for Depth-averaged Flows I will trace the history of reproducible research in geo- with Adaptive Refinement physics and its subsequent influence in other fields, such as computational harmonic analysis. A comparison of this Many geophysical flow or wave propagation problems can approach to other forms of scientific communication sug- be modeled with two-dimensional depth-averaged equa- gests an urgent need to restructure the current scientific tions, such as shallow water equations. The GeoClaw soft- publication process to encompass the reproducible research ware (www.clawpack.org/geoclaw) has been designed to principles pioneered in geophysics. solve problems of this nature, using high-resolution shock- capturing finite volume methods and handling flow on to- Victoria Stodden pography and dry states, and incorporating AMR to allow Columbia University the efficient solution of large-scale geophysical problems. Statistics This open source software consists of Fortran programs to- [email protected] gether with Python tools for the user interface and flow 108 GS11 Abstracts

MS50 show the benefits of the CUDA implementation with re- Multi-GPU Tsunami Simulation on TSUBAME spect to an OpenMP CPU implementation. GPU Supercomputer Marc de la Asunción One of the most destructive natural disasters on Earth Dpto. Lenguajes y Sistemas Inform is a Tsunami hence the importance of an accurate and ’aticos, ETSIIT early warning. A large-scale ocean-wide Tsunami simula- Universidad de Granada tion is presented utilizing the next-generation technology [email protected] GPGPU to push the envelop speeding up our computing for single and multi-GPU on desktops and Tsubame Super Computer. A highly accurate and conservative numerical MS51 scheme was used with a mesh adaptation for benchmark Moist Thermodynamics in Sound-proof Simulation tests and a real case scenario This presentation will discuss moist simulation applying Marlon R. Arce Acuña atmospheric sound-proof equations. The key issue is that Global Scientific Information and Computing center the phase changes in moist thermodynamics are affected Tokyo Institute of Technology by the temperature and pressure perturbations. In the [email protected] sound-proof system, however, pressure perturbations are not readily available and only the hydrostatically-balanced environmental pressure profile is used in the moist ther- MS50 modynamics. Accuracy of such an approach will be dis- Efficient Shallow Water Simulations on GPUs cussed and illustrated with simple numerical experiments with sound-proof and fully-compressible systems of equa- In this talk, we introduce the shallow water equations and tions. their importance in geosciences, giving an overview of application areas and simulation approaches. The main focus Wojciech Grabowski is on physical phenomena; including flooding, dam breaks, NCAR tsunamis, and storm surges; and we discuss how simula- ’[email protected]’ tions can be mapped to execution on GPUs. We further address precision aspects through validation and verifica- tion, and show that fast single precision calculations can MS51 be sufficient to capture real-world flows. On the Asymptotic Range of Validity of Sound- proof Atmospheric Flow Models Andr’e R. Brodtkorb SINTEF ICT, Department of Applied Mathematics Several versions of sound-proof model equations for atmo- [email protected] spheric flows have been suggested in the past. Ogura and Phillips (1962) assumed a stratification of potential temperature of the order of the Mach numer, M,squared, MS50 which results in the characteristic times of advection and Complex Shallow Water Simulations Through internal gravity waves to be of the same order in M. This Lattice-Boltzmann-Based Mesoscopic Numerical allowed them to adopt classical single-scale asymptotics to Treatment Exploiting Hybrid Compute Nodes eliminate the sound modes and to arrive at their anelastic model equations. However, with M 0.03, one has The talk presents stable and efficient fluid dynamics solvers M 2 1.0e − 3. Potential temperature variations across the based on Lattice-Boltzmann Methods (LBM) for Shallow pressure scale height would be restricted to less than 1 K Water type models. The mesoscopic nature of the LBM is in this regime which is in contrast with realistic values of exploited by modifying its boundary treatment and propa- 30–50 K. In this lecture I will summarize recent efforts gation/collision operators and adapting them to the spec- at systematically justifying sound-proof models for much ified scenario on the particle and/or macroscopic level. stronger stratifications in realistic three time scale asymp- With a slight focus on GPUs, the hardware-oriented de- totic regimes. sign and parallelisation on all levels is addressed – from vectorisation via the multi-core-level up to full (hybrid) Rupert Klein clusters. Freie Universität Berlin [email protected] Markus Geveler Institute for Applied mathematics, TU Dortmund University MS51 Germany Baroclinic Instability in Sound-Proof Global Sim- [email protected] ulations We use an anelastic model, EULAG, to simulate the MS50 growth, propagation, and breaking of planetary waves Improving PVM finite volume schemes using in the baroclinic instability test of Jablonowski and GPUs. Application to shallow flows Williamson. Solutions yield very similar growth rates, dis- turbance amplitudes, and phase speeds during the linear In this work, we extend the PVM finite volume numerical growth regime. After ∼ 8 days, wavebreaking commences, schemes introduced recently by Castro and Fernández for at which point EULAG results begin to depart in some de- non-conservative hyperbolic systems to non-structured tri- tails from those of JW. Nevertheless, general agreement in angular meshes. An efficient GPU implementation using the global structure of the solution remains. the Compute Unified Device Architecture (CUDA) framework has been performed, and applications to two-layer Joseph M. Prusa shallow water systems are carried out. The numerical tests Teraflux Corporation GS11 Abstracts 109

[email protected] research.

William Gutowski Luis Dalguer Iowa State University Swiss Seismological Service, ETH Zurich [email protected] Sonneggstrasse 5, CH-8092 Zurich, Switzerland [email protected]

MS51 Jean P. Ampuero Sound-proof Simulations of Atmospheric Wave California Institute of Technology Phenomena Seismological Laboratory [email protected] We investigate the performance of several sound-proof models, including the anelastic Lipps-Hemler and the pseudo-incompressible Durran nonhydrostatic equations. MS52 Physics wise, our primary interests are with the dynamics Tsunami Simulation and Earthquake Source Iden- of inertia-gravity waves, an important element of weather tification using GeoClaw and climate. Our numerical developments are based on a class of nonoscillatory forward-in-time methods and are GeoClaw (www.clawpack.org/geoclaw) is an open source applicable to global and limited area models. Challeng- software package that solves the shallow water equations ing simulations of atmospheric wave phenomena involve modeling tsunami propagation and inundation using adap- structured-grid and unstructured-mesh discretizations. tive mesh refinement, allowing for rapid simulation of tsunamis from known sources. Recently we have experi- Piotr Smolarkiewicz mented with tsunami source inversion using the GeoClaw NCAR code together with data from NOAA’s DART buoys, which MMM provide real-time data on sea surface elevation as a tsunami [email protected] passes by. The goal is to rapidly estimate the seafloor deformation that caused the tsunami in order to simulate the Joanna Szmelter further propagation of the tsunami. Loughborough University [email protected] David George USGS Cascades Volcano Observatory [email protected] MS52 Rupture Arresting due to 3D Effects in Large Randall J. LeVeque Earthquakes Applied Mathematics University of Washington (Seattle) Large events are originated in large aspect-ratio faults in [email protected]; [email protected]; rjl@washingt which the fault length (L) is very larger than fault width (W). Previous studies (Day, 1982) shows that this kind of fault initially ruptures as a crack-like, but subsequently MS52 the rupture bifurcates into two separate pulses traveling The Discontinuous Galerkin Method for Modeling in opposite directions. When this process occurs in the Dynamic Earthquake Rupture on Complex Faults bi-material case (Dalguer and Day, 2009), it evolves interacting with the normal stress perturbation (characteristics Modelling the dynamics of the earthquake rupture process of bimaterial fault rupture) and under very limited condi- is a key component for physics-based simulation of the slip tions it can lead to unilateral rupture, in which rupture is distribution. For undersea earthquakes the resulting ocean arrested in the non-preferred direction and rupture propa- bottom displacement is crucial for tsunami generation. We gates indefinitely in the preferred direction. Here we con- present the discontinuous Galerkin finite element method tinue the investigation in this direction to further under- for modeling the behaviour of geometrically complicated stand the W effect on rupture propagation. Our numerical faults in realistic subsurface conditions using unstructured investigation in homogeneous fault shows that W takes an tetrahedral meshes. The approach is based on the numer- important role on rupture arresting and the generation of ical solution of the elasto-dynamic waves equation using steady-state pulse-like rupture in strike slip as well as dip- well-established friction laws as internal boundary condi- ping faults due to the arrival of the stopping phases at the tions at element interfaces aligned with the fault plane. rupture front. Rupture velocity depends on W. This dependence leads to slowdown the rupture speed, capable to Martin Kaeser, Christian Pelties arrest the rupture for small Ws. For W/Lc less than 4 and LMU Muenchen 5.3, respectively for strike and dipping faults, rupture is [email protected], arrested, in which Lc is the critical length. At large dis- [email protected] tance, the rupture propagates with a steady-state velocity pulse. In a bimaterial fault, for the same problems, rup- MS52 ture never stops. These results suggest that the bimaterial effects promote rupture and W effects promote rupture ar- Earthquake Dynamics and Potential Tsunamis in resting. When combining W and bimaterial effects, both the Greater Antilles Subduction Zone are competing, and only under some limited conditions uni- Using the 3D finite element method, we model the dynam- lateral rupture originates. In these cases, the W effects ics of potential earthquakes in the Greater Antilles Subduc- successfully arrest the rupture in the non-preferred direction Zone, including the plate boundary thrust fault and tion, while in the preferred direction the bimaterial effect the strike-slip Septentronial and Bunce faults. We find that enhance rupture propagation. Such as effect can also be earthquakes may propagate from the Septentronial fault to significant on tsunami generation, a topic currently under the plate boundary thrust and vice versa; thus, there may 110 GS11 Abstracts

be more routes to a tsunamigenic earthquake than have Division of Mathematical and Computer Sciences & been previously assumed in this region. We will discuss Engineering implications for tsunami generation. King Abdullah University of Science and Technology (KAUST) David D. Oglesby [email protected] Department of Earth Sciences, Univ. of CA, Riverside 900 University Ave. Riverside, CA 92521 Omar Hinai [email protected] ICES University of Texas at Austin Eric L. Geist [email protected] US Geological Survey [email protected] Mary F. Wheeler Center for Subsurface Modeling Uri ten Brink University of Texas at Austin US Geological Survey [email protected] Woods Hole, MA [email protected] MS53 Local Velocity Postprocessing for Multipoint Flux MS53 Methods on General Hexahedra Transient Non-isothermal Fully Coupled Well- bore/Reservoir Modeling In multiphase flow simulations, if one uses a finite volume method with a piecewise constant approximation for the Abstract not available at time of publication. saturation/concentration equation, accurate face velocities are sufficient. For higher order methods such as discon- Zhangxing Chen tinuous Galerkin method with piecewise linears, one needs University of Calgary accurate velocity in the interior gridblocks. In this work, an [email protected] efficient postprocessing technique is developed to get an accurate interior velocity based on an accurate face-velocity MS53 of the multipoint flux approximation method. Enhanced Successive Substituion Algorithm for Mary F. Wheeler Multiphase Flash Calculations Center for Subsurface Modeling University of Texas at Austin Flash calculations are performed billions of times during a [email protected] compositional flow simulation. The reliability of flash calculations greatly affects the robustness of the entire flow simulation. Consequently, reducing its CPU time, as well Guangri Xue as improving its robustness enormously impacts compo- Institute for Computational Engineering and Sciences sitional flow modeling. Anderson Acceleration represents University of Texas at Austin an efficient and elegant approach to enhance these calcu- [email protected] lations. Anderson Acceleration is a general algorithm for enhancing convergence of fixed-point iterations. The idea Ivan Yotov of Anderson acceleration is to take advantage the informa- Univeristy of Pittsburgh tion obtained from multiple previous iterations to better Department of Mathematics predict the next iterate. We do not store all of the pre- [email protected] vious iterates, nor we assign equal weights to all of them, since the early iterates may contain less predictive information. This acceleration approach has been applied to MS53 wide ranges of problems, most notably in computations of A Multiscale Stochastic Framework for Coupled electronic structure. When applied to linear problems, An- Subsurface and Surface Flows derson Acceleration is equivalent to the well-known GM- RES algorithm. We investigate the application of Ander- We discuss a multiscale stochastic framework for uncer- son Acceleration as a method to enhance phase behavior tainty quantification in modeling flow and transport in flash calculations within the framework of reservoir com- surface-subsurface hydrological systems. The governing positional modeling. In particular, we seek to improve the flow equations are the Stokes-Darcy system with Beavers- convergence rate and convergence region of the common Joseph-Saffman interface conditions. The permeability in Successive Substitution algorithm for oil-gas flash. We ob- the Darcy region is stochastic and it is represented with a tain results relating to the Simple Mixing algorithm, a spe- Karhunen-Loève (KL) expansion. The porous media can cial case of Anderson Acceleration, with improved perfor- be statistically non-stationary, which is modeled by differ- mance of the Successive Substitution algorithm. We utilize ent KL expansions in different regions. Statistical moments brute-force investigation to examine convergence behavior of the solution are computed via sparse grid stochastic col- for various initial equilibrium ratios (K-values). We ob- location. The spatial domain is decomposed into a series of serve that the convergence regions appear to widen out for small subdomains (coarse grid) of either Stokes or Darcy certain cases. We also compare this accelerated Succes- type. The flow solution is resolved locally (on each coarse sive Substitution with plain Successive Substitution and element) on a fine grid, allowing for non-matching grids Newton-type iterations, and we discuss its inclusion into an across subdomain interfaces. Coarse scale mortar finite iterative-IMPEC finite-element multiphase computational elements are introduced on the interfaces to approximate flow simulator. the normal stress and impose weakly continuity of flux. The transport equation is discretized via a local discon- Shuyu Sun tinuous Galerkin method. Computational experiments are GS11 Abstracts 111

presented. Xiaoli Liu ExxonMobil Ivan Yotov xiaoli [email protected] Univeristy of Pittsburgh Department of Mathematics [email protected] MS54 Phase Transitions in Coupled Models: Equilibrium Benjamin Ganis and Kinetic Models University of Texas at Austin Center for Subsurface Modeling We consider phase change in multiphase multicomponent [email protected] models in carbon sequestration, hydrate evolution, or black-oil. The phase change from liquid to gas or hydrate Vivette Girault results from a constraint of maximum solubility of a com- University of Paris VI ponent in the prevalent liquid phase. In computations, [email protected] this can be realized in equilibrium. Alternatively, a kinetic model guides the system through phase change on a local time scale via an auxiliary ODE. We discuss advantages Danail Vassilev, Ming Zhong and disadvantages of different approaches. University of Pittsburgh [email protected], [email protected] MPeszynska Oregon State University [email protected] MS54 Thermodynamical Modelling of the Hydrogen Mi- gration in Argillite for a Deep Geological Radioac- MS54 tive Waste Repository - Numerical Validation Modelling Gas Transport in Coalbeds During Pri- mary and Enhanced Methane Recovery We introduce a compressible 2-phases 2-components model of flow in porous media, with vaporisation and gas solu- As both a source and a reservoir rock, coalbeds can be char- bility, based on thermodynamical principles, and consis- acterised by two distinctive porosity systems: a network tent with the any phase state: one single phase (liquid of extensively-distributed natural fractures (termed cleats) or gaseous) or two phases. Synthetic numerical simula- and matrix blocks with a wide-range pore size distribution. tions are presented for validation. They include the three Coal gas is mainly stored by adsorption, primarily in the main problems which appeared in the ANDRA (Radioac- micropores. During methane production, desorbed gas dif- tive waste disposal French Agency) benchmark Couplex- fuses through matrix to enter cleats. This paper presents Gas: phase appearance/disappearance - non equilibrium numerical approaches used for modelling gas transport in of the initial state - very high contrast in materials. coalbeds during both primary and enhanced methane recovery. Alain P. Bourgeat UniversitéLyon1 Ji-Quan Shi, Sevket Durucan UMR CNRS 5208 Imperial College [email protected] [email protected], [email protected]

Magdalena Dymitrowska Institut de Radioprotection et de SretéNucléaire MS55 [email protected] Numerical Simulation of Anomalous Transport in Porous Media Described by Fractional-advection Farid Smai Dispersion Equation IRSN/DSU/SSIAD/BERIS F -92262 Fontenay-aux-Roses cedex,France In the contribution, we present computational studies of [email protected] the fractional-advection dispersion equation containing the fractional-derivative multidirectional diffusion term which can be responsible for anomalous transport effects. Known MS54 justification of this model relies on the relation with the 3-Phase Stability in Methane Hydrates Through Levy stochastic processes. The solution of the model ex- Capillary Inhibition and Pore Water Salinity hibits anisotropic features and variety of interesting phenomena not observed in the Brownian diffusion. Numerical A common view of hydrate systems is that hydrate and solution of the transport equation leads to the linear sys- water are present in the stability zone, gas and water are tems of equations with full matrices which slows down the present below, and gas, liquid and water coexist at their solution process. We couple the transport equation to the interface. However, we show that the three phase region single-phase saturated flow in a heterogeneous medium and can exist over a broad zone through two approaches: 1) study the anomalous contaminant transport in it. gas flow and hydrate solidification elevates salinity; and 2) hydrate and free gas are present in pores of different size Michal Benes due to capillary effects. Department of Mathematics Czech Technical University in Prague Peter B. Flemings [email protected]fi.cvut.cz The University of Texas at Austin Jackson School of Geosciences Tissa H. Illangasekare pfl[email protected] CESEP Colorado School of Mines 112 GS11 Abstracts

[email protected] length of a time step and it is second order accurate for smooth solutions in general. The matrix of the system is determined by the inflow fluxes which results in a M-matrix MS55 yielding favourable stability properties for the scheme. The Application of Level Set Methods for Groundwater method allows large time steps at a fixed spatial grid with- Flow with Free Surface out losing stability and not deteriorating precision. This makes it attractive for practical applications. The scheme Level set methods are popular numerical tools for descrip- is well suited for variable velocity vector fields in higher tion and tracking of moving interfaces in many fields of dimensions and for nonlinear advection-diffusion problems applied mathematics. We present a level set formulation which is documented by a series of numerical experiments. for mathematical model of groundwater flow with free water table that separates the saturated zone from unsatu- Karol Mikula rated one in porous media. The advantage of our level Department of Mathematics set formulation is the possibility to use static (enlarged) Slovak University of Technology computational domain with fixed computational grid for [email protected] the flow equation. The zero pressure boundary conditions defined on the water table are resolved numerically by ap- Mario Ohlberger plications of immersed interface method in the framework Universität Münster of finite volume discretization. The movement of ground- Institut für Numerische und Angewandte Mathematik water table and the extrapolation of physical quantities [email protected] known only on the water table are given by numerical solution of related advection equations. Several numerical experiments will be presented that confirm the accuracy MS56 and the robustness of our level set methods. Numerical Homogenization for Complex Multi- phase Porous Media Flow Peter Frolkovic Department of Mathematics We present a multiscale approach for multiphase porous Slovak University of Technology media flow based on numerical homogenization. The mul- [email protected] tiscale method consists of a pore scale phase-field multiphase flow solver coupled to a macroscopic finite volume solver. The coupling between the solvers is done through a MS55 macroscopic pressure gradient which enters the pore-scale Compact and Stable Discontinuous Galerkin Meth- simulations and averaged microscopic fluxes which are used ods for in the finite volume solver. The method is able to handle Convection-Diffusion Problems arbitrary number of flow phases and allows to include nonlinear effects such as contact angles and surface tension We present a new method, the Compact Discontinu- in a straightforward way. For single phase and simplified ous Galerkin 2 (CDG2) method, for solving nonlinear two-phase flow problems the approach is consistent with convection-diffusion problems. Theoretical results showing existing homogenization results. stability of CDG2 for the heat equation are given, providing explicit bound on any free parameters in the scheme. Lubomir Banas We present numerical tests for different problems, such as Department of Mathematics scalar advection-diffusion equations, two-phase flow , and Heriot-Watt University for compressible Navier-Stokes. We compare SIPG, BR2, [email protected] CDG, CDG2, and LDG in terms of L2-accuracy and CPU time. MS56 Robert Kloefkorn CTRW-based Methodology for Studying the Im- University of Freiburg pact of Heterogeneities on Transport at Multiple [email protected] Scales

Andreas Dedner The advantages offered by a methodology that unifies pore University of Warwick network modeling, CTRW theory and experiment in up- [email protected] scaling solute transport in porous media are presented. Temporal probability density functions of tracer particles Slavko Brdar explain the physical origin of the power-law scaling of dis- University of Freiburg persion coefficient vs. Peclet number. The rich Peclet- [email protected] number dependence of asymptotic dispersion coefficient is predicted from first principles and compares well with experimental data for restricted diffusion, transition, power- MS55 law and mechanical dispersion regimes. However, until the A New Inflow-Implicit/Outflow-Explicit Finite velocity field is fully sampled, transport is non-Gaussian. Volume Method for Solving Variable Velocity Ad- This opens up the question on the nature of dispersion in vection Equations natural systems where the heterogeneities at larger scales significantly increase the range of velocities in the reser- We discuss a new method for solving non-stationary advec- voir, thus delaying approach to Gaussian behaviour. To tion equations. The method is based on finite volume space describe it, the multi-scale approach is used in which trans- discretization and a semi-implicit discretization in time. Its port at core, gridblock and field scale is viewed as a series basic idea is that outflow from a cell is treated explicitly of particle transitions between discrete nodes governed by while inflow is treated implicitly. The method is exact for probability distributions. At each scale of interest a distri- constant velocity transport of quadratic functions for any bution that represents transport physics (and heterogene- GS11 Abstracts 113

ity) is used as an input to model a subsequent reservoir of the simulations, the local information are averaged us- scale. Statistically rare events such as an encounter with ing moving window averaging to obtain the Darcy-scale a low velocity zone, have an especially large effect on the entities, required for analysis of the Darcy-scale formula- plume transport. The cause of anomalous behavior is the tions. c) Defining the Darcy-scale parameters: this post- broad spectrum of rates or transition times engendered by processing step involves determination of the parameters the heterogeneities. introduced in extended two-phase flow equations using the data obtained in the previous step. The relations derived Branko Bijeljic in this step can be incorporated in continuum-scale simu- Department of Earth Science and Engineering lators for two-phase flow in porous media to model large Imperial College London scale domains. [email protected] Vahid Joekar-Niasar Martin Blunt Department of Earth Sciences Dept. Earth Science and Engineering University of Utrecht Imperial College London [email protected] [email protected] S. Majid Hassanizadeh Matthew Rhodes Utrecht University Chevron North Sea Ltd [email protected] Chevron Energy Technology Company [email protected] MS57 Mixed Multiscale Finite Element Methods for MS56 Two-phase Flow in High-contrast Porous Media Unstable Displacements in Multiphase Flow in Porous Media: Continuum Modeling and Simula- The simulation of fluid flow in fractured rock is challenging tion Challenges due to the high contrast in the permeability. We present a mixed multiscale finite element method with a coarse-scale Continuum modeling of wetting phenomena is important approximation space which captures fine-scale effects of in many scientific and engineering applications, from mi- flows in such high-contrast applications. The coarse space crofluidics and multiphase flow to flow and transport in is related to a domain decomposition method designed for permeable media. Here we discuss the development of preconditioning the fine-scale problem. We demonstrate phase-field models of multiphase flow, with particular em- the effectiveness of our approach with numerical examples phasis on viscous-unstable displacements. The proposed and discuss the use of these coarse spaces in precondition- model is used to simulate the transport of a passive scalar ing of mixed finite element methods. through one of the fluids. We show that viscous fingering instabilities enhance mixing at low Reynolds numbers, and Dylan Copeland discuss the discretization techniques used in our simula- Texas A&M University tions. [email protected]

Luis Cueto-Felgueroso, Ruben Juanes Yalchin Efendiev MIT Dept of Mathematics Civil and Environmental Engineering Texas A&M University [email protected], [email protected] [email protected]

MS56 MS57 Analysis and Parameterization of Continuum-Scale A Multiscale Preconditioner for Nonlinear Multi- Theories using Pore-Network Models- Application physics Problems in Porous Media for Non-equilibrium Capillarity Theories The mortar mixed finite element method can be viewed Among different numerical and experimental methods as a multiscale method, with recent developments showing for investigation of flow and transport in porous me- that the construction of a multiscale flux basis can greatly dia, pore-scale simulators are of great importance due reduce the computational cost for the domain decompo- to their detailed physical-based structure compared to sition problem. Computing this multiscale basis can be the continuum-scale models as well as their inexpen- expensive, but we show that the basis does not need to be sive tractability compared to the laboratorial methods. recomputed for each time step if used as a preconditioner. Although there are different pore-scale simulators such This approach can also be extended to nonlinear interface as Lattice Boltzmann, smoothed particle hydrodynamics, problems and we provide numerical results illustrating the level set, etc., pore-network models are still the most efficiency of this technique on fully implicit formulations extensively-used approach due to their rather inexpensive for multiphase flow. computational cost that allows simulating larger domains. We have employed dynamic pore-network modelling to Gergina Pencheva,BenGanis analyse the non-equilibrium capillarity effects in porous University of Texas at Austin media and parameterize the phenomena for continuum- [email protected], [email protected] scale models. This study is fulfilled in three steps: a) Pore- scale simulation of two-phase flow: using a dynamic pore- Tim M. Wildey network simulator, DYPOSIT, two-phase drainage process The University of Texas at Austin in a conceptual porous medium is simulated under Dirich- Austin, USA let boundary conditions. b) Averaging the pore-scale infor- [email protected] mation to obtain the Darcy-scale entities: after fulfillment 114 GS11 Abstracts

Mary F. Wheeler MS58 Center for Subsurface Modeling Unstructured Hybrid Element Meshing for Reser- University of Texas at Austin voir Simulation [email protected] Although popular in civil engineering, fully unstructured Ivan Yotov finite-element meshing is rarely used in reservoir simula- Univeristy of Pittsburgh tion. Critics argue that it is too complicated to apply to Department of Mathematics geologic structures. Here, we show that it is feasible and [email protected] has many advantages over structured gridding. We present a workflow including indirect meshing strategies for large aspect ratio features like faults and fractures. When this MS57 discretization is permitted by the physics of interest we also Two-Stage Algebraic Multiscale Linear Solver for use lower dimensional finite-element representations. Flow in Highly Heterogeneous Formations Stephan K. Matthai We address two aspects that pose a serious challenge Montan University of Leoben to existing multiscale finite-volume formulations, namely, Leoben, Austria channel-like features and strongly anisotropic transmissi- [email protected] bility. We describe a Two-stage Algebraic Multiscale Solver (TAMS) for the pressure linear system. One stage deals Julian Mindel with a global coarse-grid problem and the second stage uses Montan University of Leoben, Austria a local preconditioner on the fine-grid. TAMS converges to [email protected] the fine-grid solution efficiently in those challenging cases and guarantees conservation after every iteration. MS58 Hamdi Tchelepi On Reservoir Gridding for Assessment of Struc- Petroleum Engineering Department tural Uncertainty Stanford University [email protected] Structural uncertainty refers to uncertainties of the structural framework; i.e. position, orientation, shape and trun- Hui Zhou cations of geological faults and horizons. Structural un- Stanford Univ. certainty is in general a major uncertainty in the sub- [email protected] surface description, but has been cumbersome to assess explicitly. We will discuss and exemplify limitations of the industry standard for 3D gridding with respect to geomet- MS58 ric representation the structural framework. Moreover, we On The Tyranny Of Corner Point Grids will present methodology for parametric updating of the structural-framework representation in 3D grids. The corner point grid is ubiquitous in the petroleum industry. It is used to represent reservoir structure and Vegard R. Stenerud, Oddvar Lia faults, reservoir stratigraphy and layering, and static and Statoil ASA dynamic properties on the grid. A corner point grid has [email protected], [email protected] three main characteristics: geometry, topology, and transformed transport properties. Of these three characteristics, we will provide examples of the limitations of each, and de- MS59 scribe how the topology of the grid is typically the most Computational Infrastructure for Geodynamics restrictive aspect of the description. Scientific computation has long played a key role in solid Michael J. King Earth geosciences; quantitative numerical models provide Texas A&M University a critical link between observations at Earth’s surface and [email protected] dynamic processes in the interior. With increases in computational power and sophistication of algorithms, solid Earth geoscience has seen a proliferation of powerful and MS58 predictive models for these problems. Targets for devel- Simple Grid Generation Algorithms for Fractured opment include models that leverage algorithmic advances Porous Media to enable exploration of the fundamental interactions between the different Earth systems. Such coupled, inter- This talk describes grid generation algorithms for fractured disciplinary problems are becoming a target of research in porous media. Unlike gridding techniques designed for in- solid Earth geodynamics. Examples include the interac- put geometry that is known precisely, our approach for tion of the lithosphere, plate boundaries and the deeper fractures is designed to only capture details of the fracture mantle, the role of fluids in lithospheric deformation, the network geometry larger than the specified grid resolution. behavior of faults in the crust, and long-term thermal evo- The final grids honor fractures approximately while main- lution of the planet. To improve our understanding of these taining good cell quality. Several numerical examples are problems using scientific computation, the Computational presented in two and three dimensions that demonstrate Infrastructure for Geodynamics (CIG) was established as that the algorithms are robust and practical for industrial a community partnership between geophysics and compu- applications. tational science. CIG provides advanced computational tools to the geoscience community, to enable geoscientists Brad Mallison to more effectively explore and understand the dynamics of Chevron Energy Tech. Co. our planet. This talk will discuss mathematical and com- [email protected] putational issues and directions for development in com- GS11 Abstracts 115

putational geodynamics at CIG. to consider their inﬂuence on the system.

Louise Kellogg Louis Moresi Department of Geology School of Mathematical Sciences University of California Davis Monash University [email protected] [email protected]

MS59 MS60 Thermomechanics of Mid-ocean Ridge Segmenta- Optimization Techniques for Triangular Adaptive tion Mesh Refinement Abstract not available at time of publication. The simulation of many geophysical problems comprises a large range of spatial and temporal scales. In computing Luc Lavier the effect of mixing on cloud evolution, the typical cloud Institute For Geophysics cluster length scale tens of kilometers, while accurate mix- University of Texas Austin ing is modeled with spatial resolution of approx. a meter. [email protected] In order to numerically bridge this span of scales, adaptive mesh refinement (AMR) methods play an important role. This presentation introduces recent advances in optimizing MS59 these methods. Generation and Extraction of Magma: A Multi- scale, Multiphysics Geodynamics Problem Joern Behrens KlimaCampus, University of Hamburg Upscaling algorithms and robust multiphysics solvers are [email protected] key to model the generation and extraction of melt. Heat and chemical exchange are present from grain to plate Oliver Kunst scale. Self-organization produces channels but their inter- KlimaCampus action with large-scale structures and their time evolution University of Hamburg are yet unknown. Can they result in magma chambers? [email protected] Viscosity contrasts of 1020 arepresent.Dikeintrusions occurs at much shorter time scale than mantle flow yet represent the final stage of melt delivery. MS60 Laurent Montesi A High-order Adaptive Global Shallow Water Department of Geology Model University of Maryland Unstructured meshes are becoming more and more popular [email protected] in geophysical flow models. We present a two-dimensional model solving the shallow water equations on unstructured MS59 meshes. The latter is dynamically adapted using the AMR technique to minimize the discretization error. The inter- Emerging Geodynamic Computational Techniques polation order is also adapted during the solution process. at the Victoria Partnership for Advanced Comput- Classical test cases on the sphere are used to validate the ing model, as well as the global simulation of the 2010 tsunami I will survey the parallel implementation of the particle-in- in Chile. cell finite element code, Underworld, and explain how the Sébastien Blaise methodology was designed to attack specific geodynam- National Center for Atmospheric Research ics problems. I will give an overview of the relationship [email protected] between this method and other particle-based approaches and show discuss the relative merits of this method (including its disadvantages). By tracking representative material MS60 points, the method is able to take account of the strong, An Adaptive Discontinuous Galerkin Method for history-dependent material non-linearities and fabric de- Modeling the Compressible, 2D Navier-Stokes velopment which emerge during large-scale deformation Equations and accompanying localisation. Underlying the method is a standard finite element engine which relies on a ro- Theoretical understanding and numerical modeling of at- bust, implicit multigrid-method to solve the stress-balance mospheric moist convection still pose great challenges to equations for incompressible, Stokes’ flow. The method meteorological research. The present work addresses the allows for the tracking of sharp material interfaces, dis- following question: How important is mixing between continuities and strong localisation which, in turn, creates cloudy and environmental air for the development of a very large variations in material properties. Careful tun- cumulus cloud? A Direct Numerical Simulation of a sin- ing of the solvers is required to develop efficient, scalable gle cloud is way beyond the capacity of today’s comput- parallel solvers that can also cope with these variations in ing power. The use of a Large Eddy Simulation in com- a robust manner. Application areas for Underworld typi- bination with semi-implicit time-integration and adaptive cally range from the crustal scale deformation and evolu- techniques offers a significant reduction of complexity. So tion of basins, studies of subduction zone dynamics and far this work is restricted to two-dimensional geometry. orogeny, to regional mantle convection simulations with The compressible Navier-Stokes equations are discretized many tens to hundreds of thousands of time-steps. The using a discontinuous Galerkin method introduced by Gi- method is also useful for transferring geological structural raldo and Warburton in 2008. Time integration is done models into thermal-mechanical models since it is not nec- by a semi-implicit backward difference from Restelli and essary to mesh all interfaces and structures exactly in order 116 GS11 Abstracts

Giraldo (2008). For the first time we combine these nu- manner. At the core of the algorithm, low-rank interac- merical methods with an h-adaptive grid refinement. This tions are updated in a hierarchical fashion up and down refinement of our triangular grid is implemented with the quadtrees. We review the method, its expected accuracy, function library AMATOS and uses a space filling curve ap- and applications to synthetic aperture radar imaging and proach (Behrens, 2005). Validation through different test wave propagation for geophysical applications. Joint work cases shows very good agreement between the current re- with Matt Ferrara, Nick Maxwell, and Lexing Ying. sults and those from the literature. For comparing different adaptivity setups we developed a new qualitative error Laurent Demanet measure for the simulation of warm air bubbles. With the Mathematics, MIT help of this criterion we show that the simulation of a rising [email protected] warm air bubble on a locally refined grid can be four times faster than a similar computation on a uniform mesh with the same accuracy. MS61 Homogenization of Wave Equations with Non- Andreas Müller separated Scales Institute for Atmospheric Physics Mainz University We consider the numerical homogenization of acoustic [email protected] wave equations (and elastodynamics equations) with heterogeneous coefficients, namely, when the bulk modulus Jörn Behrens (elasticity tensor) and the density of the medium are only KlimaCampus bounded. We show that if source terms, boundary condi- University Hamburg tions and initial conditions are (integrable) regular enough [email protected] then, eigenvectors associated with large frequencies are only weakly excited, and it is possible to homogenize the original problem. This homogenization is made possible, Francis X. Giraldo not by ergodicity assumptions, but by the observation that, Naval Postgraduate School if the source terms are in the unit ball of L2 (instead of [email protected] H −1), then the solution space is compact in H 1,with respect to the H 1-norm. Various parts of this talk are Volkmar Wirth joint work with L. Zhang, L. Berlyand, M. Desbrun, L. Institute for Atmospheric Physics Kharevych and P. Mullen. Mainz University [email protected] Houman Owhadi Applied Mathematics Caltech MS60 [email protected] A h-p Adaptive Simulation Environment for Atmo- spheric Sciences MS61 We present a framework aimed at problems arising in the Upscaling Finite Element Methods for Wave Prop- geosciences: it can solve the non-hydrostatic equations of agation the atmosphere, shallow-water problems, tsunami prediction and advection tests. The DG method is employed, Materials such as rock and disordered composites tend to however, any element based discretization can be sup- exhibit heterogeneity at many (ideally, a continuum) of ported. A mesh database enables parallel non-conforming scales. Recently, Owhadi has expanded upon a change- mesh refinements in both h-p. Modern coding techniques of-variables interpretation of homogenization, introduced are employed. The latter permit the seamless optimization by Kozlov, to devise accurate upscaling methods for some of compute kernels: SSE vector type are now supported wave propagation (and other) problems in the presence of but could be extended to GPUs. a scale continuum. Binford has pointed out the relation between these ideas and immersed interface methods. We Amik St Cyr review these concepts and discuss extension to discontinu- Institute for Mathematics Applied to Geosciences , ous Galerkin methods. NCAR , 1850 Table Mesa Drive, Boulder CO 80305, USA. [email protected] William Symes, Xin Wang Rice University Sébastien Blaise [email protected], [email protected] National Center for Atmospheric Research [email protected] MS61 David Hall Multiscale Aspects of Waveform Mismatch Mea- National Center for Atmospheric Research surements 1850 Table Mesa Drive, Boulder CO 80305 We consider the inference of medium velocity from trans- [email protected] mitted acoustic waves. Typically, the measurements are done in a narrow frequency band. As a result the sensitiv- MS61 ity of the data with respect to velocity perturbations varies dramatically with the scale of the perturbation. ‘Smooth’ The Butterfly Algorithm for Radar Imaging and perturbations will cause a phase shift, whereas perturba- Wave Propagation tions that vary on the wavelength-scale cause amplitude The butterfly algorithm is a robust alternative to the FFT variations. We investigate how to incorporate this scale for computing oscillatory integrals in a fast and accurate dependent behavior in the formulation of the inverse prob- GS11 Abstracts 117

lem. voirs

Tristan van Leeuwen The uncertainty based optimization for multiple realiza- Department of Earth and Ocean Science tions in reservoir modeling is a promising approach for University of British Columbia, Vancouver BC Canada efficient management of depleting hydrocarbon reserves. [email protected] The application is computationally intensive, multidisci- plinary and require proprietary standard data security. From the success through the TIGRE [Vadapalli et al. MS62 2008] project in supporting these requirements, we have Black-box Optimization in the Oil Industry created the Petroleum Engineering Grid (PEGrid) for fos- tering industry-academia-government partnerships. The Many optimization problems found in oil industry applica- promise and scope of this effort will be presented. tions present nonlinear cost function and constraints, both very often based on reservoir flow simulations. Because in Ravi Vadapalli many occasions the simulation code is not easily accessi- Texas Tech University ble, the use of invasive methodologies can be troublesome. [email protected] In this talk we will describe a number of general black- box optimization algorithms, and we will illustrate these Alan Sill approaches by a number of example cases with practical High Performance Computing Center relevance in the oil and gas industry. Texas Tech University [email protected] David Echeverria Ciaurri Stanford University [email protected] Shameem Siddiqui Department of Petroleum Engineering Texas Tech University Obiajulu J Isebor [email protected] Stanford University Department of Energy Resources Engineering [email protected] Mohamed Soliman Department of Petroleum Engineering Texas Tech University, Lubbock, TX 79409-3111 Louis J Durlofsky [email protected] Department of Energy Resources Engineering Stanford University [email protected] Franz Deimbacher Schlumberger Information Solutions Houston, TX MS62 [email protected] Modeling the Injectivity-Gap Problem in the Well- bore during CO2 Injection into Low Pressure MS63 Reservoirs Current Research in Heavy Oil Modeling Depleted gas reservoirs are appealing targets for CO2 sequestration and EGR. Low abundant pressure is advanta- While mathematical modeling has been successful in the geous but injection process is challenging. Injecting CO2 recovery of conventional oil, it is still in the early stage in liquid phase may lead to dry-ice or hydrate formation. of heavy oil modeling. As conventional oil reserves dwin- Published studies that use outflow performance tools with- dle and oil prices rise, heavy oil is now the center stage. out integration with the reservoir model may not be repre- Enhanced heavy oil recovery methods are an intensive re- sentative. In this work, we provide a comprehensive study search area in the oil industry, and have recently generated to model CO2 flow in the wellbore and the reservoir taking a battery of recovery methodsinwhatisthelargestgrow- into account the proper thermodynamics. ing sector of this industry, such as steam assisted gravity drainage (SAGD) and cyclic steam stimulation (CSS). Hussein Hoteit However, the environmental impacts of these processes and Conocophillips the use of a high volume of water and natural gas suggest [email protected] that extensive research is required for economic and en- vironmentally friendly development of heavy oil reserves. This presentation will give an overview on current research MS62 in heavy oil modeling, and the presenter will also describe Recent Advances in Closed-loop Reservoir Man- his current research program. agement Zhangxin Chen Abstract not available at time of publication. University of Calgary [email protected] Jan Dirk Jansen Delft University of Technology, and Shell Exploration and Production MS63 [email protected] Simulations of Commercial-scale Polymer Injection using a Parallel Computational Framework MS62 A comprehensive polymer flow model has been imple- Demonstration of the PEGrid Environment for Un- mented in the multiphase flow and reactive module of par- certainty Based Optimization of Subsurface Reser- allel reservoir simulator (IPARS). An efficient time splitting algorithm is used to solve the flow and transport equa- 118 GS11 Abstracts

tions independently. Large commercial scale polymerflood MS64 simulations are performed on multiple processors. The re- Discretisation Issues Related to Tensorial Relative sults of polymer flood simulations in heterogeneous reser- Permeabilities voirs and parallel scalability will be presented. The impact of grid sizes on polymer rheology near injection wells will For simulations of flow of transport in porous media, the be discussed. mobility term is commonly modeled as a scalar quantity, and it is treated by upstream weighting. However, tensorial Mojdeh Delshad relative permeability fields (and thus tensorial mobilities) Department of Petroleum and Geosystems Engineering in general arise on all scales, as is seen in both labora- The University of Texas at Austin tory and field experiments. Here, we discuss the impact [email protected] of tensorial relative permeability fields on control volume schemes, and propose new discretisation approaches for the Changli Yuan equations. Center for Subsurface Modeling The University of Texas at Austin Eirik Keilegavlen [email protected] University of Bergen [email protected] Mary F. Wheeler Center for Subsurface Modeling Annette Stephansen University of Texas at Austin CIPR / University of Bergen [email protected] [email protected]

Jan M. Nordbotten MS63 Department of Mathematics Large Scale Reservoir Simulation University of Bergen [email protected] Giant reservoirs of Middle East contain substantial por- tion of the worlds total hydrocarbons. Accurate simulation of these reservoirs requires as many as billion cells. MS64 This is needed to obtain accurate numerical solution and Optimal Flux Allocation for Streamline Simulation also utilize the available vast amount of seismic and engineering data( measurements).A billion cell parallel reser- Streamline simulation has gained acceptance in modern voir simulator was presented in 2009.This paper discusses reservoir flow simulation, its principal benefit being reduc- new cases as well as new methods to build and analyze large ing the three-dimensional transport problem into a set of reservoir models using technologies from the other indus- independent one-dimensional problems. A critical step in tries. Numerical examples include utilization of a fully im- streamline simulation is the assignment of the cumulative plicit, black oil dual, porosity dual permeability billion cell well flux to individual streamlines. The current approach reservoir simulator on worlds largest oil reservoir. Parallel generally introduces mass balance errors. In this work, performance, scalability and distribution of computational we explore optimizing the flux allocation so as to mini- work are discussed. Numerical accuracy, effect of grid size mize these errors. We apply our new approach to two- on the results as well as parallel scalability is presented. dimensional multi-well examples Growth of model size in time and future computational demand, projected new computing platforms for the giant Gunilla Kreiss reservoir models are discussed. In addition to the numeri- University of Uppsala, Sweden cal aspects, presentation will cover the usage of 3-D spatial [email protected] computing based visualization with hand gestures to build and analyze giant models. Discussion will also cover uti- Marco Thiele lization of sound in model building and analyzing. Streamsim Technologies/Stanford University [email protected] Ali H. Dogru Saudi Aramco Oil Co. Margot Gerritsen [email protected] Dept of Petroleum Engineering Stanford University MS63 [email protected] Domain Decomposition Approaches for Modeling Multiphysics Multiphase Flow in Porous Media Brad Mallison Chevron Energy Tech. Co. In this presentation we discuss applying algorithms based [email protected] on domain decompositions for treating multiphysics, multiscale multiphase flow in porous media. Applications include contaminant transport, carbon sequestration and MS64 polymer flooding. Using Helmholtz Decomposition to Optimize Nu- merical Methods for Transport in Porous Media Mary F. Wheeler Center for Subsurface Modeling We investigate the use of Helmholtz decomposition to con- University of Texas at Austin struct a fast solver for the transport equation. Our method [email protected] is based on separating the dynamics into different parts with different qualitative features. For each part we adapt the numerical method to effectively exploit specific features of this part. Then the solvers are combined to a solver for GS11 Abstracts 119

the complete system. The last part can be done for exam- MS65 ple by using our solvers as preconditioners for a traditional Hyperbolic Models for Two-phase Flows with Dis- method or in an operator splitting framework. The aim of continuous Capillary Pressure Fields this work is to demonstrate the use of Helmholtz decomposition in this setting. We consider an immiscible incompressible two-phase flow within a one dimensional porous medium made of two dif- Halvor M. Nilsen ferent rocks. The capillary pressure is supposed to be con- SINTEF stant in each subdomain, but is not neglected at the in- Oslo terface between both rocks. We show that the qualitative [email protected] behaviour of the corresponding hyperbolic scalar conservation law with discontinuous flux function depends strongly Jostein R. Natvig on the orientation of the gravity with respect to the cap- SINTEF IKT illarity at the interface. A convergent numerical scheme is [email protected] then proposed to approximate the unique solution to the problem. Knut-Andreas Lie SINTEF ICT, Dept. Applied Mathematics Clément Cancès [email protected] Lab. Jacques-Louis Lions Paris 5ème, France [email protected] MS64 Numerical Methods for Coupled Flow and Trans- MS65 port Physical Continuity Conditions in HMFE Approxi- Simulation of coupled phenomena in subsurface sciences mation for Compositional Two-Phase Flow in Het- is a challenge of complexity, both modeling and compu- erogeneous Porous Media tational. Despite inevitable simplifying assumptions, the mathematical model should faithfully represent coupled A key point in modeling phase transition in multiphase processes, domains, phases, and components. A compu- compositional flow is the choice of main variables for solv- tational algorithm that maintains these couplings at all ing the resulting system of PDEs. Unfortunately, in the intermediate steps is unlikely to be practical for large-scale case of heterogeneous porous media, the ideal choice of problems. It is crucial to construct ‘smart’, robust algo- variables for describing phase transitions is not the best rithms that first decouple judiciously at intermediate steps, for ensuring physical continuity conditions. We present a in order to perform efficient computations on parts of the modification of the generalized HMFE approximation to larger system, and then restore couplings upon iterative handle this difficulty. convergence. Such algorithms would attempt to find sub- Peter Knabner systems that are weakly coupled in the full system, so that Friedrich-Alexander University Erlangen-Nurenberg, neglecting these couplings in intermediate iterations would Germany degrade convergence of the full system as little as possi- Department of Mathematics ble. The talk will present some examples that can serve as [email protected] background for later presentations in this minisymposium. Estelle Marchand Thomas F. Russell Department Mathematik, AM1 National Science Foundation Friedrich-Alexander-Universitaet Erlangen-Nuernberg Ofc. of Integrative Activities [email protected] [email protected] MS65 MS65 Generalized HMFE Approximation for Composi- Modeling Hydrogen-water Flow with Hydrogen tional Two-Phase Flow Dissolution as a Problem with Complementarity Constraints Two-phase two-components flow with phase-exchange is considered. The presented model is reduced to a system of In an underground nuclear waste disposal hydrogen will be two conservation PDEs. Two main unknown fields x,y are produced by the corrosion of the waste packets. This hy- chosen and all state variables are locally recovered from x drogen migrates with the underground water flow and is and y by solving a double-complementarity problem. The partially dissolved. The problem is modeled as a water-gas fluxes can be eliminated explicitely and static condensa- flow nonlinear system of PDEs with complementarity con- tion leads to a nonlinear system of equations dependent on straints. A nonsmooth Newton method is applied to solve Lagrange multipliers for x,y at each time step. our system. This method can be regarded as an Active set strategy. Numerical examples will be presented to show Torsten Mueller the ability of our solver. University of Erlangen-Nuremberg Department of Mathematics Ibtihel Ben Gharbia,Jérôme Jaffré, Jean Charles Gilbert [email protected] INRIA-Rocquencourt ibtihel.ben [email protected], Jerome.Jaff[email protected], jean- [email protected] MS66 Development of Upscaling Techniques for General- 120 GS11 Abstracts

Purpose Coarse-Scale Compositional Simulation MS66 Adaptive Multiscale Finite-Volume Method for Upscaling of compositional simulation is challenging due Gravity Instability to the interaction of small-scale heterogeneity and phase behavior. We present a framework to upscale two-phase The standard Multiscale Finite Volume (MsFV) method multi-component flow in compositional simulation. It is fails to accurately reproduce finger evolution since small shown that the oil and gas phases are not at chemical equi- errors grow in time in unstableflowregimes.Theitera- librium on coarser scales. This non-equilibrium behavior tive MsFV method overcomes this issue at the expenses of is modeled by upscaled thermodynamic functions, which computational efficiency. Here we introduce an adaptive measure the difference between component fugacities. We iMsFV technique that resolves local problems only in ar- also introduce upscaled flow functions to account for the eas close to the unstable front. In this context, the iMsFV effects of compressibility. method can be seen as an adaptive grid-refinement technique. Alireza Iranshahr Stanford University Rouven Kuenze, Ivan Lunati [email protected] University of Lausanne [email protected], [email protected] Denis Voskov Energy Resources Engineering Department Stanford Univeristy MS67 [email protected] Application of Advanced Unstructured Gridding Techniques to Reservoir Simulation Yuguang Chen Chevron Energy Technology Company Prismatic grids constructed by projection of a 2D grid can [email protected] resolve stratigraphic layers and are well suited for high aspect ratios of reservoir dimensions. In this talk, we address challenges of choosing a projection technique applicable to MS66 structurally complex models with fault surfaces deviating An Efficient Multiscale Finite Volume Method from vertical. We use topological parametric space of a ge- for Multiphase Flow in Heterogeneous Fractured ologic model as a pre-image for prismatic grid generation, Porous Media and further reduce limitations of prismatic grids in resolving 3D geometries and property distributions by utilizing The i-MSFVM is extended to include multiphase flow in a zonal gridding strategy. heterogeneous fractured porous media using a hierarchical approach. Local fracture functions are introduced to accu- Larisa V. Branets rately capture fractures at the coarse scale. Only one de- ExxonMobil Upstream Research Company gree of freedom per fracture network appears in the coarse [email protected] system and independent grids are employed for matrix and fractures. Important is that neither local grid refinement Elena Kartasheva, Olga Kroshkina, Valeriy Kubyak, nor grid alignment are needed in this approach. Conver- Valeriy Shmyrov gence of the method is investigated and shown for various NeurOK representative cases. [email protected], [email protected], [email protected], [email protected] Hadi Hajibeygi, Dimitrios Karvounis, Patrick Jenny Institute of Fluid Dynamics Xiao-Hui Wu ETH Zurich ExxonMobil Upstream Research Company [email protected], [email protected], [email protected] [email protected]

MS67 MS66 The UVT Transform: A Unified Approach to Upscaling Technique for Modeling of Well- Reservoir Modeling and Uncertainty Assessment Reservoir Interaction Current reservoir modeling practices revolve around the The complexity of the interaction between the well and the construction of a single 3D grid that is used for both dis- reservoir depends strongly on the way the well region is iso- tributing reservoir properties and simulating fluid flow. lated from the reservoir region. In this work we present the The most common types of grid structure used have limita- concept of expanded well model, where the well region is tions in terms of the complexity of the reservoir structure geometrically expanded to include the relevant part of the that they can represent and often require distortions of the reservoir. The effectiveness of this technique is illustrated individual grid cells that impact both the spatial distri- for challenging problems such as fractured well and pro- bution of properties and numerical results of flow simula- duction from tight-gas reservoir. tion. The UVT Transform has been introduced to enable a 3D transformation from today s space into the paleo- Mohammad Karimi-Fard geochronological domain. Fit for purpose grids are con- Stanford structed in the transformed space alleviating structural [email protected] limitations and artificial cell deformations. This unified approach ensures consistency between seismic and geolog- Lou Durlofsky ical interpretation and the various representations of the Energy Resources Engineering Department subsurface optimized for petrophysical property modeling, Stanford University [email protected] GS11 Abstracts 121

fluid flow simulation or geomechanical studies. of the Sichuan basin. With constraints from GPS data and focal mechanisms, we first calculated the velocity and Emmanuel Gringarten, Jean-Laurent Mallet stress fields of the region. Then, we numerically simu- Paradigm lated the rupture process of the seismogenic fault of the [email protected], 2008 Wenchuan earthquake in overthrust form with a right [email protected] strike-slip component. We then studied the movement and deformation of the tectonic blocks that was caused by the earthquake and its influence on the stress state of the MS67 boundary faults. The numerical simulation indicates that Upgridding by Amalgamation: Flow-Adapted the large earthquake causes the most tectonic blocks in the Grids for Multiscale Simulations study zone at approximately a 1-mm deviation toward the northeast; in particular, the Wenchuan seismogenic fault We discuss the creation of flow-adapted grids by amal- obviously deviated eastwards, and the maximum devia- gamating cells from an original fine grid, using cell-wise tion reaches 1.5 m. It seems that the large earthquake indicator functions to guide the amalgamation directions causes the Bayankala block at the west side of the Long- and the new grid resolution. We present an algorithmic menshan fracture zone to extend farther eastward. The framework with a set of modular components that can be Wenchuan earthquake causes the Coulomb failure stresses combined in different ways to create fit-for-purpose grids, on the boundary faults of the tectonic blocks in the study which can be used to develop highly efficient multi-fidelity zone to change to different extents. The maximum change transport solvers accompanying multiscale flow solvers. of the Coulomb failure stress reaches about 0.2 MPa at Knut-Andreas Lie both ends of the Wenchuan seismogenic fault, the south SINTEF ICT, Dept. Applied Mathematics section of the Xianshuihe fracture zone and part of the [email protected] southeast section of the Dongkunlun fracture zone in the upper crust. Additionally, the Coulomb failure stresses also increase to different extents between 0.01 and .02 MPa in Jostein R. Natvig regions such as the southernmost end of the Xianshuihe SINTEF ICT fracture zone, part of the southeast section of the Dongkun- Dept. Applied Mathematics lun fracture zone, the southwest and southeast edges of the [email protected] Eerdos block, just to name a few. Zuan Chen MS67 Institute of Geology and Geophysics Gridding Diplomacy - Balancing Requirements Chinese Academy of Sciences [email protected] Grid construction for the complex geometries arising in reservoir modelling can be regarded as an act of diplomacy, where multiple requirements have to be balanced. MS68 For most practical applications, corner-point grids have Rifting and Faulting been the preferred solution, applicable to both geological modelling and dynamic flow simulations. The presenta- Abstract not available at time of publication. tion will discuss how conflicting requirements are balanced in current state-of-the-art gridding technology. Examples Eunseo Choi will be presented, illustrating challenges and solutions from Lamont-Doherty Earth Observatory field applications. Columbia University [email protected] Tor Barkve, John Neave Roxar [email protected], [email protected] MS68 GAMR: A Free Paralell Adaptive Tectonics and Mantle Convection Code MS68 Rifting and Diking The Computational Infrastructure for Geodynamics (CIG) has begun development of Gamr: a new community code Abstract not available at time of publication. for tectonics and mantle convection. The principle new improvement of Gamr over existing community codes such Roger Buck as CitcomS and Gale is the use of parallel adaptive mesh Lamont-Doherty Earth Observatory refinement (AMR) to better resolve fine features such as Columbia University faults, plate boundaries, and mantle plumes. I will discuss [email protected] the current status of Gamr and outline future milestones.

Walter Landry MS68 Geological and Planetary Sciences A Study on the Inﬂuence of the 2008 Wenchuan California Institute of Technology Earthquake on the Stability of the Qinghai-Tibet [email protected] Plateau Tectonic Block System

In this paper, the 3D Finite Element Method was combined MS69 with a Discontinuous Deformation Analysis (DDA+FEM) On Conservative Remapping Transport Schemes to study the inﬂuence of the Wenchuan earthquake on using Icosahedral-hexagonal Grids the stability of the tectonic blocks system of the Qinghai- Tibet Plateau under the background of northward extru- A high order incremental remapping scheme has been sion of the Indian Plate and obstruction of the strong crust designed using the Icosahedral-hexagonal meshes. The 122 GS11 Abstracts

scheme has been tested for the advection of smooth scalar Simulating Atmospheric Flows fields in both deformational and non-deformational flow fields. The incoming flux areas are approximated by great We present our ongoing research on developing a set circle arcs using exact analytical trajectories. The bi- of numerical methods for simulating atmospheric flows. quadratic reconstruction functions are computed on projec- We have harnassed a high-order unstaggered finite-volume tion space to approximate the tracer field. The overall or- based approach in developing a family of both advective der of a transport scheme is thus determined completely by and shallow-water models on the cubed-sphere and veri- accuracy of reconstructed tracer field and geometry of the fied our results against existing test cases. This approach flux areas. A comparison of errors due to reconstruction has been shown to satisfy a relatively weak CFL condition functions obtained by weighted least squares fits to point and leads to more accurate results for the same order-of- values versus area-averaged values will presented. Also the accuracy, as compared with Galerkin-based approaches. various simplifications to the shapes of flux areas have been analyzed. A comparison of loss in accuracy due to simpli- Paul Ullrich fication of flux area geometry with respect to the gain in University of Michigan computation efficiency will be presented. Finally the effect [email protected] of three very different limiters: Flux corrective transport, Multi dimension flux and multidimensional extension of Christiane Jablonowski vanLeer limiting will be presented. University of Michigan Ann Arbor MI 48109-2143 Rashmi Mittal [email protected] NCAR Boulder, CO, USA [email protected] MS70 Shaping Regularization in Geophysical Inverse Peter H. Lauritzen Problems NCAR CGD Shaping regularization is a general method for imposing [email protected] constraints on the estimated model in the process of solving an inverse problem. In the shaping framework, regularization enters the inverse problem in the form of a model or MS69 shaping operator, which maps the estimated solution into A 2D Non-Hydrostatic Atmospheric Model Based the space of admissible solutions. Although this frame- on a Non-Oscillatory Finite-Volume Method work does not explicitly involve optimization, a connection with the optimization framework can be established via the Non-hydrostatic atmospheric modeling based on the finite- theory of proximity operators. Shaping regularization has volume methods is becoming increasingly popular for the been applied to a wide range of geophysical problems, from weather and climate simulations. A new two-dimensional seismic velocity estimation to adaptive filtering, definition non-hydrostatic model (compressible Euler system) has of local seismic attributes, and time-frequency analysis. I been developed. A semi-discrete central finite-volume will describe both the general theory and the known appli- method is used for the spatial discretization, and time cations. integration relies on explicit Runge-Kutta method. The scheme does not employ expensive Riemann solvers and Sergey Fomel characteristic decomposition or any staggered grid system; University of Texas at Austin and is computationally efficient. The non-oscillatory re- [email protected] construction removes spurious oscillations, and improves the quality of numerical simulations. The model is tested MS70 for various non-hydrostatic benchmark test-cases, and the results will be presented in the seminar. DG-based, UQ-equipped, Parallel, Adaptive, Scal- able Elastic-acoustic Seismic Inversion Ram Nair NCAR We describe mathematical and computational issues under- Institute for Mathematics Applied to Geosciences lying an effort to create a new generation seismic inversion [email protected] code. These include: elastic-acoustic coupling, discontinuous Galerkin discretization, gradient and Hessian consistency, parallel adaptivity on forest of octree meshes, uncer- MS69 tainty quantification via Bayesian inference, and scalability A Flux-based Characteristic to petascale systems. Illustrations from global seismology semi-Lagrangian Method for Atmopspheric Mod- are provided. eling Tan Bui-Thanh, Carsten Burstedde Abstract not available at time of publication. The University of Texas at Austin [email protected], [email protected] Matthew Norman North Carolina State University Omar Ghattas Raleigh, NC University of Texas at Austin [email protected] [email protected]

James R. Martin MS69 University of Texas at Austin A Family of High-Order Finite-Volume Schemes for Institute for Computational Engineering and Sciences [email protected] GS11 Abstracts 123

Georg Stadler, Lucas Wilcox completely in reduced space with negligible computational University of Texas at Austin costs. In many reservoir models the adjoint states can be [email protected], [email protected] computed relatively easy and only the Jacobians with respect to parameters are hard to obtain. This makes a balanced POD-based method very attractive. MS70 A Fresh Look at Simultaneous Source Arnold Heemink Delft University of Technology Many parameter estimation problems involve with a [email protected] parameter-dependant PDEs with multiple right hand sides. The computational cost and memory requirements of such Malgorzata Kaleta problems increases linearly with the number of right hand Shell sides. For many applications this is the main bottleneck of [email protected] the computation. In this talk we show that problems with multiple right hand sides can be reformulated as stochastic optimization problems that are much cheaper to solve. We MS71 discuss the solution methodology and use the direct current Parameter Identification for a Coupled Fluid Flow resistivity as a model problem to show the effectiveness of and Geomechanical Deformation Model our approach. We present an application of iterative regularization for Eldad Haber data inversion from a coupled single-phase flow and a Department of Mathematics poroelastic reservoir. Production data and measurements The University of British Columbia of surface deflection are inverted to reconstruct petrophysi- [email protected] cal and elastic properties of the reservoir. By means of synthetic experiments we evaluate the contribution of surface deformation data in the estimation of uncertain proper- MS70 ties. Our evaluations can be potentially applied to design Seismic Volume Reconstruction Via Multilinear cost-efficient InSAR and GPS configurations for optimal Rank Reduction monitoring of reservoirs.

Consider a matrix S(n, m) where some entries are miss- Marco Iglesias ing. For instance, the entries S(m, n) can be the scores Civil and Environmental Engineering assigned by buyer m to product n. Because not all buy- MIT ers have bought and scored all products, the matrix con- [email protected] tains empty entries. The goal of Collaborative Filtering (CF) is to predict the empty entries and therefore, predict Dennis McLaughlin products that a consumer might like. Seismic data recon- Civil Engineering MIT struction can also be interpreted as a matrix completion [email protected] problem similar to those arising in the field of CF. Seismic completion, however, entails reconstructing a 5D volume (a tensor). Similar to the matrix completion problem, tensor MS71 completion can be achieved via rank reduction methods. The Large Dimensional Bayesian Inversion Proem The intention of this talk is to present our recent research with Application to a Reservoir Model in rank reduction methods for seismic data reconstruction and de-noising. We will discuss some of challenges that Petroleum reservoirs are complex geological formation en- one needs to solve in order to create industrial-strength compassing a wide range of physical and chemical hetero- algorithms for multilinear seismic data processing. geneities. These heterogeneities span over multiple length scales and are impossible to describe in deterministic detail. Mauricio D. Sacchi Geostatistics and, more specifically, stochastic modeling of University of Alberta reservoir heterogeneities are being increasingly considered [email protected] by reservoir analysts and petroleum engineers for their potential in generating more accurate reservoir models to- MS71 gether with usable measures of spatial uncertainty. The goal of reservoir characterization is to provide a numeri- Model Reduced Variational Data Assimilation for cal model of reservoir attributes such as hydraulic conduc- Reservoir Models tivities (permeability), storativities (porosity) etc.. These Variational data assimilation or ”the adjoint method” has attributes are then used as inputs into complex transfer been used very often for model calibration problems in functions represented by various flow simulators to fore- reservoir models. This method however requires the im- cast future reservoir performance and oil recovery poten- plementation of an adjoint model. Even with the use of tial. Permeability is one of the most important quanti- the adjoint compilers that have become available recently ties for prediction of fluid flow pattern.The estimation of this is a tremendous programming effort. Therefore we permeability fields is therefore, critical and necessary for propose another approach to variational data assimilation the prediction of the behavior of contaminant plumes in using model reduction that does not require the implemen- aquifers and the production of petroleum from oil fields. tation of the adjoint of the original model. Model reduced In this paper, we employ a Bayesian hierarchical model variational data assimilation is based upon a POD (Proper to quantify the uncertainty by formulating the posterior Orthogonal Decomposition) approach to determine a redistribution of the fine-scale permeability field condition duced model for the original reservoir model. Once this on both the coarse-scale data and production data and reduced model is available, its adjoint can be implemented the observed fine-scale data at the well locations. To rep- very easily and the minimization process can be solved resent the spatial dependence in the permeability fields, Karhunen-Loéve expansion is used to reduce the number 124 GS11 Abstracts

of parameters. We assume the number of terms in this of reduced/adapted complexity. By coupling these mod- expansion is unknown and develop a two stage reversible els of reduced complexity the model efficiency is increased jump based MCMC algorithm to efficiently explore the pos- without neglecting the relevant phenomena. terior distribution. Furthermore, we introduce a multiscale data integration method with upscaling technique for spa- Bernd Flemisch tial modeling of the permeability. Numerical results are University of Stuttgart, Germany presented by analyzing simulated as well as real data. bernd.fl[email protected]

Bani Mallick Department of Statistics MS72 Texas A&M University A Multiphysics Approach for the Simulation of [email protected] Multiphase Flow Processes in Porous Media The contamination of the unsaturated zone with a light MS71 non-aqueous phase liquid is studied, corresponding to a Bayesian Uncertainty Quantification for Flows in domain with randomly distributed heterogeneities where Heterogeneous Subsurface Formations complex three-phasethree-component processes are relevant only in a small (local) subdomain. This subdomain We study the uncertainty quantification for flows in het- needs fine resolution as the complex processes are governed erogeneous porous media. The permeability field is as- by small-scale effects. For a comprehensive fine-scale model sumed to have channelized structure that are represented taking into account three-phasethree-component processes using level sets approaches. In particular, the parameteri- as well as heterogeneities in the whole (global) model zation of the channel boundaries is represented via the pa- domain, data collection is expensive and computational rameterization of velocity field in the level sets equations. time is long. Therefore, we developed a general con- The truncation in the parameter space introduces errors in cept where on the one hand, the global flow field influ- the posterior measure that are investigated. Multi-stage ences the local three-phasethree-component processes on MCMC algorithms are used for efficient sampling from the the fine-scale. On the other hand, a coarse-scale satura- posterior. We present numerical results. This is a joint tion equation is solved where the effects of the fine-scale work with Y. Efendiev, A. Mondal, B. Mallick, and A. multi-phasemulti-component processes in the subdomain Datta-Gupta. are captured by source/sink terms and the effects of fine- scale heterogeneities by a macrodispersion term. Jia Wei Texas A and M Rainer Helmig [email protected] IWS, University of Stuttgart, Germany Institut fur Wasserbau [email protected] MS72 Simulation of CO2 Migration Using Vertical Equi- librium Models MS72 Finite Volume Discretization of Multiphase Porous Recently, methods based on an assumption of vertical equi- Media Flows for CO2 Geological Sequestration librium (VE) has obtained renewed interest in the context of modeling CO2 migration over long time- and spa- This talk deals with the simulation of multiphase compo- tial scale. It is expected that after the injection period, sitional Darcy flow for CO2 injection in saline aquifer. It CO2 will migrate over several kilometers in the horizon- will focus on the finite volume discretization of both Darcy tal direction, but only tens of meters in the vertical di- fluxes and transport terms. The efficiency of the algorithms rection limited by the vertical boundaries of the aquifer. is illustrated on near well CO2 injection test cases includ- When the horizontal to vertical time scale becomes large, ing dissolution of CO2 in the water phase, drying of the it is reasonable to approximate CO2 migration using ver- near well region and salt precipitation. tically averaged models. The fact that VE-methods reduces the spatial complexity of the problem from 3D to 2D Roland Masson may give important savings in computational time. Fur- Institut francais du petrole thermore, because of improved vertical resolution the VE- [email protected] approximation in many situations gives better solutions than standard 3D formulations. In this presentation we Cindy Guichard show results from field simulations taken from the Utsira IFP Energies Nouvelles and Johansen formation in the North Sea. [email protected]

Helge K. Dahle Robert Eymard University of Bergen, Norway University Paris East Department of Mathematics [email protected] [email protected]

MS73 MS72 A Non-linear Correction and Maximum Princi- Model Coupling for CO2 Sequestration Scenarios ple for Diﬀusion Operators Discretized using Cell- Models for CO2 storage need to be able to describe non- centered Finite Volume Schemes isothermal, multiphase and compositional processes. How- In the present work, we propose a nonlinear correction ever, in most cases it is not necessary to describe all the which gives nonoscillating solutions and which can be ap- physical processes for the whole simulation time period. plied to standard cell-centered ﬁnite volume schemes. Us- It is possible to describe a certain time scale with models GS11 Abstracts 125

ing an analytical solutions, we show the robustness and the from that of Cosserat media. accuracy of this algorithm in comparison with results obtained by linear finite volume schemes which do not satisfy Claude Boutin the minimum principles on this test. Université de Lyon- Ecole Nat. des Travaux Publics de l’Etat Christophe Le Potier DGCB - CNRS 3237 CEA [email protected] Gif sur yvette [email protected] Jean Soubestre universitédeLyon-ENTPE CNRS 3237 MS73 [email protected] The Finite Volume Scheme Preserving Maximum Principle for Diffusion Equation MS74 We construct a new nonlinear finite volume scheme for Some Theoretical and Numerical Problems Related diffusion equation on polygonal meshes and prove that to the Modeling of Strain Localization by Second the scheme satisfies the discrete extremum principle. Our Gradient Continuum Theory scheme is locally conservative and has only cell-centered unknowns. Numerical results are presented to show how Generalized theories of continuum mechanics, our scheme works for preserving discrete extremum princi- as Cosserat’s, micromorphic or, with regards to this pre- ple and positivity on various distorted meshes. sentation, second grade theories, have proven efficient to model the post strain localization behaviour of non-elastic Zhiqiang Sheng media which the classical Cauchy’s theory cannot do prop- Université Pierre et Marie Curie - Paris VI erly. The purpose of this presentation is to expound some [email protected] theoretical and numerical results related to strain loaliza- tion and second grade computations as analytical evidence Guangwei Yuan of localization, analytical solutions for second grade elastic Institute of Applied Physics and Computational problems, locking in FE computations. Mathematics yuan [email protected] Denis CAILLERIE,RenéChambon Laboratoire 3SR Universit MS73 ’e de Grenoble Monotone Subfamily of Mimetic Finite Difference [email protected], Discretization Methods [email protected] The family of the Mimetic Finite Difference (MFD) methods provides flexibility in the choice of parameters which MS74 define a particular member of the family. The correct Micromechanics of Ductile Porous Geomaterials choice of these parameters may guarantee that the resulting with Account of Pressure Sensitivity. linear numerical scheme satisfy the DMP principle. The monotonicity limits of MFD method are investigated in D. KONDO : Institut D’Alembert, UMR 7190, CNRS, several practically important cases including meshes gener- UPMC, Paris, ated using the Adaptive Mesh Refinement (AMR) strategy. J. LIN : University of Strasbourg, Department of Civil En- gineering, Strasbourg, Gianmarco Manzini Istituto di Matematica Applicata e Tecnologie W. SHEN and J-F. SHAO : LML, UMR 8107, CNRS, Informatiche USTL, Lille Pavia, Italy Porosity strongly affects the overall ductile behavior of co- [email protected] hesive geomaterials undergoing plastic deformation. In the present study, we propose an original micromechanical ap- Daniil Svyatskiy, Konstantin Lipnikov proach which suitably couples Drucker-Prager type plastic- Los Alamos National Laboratory ity and evolving porosity under general triaxial loadings. [email protected], [email protected] The resulting model has the advantage to be based on a single macroscopic yield function which also plays the role of plastic potential. It is shown that this yield function is MS74 particularly appropriate to account for the voids collapse Generalized Continua for Reinforced Geomaterials and plastic shearing mechanisms which govern the mechanical behavior of various porous geomaterials. The effective behaviour of soft elastic materials periodically reinforced by stiff slender elastic inclusions is investigated Djimedo Kondo through the homogenization method of periodic media. A Universite Pierre et Marie Curie large stiffness contrast induces a full coupling between the [email protected] beam behaviour of the inclusions and the shear behaviour of the matrix. Instead of the Cauchy continua usually obtained for homogenized composites, the macro behaviour MS74 is of second gradient type at the leading order, and differs Darcy Vs Brinkman

Diﬀerent ﬁltration laws have been proposed in history to 126 GS11 Abstracts

describe a ﬂuid ﬂow through porous medium. We focus Convergent Sequences of Gradient Fields in Ho- here on Darcy’s law mogenization

v = K(f −∇p) We identify local representation formulas that in the fine phase limit provide upper bounds on the limit superior of and Brinkman’s law ∞ the L norms of gradient fields inside homogenized porous B v + ∇p − μΔv = f. media. The local representation formulas are expressed in terms of the weak limit of the gradient fields and local cor- Using the method of homogenization we derive both laws, rector problems. The upper bounds may diverge according in case of porous medium with special structure. The goal to the presence of rough interfaces. We identify explicit of this work is to compare the two laws and see that they local formulas for the limit of the L∞ norms of the asso- can be related with an appropriate choice of parameters. ciated sequence of gradient fields inside smooth periodic microstructures. Eduard Marusic-Paloka Department of Mathematics, Robert P. Lipton University of Zagreb, Croatia Department of Mathematics [email protected] Louisiana State University [email protected] MS75 Tadele Mengesha Super-resolution in Time-reversal by Homogeniza- Louisiana State University tion Department of Mathematics Over the past decades, much attention has been devoted [email protected] to the detection of small inhomogeneities in materials or tissues, using non-invasive techniques, primarily electro- MS75 magnetic wave-fields. The characterization of the signa- ture of small inclusions is now well understood. But many Homogenization of Pseudo-parabolic Systems questions remain regarding their accurate localisation, es- Pseudoparabolic systems with periodic data are homoge- pecially in non-homogeneous media. In contrast, during nized to obtain upscaled limits. The limit is characterized the same period it was shown that inhomogeneous media and convergence is established in various linear cases for are more favorable than homogeneous ones for time rever- both the classical binary medium model and the highly- sal experiments, involving active sources. This talk will be heterogeneous case. The limit of vanishing time-delay pa- devoted to recent results on the enhanced resolution avail- rameter in either medium is included. The double-porosity able in structured media, and their consequences for the limit of Richards’ equation with dynamic capillary pressure imaging of small inhomogeneities. is included. Yves Capdeboscq Ralph Showalter, Malgorzata Peszynska Mathematical Institute, University of Oxford Department of Mathematics [email protected] Oregon State University [email protected], MS75 [email protected] Homogenization Effects in Domains with Oscillat- ing Boundaries Son-Young Yi University of Texas at El Paso We consider domains with microinhomogeneous bound- [email protected] aries. We study the asymptotic behavior of solutions to boundary value problems in domains with rapidly oscillating or rough boundaries and in multilevel and cascade thick MS76 junctions with rapidly oscillating transmission zone. In- A Stochastic Approach to Modeling Effective Mul- homogeneous Fourier boundary conditions with perturbed tiphase Flows in Heterogeneous Porous Media coefficients are set on the oscillating boundaries. We prove the homogenization theorems and convergence of energy Heterogeneity and buoyancy can compete or combine to- integrals as the small parameter characterizing the microin- gether to influence spreading in multiphase flows through homogeneity, tends to zero. It is shown that there are sev- porous media. In this work we study the interaction of eral qualitatively different cases in the asymptotic behavior the two with the goal of deriving an effective large scale of the solutions. equation that accurately quantifies the rate of spreading. To do so we work in a stochastic framework treating the Grigory A. Chechkin medium permeability as random. In particular the rate of Department of Differential Equations spreading is quantified by an effective dispersion (and ef- Moscow Lomonosov State University, Moscow fective permeability) coefficient. To validate the approach [email protected] we perform a series of numerical simulations, which show good qualitative agreement. We find that the interplay be- Tatiana P. Chechkina tween density and heterogeneity leads to an enhancement Moscow Engineering Physics Institute of the front spreading as well as a renormalization of the National Research Nuclear University evolution of the mean front position relative to an equiv- [email protected] alent homogeneous medium. The quantification of these phenomena plays an important role in several applications, including for example carbon sequestration and enhanced MS75 Representation Formulas for L∞ Norms of Weakly GS11 Abstracts 127

oil recovery. [email protected]

Diogo Bolster Department of Civil Engineering and Geological Sciences MS76 University of Notre Dame Modeling Dispersion in Heterogeneous Porous Me- [email protected] dia with Stochastic Diffusion Processes for Fluid Particle Velocities Marco Dentz IDAEA To model the dispersion of fluid particles induced by con- Spanish National Research Council (CSIC) ductivity heterogeneity, we propose stochastic diffusion [email protected] processes for the Lagrangian velocity of fluid particles. The corresponding processes are continuous in time and are able to accurately capture the dispersion behavior for Insa Neuweiler σ2 . ... Institute for Fluid Mechanics and Environmental Physics log-conductivity variances Y ranging from 0 06 4. By in C validation with Monte Carlo data it is demonstrated that [email protected] the model reproduces non-Gaussian velocity statistics and long-term velocity correlation effects very accurately.

Jesus Carrera Daniel W. Meyer IDAEA, CSIC, Spain Institute of Fluid Dynamics [email protected] [email protected]

MS76 Patrick Jenny Institute of Fluid Dynamics Nonlinear Transport Problems with Time-memory ETH Zurich Effects [email protected] Contaminant transport in heterogeneous porous materials can be described by the convolution of a PDE with a time- Hamdi Tchelpi memory kernel that accounts for the long correlations in- Stanford University duced by the underlying flow. In this talk we will discuss [email protected] how to extend this transport formalism to include nonlinearities (e.g., geomechanical, and geochemical effects), what is the interplay between nonlinearities and memory MS77 effects, and what are the mathematical challenges associ- High-resolution Modelling of Geodynamic and ated with the solution of such equations. Planetary Processes with Finite Differences and Marker-in-cell Techniques Andrea Cortis Earth Sciences Division, 90-1116 Modern gross challenges in geodynamic and planetary Lawrence Berkeley National Laboratory modelling are: (i) creating high-resolution realistic 3D [email protected] numerical models applicable to nature, and (ii) obtaining a rigorous understanding of geodynamic and planetary processes and the key physical parameters control- MS76 ling them. One possible pragmatic strategy is to use a Efficient Solution of Advection-Reaction Diffusion combination of conservative finite differences with marker with Stochastic Forcing in cell techniques on fully staggered rectangular Cartesian grid. This approach allows for both simplicity of numeri- We consider exponential based integrators for porous me- cal implementation and stability and robustness of numer- dia flow in two and three dimensions. These methods are ical solutions. Possible drawback is in limited possibility based on solving the linear problem exactly and exploit ef- of grid refinement that can indeed be efficiently compen- ficient methods for computing large matrix exponentials. sated by low memory requirements and high speed of com- We are particularly interested in the effects of time de- putations allowing for high resolutions in both 2D (thou- pendent stochastic forcing. The forcing is taken to model sands of points in each direction with direct solvers) and unknown movement between trapped and flowing solutes, 3D (hundreds of points in each direction with multigrid unknown small scale variations in the reaction term or time solvers) by using only few CPUs. We developed a family dependent changes in permeability. We examine conver- of finite-difference, marker-in-cell codes I2ELVIS/I3ELVIS gence and efficiency of new schemes for the stochastic PDEs which can handle visco-(elasto)-plastic rheology, miner- for both additive and multiplicative noise and present nu- alogical phase changes, free surface and (when needed) merical results for realistic flow type problems. self-gravitation. With these tools we created a number of predictive numerical models for various geodynamic Gabriel J. Lord and planetary processes, such as self-consistent mid-ocean Heriot-Watt University rift formation with transform faults, oceanic and oceanic- [email protected] continental subduction initiation and long-term evolution, continental collision with spontaneous slab breakoff, intru- Antoine Tambue sion emplacement into the crust, planetary accretion and Heriot Watt University metallic core formation. [email protected] Taras Gerya Sebastian Geiger Geophysical Institute Heriot-Watt University ETH-Zurich Edinburgh [email protected] 128 GS11 Abstracts

MS77 tiation of velocity components on a stencil across the inter- On Geothermal Processes within the Lithosphere face is aided by using the coupled fictitious velocity values, whose representations are solved by using the coupled ve- Most heat and fluid flow simulations for geothermal plays locity interface conditions. These fictitious values and the couple thermal and darcy flow at the reservoir scale, how- non-staggered grid allow a convenient and accurate approx- ever, non-conventional geothermal exploration requires cer- imation of the pressure and potential jump conditions. A tainty of heat and fluid flow at depth over much larger compact finite difference method is adopted to explicitly scales. We demonstrate approaches to assimilating 3D compute the pressure derivatives at regular nodes to avoid basin (and beyond) geological provinces to simulations that the pressure-velocity decoupling. Numerical experiments capture meter scale coupled thermal - fluid flows. These verify the designed accuracy of the numerical method. Ap- include utilizing a material point approach to the finite el- plications to geophysical problems demonstrate that the ement method, a simplified PDE compositional language, sharp pressure jumps on the clast-Newtonian matrix are SPH methods for geometry interpolation, simple forms of accurately captured for various shear conditions, moderate mesh refinement, parallelization to 1000s of CPUs and viscosity contrasts and a wide range of density contrasts. It some of the benchmarks addressed. is also shown that a large absolute difference of the viscosity across the interface will cause the simulation unstable, Steve Quenette due to the large transfer error in computing the jumps in Victorian Partnership for Advanced Computing the pressure and potential interface conditions from the [email protected] numerical solutions of the velocity field.

John Mansour Yongcheng Zhou,JamesLiu VPAC Department of Mathematics [email protected] Colorado State University [email protected], [email protected] Dave Lee Monash University Dennis Harry [email protected] Department of Geosciences Colorado State University Louis Moresi [email protected] School of Mathematical Sciences Monash University MS78 [email protected] A Semi-Implicit, Semi-Lagrangian, P-Adaptive Discontinuous Galerkin Method for the Shallow MS77 Water Equations Positivity Preserving Well-balanced Methods for A semi-implicit and semi-Lagrangian Discontinuous the Shallow-water Equations Galerkin method for the shallow water equations is pro- Shallow-water equations with a non-flat bottom topogra- posed and analyzed. The method is equipped with a simple phy have been widely used to model flows in rivers and p-adaptivity criterion, that allows to adjust effectively the coastal areas. An important difficulty arising in these sim- number of local degrees of freedom employed to the local ulations is the appearance of dry areas, and standard nu- structure of the solution. Numerical results in the frame- merical methods may fail in the presence of these areas. work of one dimensional test cases prove that the method These equations also have steady-state solutions in which captures accurately and effectively the main features of lin- the flux gradients are non-zero but exactly balanced by the ear gravity and inertial gravity waves, as well as reproduc- source term. In this presentation, we propose some recently ing correct solutions in nonlinear open channel flow tests. developed high-order discontinuous Galerkin and weighted The effectiveness of the method is also demonstrated by nu- essentially non-oscillatory methods, which can preserve the merical results obtained at high Courant numbers and with steady-state exactly, and at the same time are positivity automatic choice of the local approximation degree. Per- preserving without loss of mass conservation. Some nu- spectives for extensions to geophysical flows applications merical tests are performed to verify the positivity, well- are discussed. balanced property, high-order accuracy, and good resolu- Luca Bonaventura tion for smooth and discontinuous solutions. MOX Politecnico di Milano Yulong Xing Milan, Italy 20133 Department of Mathematics [email protected] Univeristy of Tennessee / Oak Ridge National Lab [email protected] Marco Restelli Polytechnic University Milan [email protected] MS77 High Order Interface Method for Solving Multi- Giovanni Tumolo flow Navier-Stokes Equations in Geophysics ICTP, Trieste, Italy [email protected] We developed a second-order accurate interface method, based on the matched interface and boundary approach, to solve the Navier-Stokes equations with discontinuous viscosity and density on non-staggered Cartesian grid. We derive for the first time the interface conditions for the intermediate velocity field and the pressure potential function that are introduced in the projection method. The differen- GS11 Abstracts 129

MS78 MS78 Jacobian Free Efficient Implicit Solver for HOMME The Variable Resolution Spectral Element Dynam- ical Core in the Community Atmospheric Model Abstract not available at time of publication. (cam) Kate Evans NCAR’s High Order Method Modeling Environment Oak Ridge National Laboratory (HOMME) uses high-order element-based Galerkin meth- [email protected] ods and the cubed sphere geometry to solve global PDEs on massively parallel computers in a coordinate system that is free of polar singularities. HOMME has been updated to MS78 allow static refinement via conforming quadrilateral meshes CG/DG Formulation of the Non-Hydrostatic Uni- and this talk discusses the implementation of refinement in fied Model of the Atmosphere (NUMA) HOMME’s spectral element dynamical core as used by the Community Atmospheric Model (CAM-HOMME). We describe our progress in the development of a parallel 3D compressible Navier-Stokes model for use in non- Michael N. Levy hydrostatic atmospheric modeling. The explicit time- Sandia National Laboratories integration version of NUMA currently scales up to tens NM, USA. of thousands of processors but we would like to extend it [email protected] to hundreds of thousands. We will describe our MPI implementation and challenges facing us in scaling the im- James Overfelt plicit solvers. NUMA is based on continuous and dis- Sandia National Laboratories continuous Galerkin methods (CG/DG) and is high-order [email protected] (arbitrarily high-order polynomials can be used), fully unstructured, and capable of using explicit, semi-implicit, and fully-implicit time-integrators. Finally, NUMA can be used Mark A. Taylor both for regional and global modeling. We will report on Sandia National Laboratories, Albuquerque, NM benchmark test cases to show the accuracy and efficiency of [email protected] the model and will discuss the many challenges remaining in the development of this model. MS79 Francis X. Giraldo Title Not Available at Time of Publication Naval Postgraduate School [email protected] Abstract not available at time of publication. Biros George James Kelly We have 13 speakers. Department of Applied Mathematics Web-site does not let speaker field be blank. Naval Postgraduate School [email protected] [email protected]

MS79 MS78 Assimilation of Production and 4D Seismic Data in Quasi-Monotone Advection Methods for Spectral Oil Reservoir Modeling by Virtual Sensing Elements Time-lapse (4D) seismic attributes can provide valuable High Order Method Modeling Environment (HOMME) information regarding the subsurface fluid flow. This is a spectral element dynamical core option in Commu- spatially-rich source of information supplements the poor nity Earth System Model (CESM). The spectral element areal information attainable from production well data. method in HOMME is a forth-order accurate continuous While fusion of information from multiple sources holds Galerkin method on quadrilateral elements. In this talk great promise, in practice, this task is far from trivial. Joint we discuss new quasi-monotone limiters for HOMME. We inversion is complex for many reasons, including dissimilar compare Zalesak-type FCT limiters with ones using opti- temporal and spatial scales, ambiguous coupling mecha- mal reconstruction. The optimal reconstruction is obtained nisms between the various parameters, and unclear rela- by solving a quadratic programming problem local to each tive statistical fidelity of the different data sources. These element. To illustrate our ideas, we use divergent and non- concerns limit the applicability of many data-assimilation divergent advection tests for geophysical flows with dis- techniques. Adjoint-based methods offer great efficiency tortive winds from the paper by Nair & Lauritzen, 2010. and consistency; however their implementation generally requires extensive coding effort. In this study we present Oksana Guba a formulation that exploits the adjoint functionality that Sandia National Laboratories modern simulators offer for production data, to consis- NM, USA. tently assimilate inverted 4D seismic attributes. The cen- [email protected] tral idea is to incorporate seismic inverted attributes by virtual sensors. These sensors mimic production wells and Mark A. Taylor thereby leverage adjoint functionality for the seismic data. Sandia National Laboratories, Albuquerque, NM Precautions are taken to ensure that such sensors will not [email protected] interfere with the fluid dynamics. Other than the obvi- ous consistency advantage in the proposed methodology, Amik St-Cyr its implementation does not require re-programming legacy National Center for Atmospheric Research adjoint code, and in principle can be utilized for the incor- Institute for Mathematics Applied to the Geosciences poration of a broad range of data sources and attributes. [email protected] We present numerical results demonstrating considerable 130 GS11 Abstracts

improvement in matching saturation distribution in diﬀer- [email protected] ent assimilation setups. This work was carried out as part of a joint Shell-IBM research project. MS80 Lior Horesh Data Assimilation Applications in Large Scale Re- Business Analytics and Mathematical Sciences servior Models IBM TJ Watson Research Center [email protected] Abstract not available at time of publication.

Gijs van Essen, Eduardo Jimenez Remus Hanea Shell Innovation Research & Development Delft University, Netherlands [email protected],, eduardo.jimenez@shell@com [email protected]

Sippe Douma MS80 Shell Particle Ensemble Kalman Filtering with Applica- [email protected] tion to a Reservoir Model Andrew R. Conn Abstract not available at time of publication. IBM T J Watson Research Ctr [email protected] Hussein Hoteit Conocophillips Ulisses Mello [email protected] IBM Watson Research Center [email protected] MS80 Reservoir Applications of the Adaptive Gaussian Paul van den Hoek Mixture Filter Shell Innovation Research & Development [email protected] The ensemble Kalman filter (EnKF) is currently considered as a promising method for conditioning reservoir simulation models to production data. However, it has some short- MS79 comings in estimating the correct posterior distribution. Joint Electromagnetic-Seismic Inverse Modeling An alternative that avoids some of these shortcomings is the adaptive Gaussian mixture filter (AGMF) [Stordal et. Seismic data are first transformed into the Laplace-Fourier al., 2010]. Here we will present a comparison between the Domain, which changes the modeling of the seismic wave EnKF and the AGMF on a well known test case, the PUNQ field from wave propagation to diffusion. Several bene- S3 model. high-level commands. fits follow: (1) seismic and EM data are better matched in resolution, governed by the same physics of diffusion, Geir Nvdal (2) standard least squares inversion works well with dif- International Research Institute of Stavanger fusive type problems, and (3) possibilities to image across & Centre of Integrated Petroleum Research, UoB multiple scale lengths, incorporating different types of geo- [email protected] physical data and attributes.

Gregory Newman Andreas Stordal, Randi Valestrand LBL International Research Instititue of Stavanger (IRIS) [email protected] [email protected], [email protected]

MS79 MS80 Including Multiply-Scattered Waves in Seismic Multi-level Parallelization of Ensemble Kalman Fil- Imaging ter (EnKF) for Reservoir History Matching Imaging the subsurface in exploration seismology con- The ensemble Kalman filter (EnKF) has been successfully ventionally only makes use of primaries (singly reflected implemented in parallel to assimilate data in reservoir his- waves). In certain circumstances, multiples (waves that tory matching problems. In the EnKF method, a suite of reflected more than once on the path from source to re- reservoir models (set of ensemble members) runs indepen- ceiver), can be used to form an image. This allows better dently forward in time (forecast step), and is continuously illumination of the bottom of subsurface structures, and updated as new data becomes available (assimilation step). near-vertical features. A method for jointly imaging using An efficient implementation of the EnKF is presented in both primaries and multiples to enhance the result, will be which three-level parallelization is employed. The first level presented. of parallelization is for the forecast step by running each ensemble member on a different computer processor. This Alan Richardson is very efficient for a large number of ensemble members, Department of Earth, Atmospheric and Planetary but without additional parallization, the memory of a sin- Sciences gle processor constrains the size of the reservoir simulation. Massachusetts Institute of Technology Therefore, a second level of parallelization which uses a alan [email protected] parallel reservoir simulator for each realization is implemented. The assimilation step requires collecting a state Alison Malcolm vector from each ensemble member. If this data is collected MIT on a single processor, this poses an additional limitation on the size of the EnKF problem in terms of both memory and GS11 Abstracts 131

computation time. Therefore, we propose an algorithm in University of Bergen which a third level of parallelization is acheived for the [email protected] assimilation step.

Reza Tavakoli MS81 UT-Austin Goal Ori- [email protected] ented Upscaling for Coupled Flow/Geomechanics Simulations Gergina Pencheva University of Texas at Austin Abstract not available at time of publication. [email protected] Adolfo Rodriguez ConocoPhillips Mary F. Wheeler [email protected] Center for Subsurface Modeling University of Texas at Austin [email protected] MS81 Incorporation of Diffusion into Compositional Mul- MS81 tiphase Flow Simulation Benchmarking Multiscale Mixed Finite Element Mixing of nonequilibrium phases in both open space and in Method (MsMFEM) for Modeling Flow Accuracy permeable media is of fundamental nature with broad ap- and Computational Efficiency plications in CO2 injection in hydrocarbon reservoirs and for CO2 sequestration in saline aquifers, and measurement Multiscale Mixed Finite-Element method attempts to of diffusion coefficients. Despite the importance of mixing, capture sub-grid geological information directly into the the process has not been incorporated in current numerical coarse-scale via mathematical basis functions. These ba- reservoir simulators properly especially when one grid cell sis functions contain essential multiscale information and contains one of the nonequilibrium phases and the neigh- are coupled through a global formulation to provide highly boring cell contains the other phase. To be specific suppose accurate approximation of the flow solution. MsMFEM is one cell contains CO2 and the neighboring cell contains wa- used to simulate flow on highly heterogeneous geologically ter or oil phase. Current reservoir models cannot account realistic corner-point grids with faults and fractures. The properly for the flux between the two grid cells. A fun- MsMFEM is benchmarked against a proprietary simula- damental deficiency is that local equilibrium condition is tor and a fine-scale model for accuracy and computational not imposed at the interface. Consequently current simula- efficiency. tors give erroneous results even with fine gridding. In this Mayur Pal work, for the first time we incorporate the criteria of lo- Shell International Exploration and Production B.V. cal equilibrium at the interface between the neighborhood Rijswijk, The Netherlands grid cells to account for diffusion flux and convective flux [email protected] properly. We use a mixed finite element framework to account for diffusion flux calculation both within a cell and interface flux. As a result allowance is made for the con- Sadok Lamine ditions that interfacial diffusion flux is much higher than Shell International Exploration and Production B.V. interfacial convective flux while bulk phase convective flux [email protected] is much higher than bulk phase diffusion flux. Two formulations are established, one for a moving interface and the Faruk O. Alpak other for a fixed interface. Our moving interface formu- , Shell International Exploration & Production Inc., USA lation is compared with open space formulation recently [email protected] presented in another study. We also present a fixed mesh method that is much faster and appropriate for reservoir Ingeborg Ligaarden simulation. The efficiency of the fixed mesh method is SINTEF mainly due to its larger time step size compared to the [email protected] moving interface formulation. Except for CPU efficiency, the results from the two formulations are the same. Knut-Andreas Lie SINTEF ICT, Dept. Applied Mathematics Shuyu Sun [email protected] Division of Mathematical and Computer Sciences & Engineering King Abdullah University of Science and Technology MS81 (KAUST) Multiscale Simulation for Two-phase Flow in [email protected] Porous Media Abbas Firoozabadi In this contribution we develop multiscale simulation ca- Yale University pabilities, with an emphasis on robustness in terms of grid abbas.fi[email protected] irregularity and the duality between upscaling and preconditioning. We place particular emphasis on issues arising in 3 spatial dimensions, including the use of secondary (non- MS82 conserved) coarse variables. Optimization-based Postprocessing of Finite Ele- ment Solutions for Recovering Monotonicity Jan M. Nordbotten Department of Mathematics Loss of monotonicity and violation of the discrete maxi- 132 GS11 Abstracts

mum principle are typical drawbacks exhibited by the nu- the water breakthrough time. merical solutions of the conventional approximation methods, such as finite elements (FE), finite volumes (FV), Yuri Vassilevski and mixed finite elements. The problem is particularly Institute of Numerical Mathematics important in cases of highly anisotropic diffusion tensors Russian Academy of Sciences or distorted unstructured meshes. In this talk, we sug- [email protected] gest a least-change correction to available FE solution. It is aimed on recovering the monotonicity properties. This Kirill Nikitin postprocessing procedure is based on solving a monotonic Russian Academy of Sciences regression problem with some extra constraints. The post- [email protected] processed solution preserves the accuracy of the discrete FE approximation in L2-norm, satisfies the discrete max- Alexander Danilov imum principle and meets the conservativity requirement. Institute of Numerical Mathematics We present an algorithm for solving the postprocessing Russian Academy of Sciences problem. Its efficiency is demonstrated by the results of [email protected] numerical experiments.

Oleg Burdakov MS83 Linkoping University A Multiscale Model for Thermo-hydro-mechanical [email protected] Analysis of Porous Media and Constitutive Be- haviour Including Capillary effects Ivan Kapyrin Institute of Numerical Mathematics, RAS, Moscow We propose a thermo-hydro-elastoplastic model for par- [email protected] tially saturated three-phase soil. Averaging theory leads from micro to macro level. Restrictions resulting from thermodynamics are imposed thus the description of the MS82 behavior at macro scale is thermo-dynamically consistent. A Monotone Discretization Method for the Constitutive parameters are identified for a data concern- Convection-Diffusion Equation ing a see gas reservoir; capillary effects and micro collapse due to variation of load and saturation are found as an We present a non-linear monotone finite volume method interpretation of a behavior observed at macro scale. for the numerical approximation of the steady convection- diffusion equation on unstructured meshes in two spatial Marek Lefik dimension. The method is formally second-order accurate Technical University of Lodz as the convection flux is evaluated numerically by means Department of geotechnics and Engineering Structures of a piecewise linear reconstruction within each cell and marek.lefi[email protected] at mesh vertices. Non oscillatory behavior in presence of strong gradients is achieved through suitable slope limiters Bernhard Schrefler in the solution. The edge gradients, required to discretize Department of Construction and Transportation the diffusive fluxes, are defined inside additional quadrilat- Engineering, eral cells centered at mesh edges, the so-called ”diamond University of Padua cells”, by a gradient formula which is formally exact for [email protected] linear solutions. A set of numerical results documents the performance of the method in treating problems with internal layers and solutions with strong gradients. MS83 Chemical Local Non-equilibrium: Origins, Mod- Gianmarco Manzini elling and Analysis Istituto di Matematica Applicata e Tecnologie Informatiche Transport of chemical species in heterogeneous geomateri- Pavia, Italy als during the transient phase is very often characterized [email protected] by the local non equilibrium conditions. In this presentation the different origins of such conditions and their consequences on the macroscopic behaviour, are reviewed. Par- MS82 ticular attention is paid to the chemical heterogeneity of Monotone Finite Volume Discretization of Two- the geomaterial. In the second part, modelling by homoge- phase Black Oil Equations on Polyhedral Cells nization of the transport in a double porosity medium, including diffusion/dispersion, convection and reaction phe- A new monotone finite volume method with a nonlinear nomena, is presented. two-point flux approximation is applied to the approximate solution of two-phase black oil equations on 3D meshes Jolanta Lewandowska composed of polyhedral cells. In special cases of orthogo- University Montpellier 2 nal grid with isotropic or grid-aligned anisotropic perme- Laboratory LMGC ability tensor the linear and nonlinear approximations are [email protected] identical. In general case the linear two-point flux discretization provides no approximation, whereas the nonlinear two-point flux discretization is at least first order MS83 accurate. Numerical experiments with two-phase black oil Modelling and Simulation of Chemical Degradation model demonstrate that the quality of the discrete flux ap- Mechanisms in Porous Media with Evolving Mi- proximation has a great effect on the front behavior and crostructure A prototypical reaction–diffusion system in a porous GS11 Abstracts 133

medium is considered, whose microstructure undergoes an to solve a stochastic equation with additive noise. evolution with respect to time. Employing the method of homogenization in domains with evolving microstructure, Guillaume Bal the limit problems are obtained. Attention is also paid to Columbia University the scaling of the material parameters with powers of the Department of Applied Physics and Applied Mathematics homogenization parameter arising from a nondimensional- [email protected] ization. For one class of applications, an efficient adaptive finite element approach for the resulting limit problem is presented. MS84 Error Estimates on Homogenization of Free Bound- Malte Peter ary Velocities Institute of Mathematics University of Augsburg I will talk about a free boundary problem which describes [email protected] contact angle dynamics on an inhomogeneous surface. We obtain an estimate on the convergence rate of the free boundaries to the homogenization limit in periodic media. MS83 The method presented here also applies to more general Homogenization of Biot-type Multi-compartement classes of free boundary problems with oscillating bound- Medium with Double Porosity for Multiscale Mod- ary velocities. eling of Diffusion-deformation Processes Inwon Kim In the paper we report on homogenization of the dou- Department of Mathematics ble porous fluid-saturated deforming medium which is de- UCLA scribed by the Biot model. Both compressible and incom- [email protected] pressible cases were considered. It is shown, how the topology of microstructure defined w.r.t. the dual porosity influences structure of the homogenized model. Fading memory MS84 effects are explained in terms of flow in the dual porosity. Multi-scale Analysis for Problems Where Classical Also large-deforming media were subject of homogeniza- Homogenization Fails tion applied to the updated Lagrangian formulation. For layered porous media with transversally periodic structure, It is known that in many real situations, the classical ho- the homogenization leads to models with reduced dimen- mogenization theory fails to provide a robust and reliable sion: ”3D to N times 2D”. The models are developed for macroscale approximation model for the given microstruc- simulations of compact bone poroelasticity, or tissue peru- ture. In this talk I will discuss about possible alternative sion. Numerical examples are computed using our in-house ideas to deal with such situations. FEM code Sfepy. Daniel Onofrei Eduard Rohan Department of Mathematics Dept. of Mathematics, Faculty of Applied Sciences University of Utah University of West Bohemia [email protected] [email protected] Bacim Alali Robert Cimrman, Vladimir Lukes Mathematics Department University of West Bohemia, Pilsen University of Utah [email protected], [email protected] [email protected]

MS84 MS84 Equations with Random Coefficients: Convergence Corrector Estimates for a Reaction-diffusion Sys- to Deterministic or Stochastic Limits and Theory tem Modeling Sulfate Corrosion of Correctors A semi-linear partially-dissipative reaction-diffusion sys- Equations with small scale structures abound in applied tem modeling concrete corrosion in sewer pipes is consid- sciences. Such structures often cannot be modeled at the ered. The microstructure contains three non-overlapping microscopic level and thus require that one understand regions: the solid matrix, the pore water clinging on solid their macroscopic influence. I will consider the situation fabrics and the air-filled part of the pore. A particular fea- of partial differential equations with random, highly oscil- ture of the microscopic model is that two interface-reaction latory, potentials. One is then interested in the behavior of mechanisms, the Henry’s law and a nonlinear chemical re- the solutions to that equation as the frequency of oscilla- action on the boundary of pore walls, are balanced by the tions in the micro-structure tends to infinity. Depending on diffusive transport. The quality of the averaging procedure spatial dimension and the decorrelation properties of the is defined by means of error estimates. We construct first random potential, I will show that the limit is the solution order correctors and derive error estimates using the un- to either a deterministic, homogenized (effective medium) folding method, which enables the proof of error estimates equation or a stochastic equation with multiplicative noise. without additional regularity of the correctors. More precisely, there is a critical spatial dimension above Mariya Ptashnyk which we observe convergence to a deterministic solution Department of Mathematics I and below which we observe convergence to a stochastic RWTH Aachen University solution. In the former case, a theory of correctors to ho- [email protected] mogenization allows one to asymptotically capture the ran- domness in the solution to the equation with the small scale structure. Once properly rescaled, this corrector is shown Adrian Muntean 134 GS11 Abstracts

Department of Mathematics and Computer Science PP1 TU Eindhoven On the Development of An Adaptive Triangular [email protected] Discontinuous Galerkin Shallow Water Model

Tasnim Fatima The precise simulation of geophysical phenomena is essen- Department of Mathematics and Computer Science tial for the development of hazard warning systems. There- TU Eindhoven, NL fore, we develop an adaptive two-dimensional shallow wa- [email protected] ter model based on the Discontinuous Galerkin method. For spatial discretization we utilize high-order nodal basis functions as øﬁrst introduced by Giraldo et. al in 2002 and MS85 the underlying triangular mesh is generated with amatos Robust Convex Optimization for Closed Loop (see Behrens et. al, 2005). We show ﬁørst results obtained Reservoir Management from running several testcases.

Abstract not available at time of publication. Nicole Beisiegel,JoernBehrens KlimaCampus, University of Hamburg Remus G. Hanea [email protected], [email protected] TNO Built and Environment, [email protected] PP1 Pseudo-Steady State Attractors for Fully Transient MS85 Forchheimer Flows in Porous Media Integrated Dynamic Optimization and Control in Reservoir Engineering This work is focused on the dynamics of the generalized Forchheimer flows for slightly compressible fluids in porous Abstract not available at time of publication. media with given total flux on the boundary. The class of the flows which are time invariant to certain character- Jan Dirk Jansen istics is introduced and explored. We proved that each Technische Universiteit Delft of the time invariant flow attracts fully transient flows for Shell International E&P particular boundary conditions independently to the initial [email protected] data. Some applied engineering aspects of the framework are considered. MS85 Lidia Bloshanskaya Hierarchical Long-term and Short-term Produc- Texas Tech University tion Optimization Department of Mathematics and Statistics [email protected] Abstract not available at time of publication.

Gijs van Essen PP1 Delft University of Technology Developing Empirically Based Seismic Event Loca- [email protected] tion Ground Truth Criteria for Regional Seismic Network in Ethiopia and Tibet

PP1 The International nuclear monitoring community relies Iterative Solution of Non-Autonomous Bloch Equa- on selection criteria for classifying seismic events at the tions: Fluorescence Spectrum with Detuned Ground Truth 5km level, which specifies the absolute lo- Squeezed Vacuum Field cation to within 5km. Regional-network locations cannot be validated using existing criteria. Using the resam- The non-autonomous Bloch equations modelling a driven pling methodologies developed by Bondr et al. (2004) and 2-level atom in the presence of an off-resonant broadband (Boomer et al., 2010), we have obtained empirical criteria squeezed vacuum (SV) field is treated analytically. This based on measures of uniformity of azimuth and distance concerns iterative solutions valid for large SV detuning pa- coverage. Criteria are being developed for Ethiopia and rameter but for arbitrary strength of the laser field. Com- Tibet. putational results are presented for the averaged atomic variables for various data and compared with the resonant Richard A. Brazier SV field case. The iterated analytical results for nonzero The Pennsylvania State University Dubois Campus SV detuning are compared with the (exact) numerical so- Commonwealth College (Math Division) lutions of the Bloch equations, hence we have an insight [email protected] about the range of other system parameters (other than the Rabi frequency) for which the iterated solutions are valid Kb Boomer to O(10-2) or less. The main purpose of deriving these Bucknell University analytical results is to calculate analytically the transient [email protected] fluorescent spectrum. For an initially ground-state atom, both the SV phase and detuning parameters induce pro- nounced asymmetrical spectrum in the strong field case. PP1 Reduced Order Models for Uncertainty Quantifica- Rania A. Alharbi tion and Parameter Estimation in Subsurface Flows King abdullaziz university, mathematics department,KSA Modern reservoir simulations with millions of degrees of Po. Box 42696 Jeddah 21551 freedom can be extremely costly to evaluate given a set [email protected] GS11 Abstracts 135

of input parameters representing boundary/initial condi- Stefan Finsterle tions and flow field properties. Thus, studies that require Lawrence Berkeley National Laboratory (LBNL), many model evaluations at varying input parameters such Berkeley as sensitivity analysis, uncertainty propagation, or history Hydrogeology & Reservoir Dynamics Department matching can be prohibitively expensive. Cheaper reduced [email protected] order models are necessary for such analyses. We propose a method for reduced order modeling of nonlinear dynam- Quanlin Zhou ical systems. The model reduction method is comparable Lawrence Berkeley National Laboratory (LBNL) to reduced basis methods and POD-based model reduc- [email protected] tion, where the reduced model is a linear combination of a small set of model runs. The coefficients of the linear combination are computed with a nonlinear least squares PP1 method, and the minimized residual is used as an a pos- Flow of Compressible Fluids Through Cracks in teriori error estimate on the reduced model. This error Elastic Bodies and Excitation of Seismic Waves in estimate can also be used to find points in the parameter Volcanic Eruptions space whose solution will maximally enhance the reduced basis, i.e. as a guide for how to choose the parameters We investigate the eruption of fluids through conduits in to run the full model. We consider as our model prob- elastic bodies, with particular focus on the excitation of lem a one-dimensional two-phase, three-component com- seismic waves by conduit wall oscillations induced by fluid positional displacement. The parameters in our study are flow. The fluid, an isothermal mixture of exsolved gas and the component K-values, i.e., ratio of the each components liquid melt, obeys quasi-one-dimensional mass and momen- phase composition; for simplicity we use a constant K-value tum balance equations and a nonlinear equation of state model. The predicted recovery from a reservoir is depen- describing compressibility changes during gas exsolution. dent on the solution path which in turn has a highly non- Both the elastic wave equation and the fluid equations are linear dependence on the K-values (even when these are solved with high order finite differences. taken to be constants). As a proof of concept, we use the reduced order model as a surrogate in a maximum entropy Eric M. Dunham,DarcyOgden inversion method to find the K-values that are consistent Department of Geophysics with a given production history. Stanford University [email protected], [email protected] Paul Constantine Sandia National Labs [email protected] PP1 A Fully Implicit Solution Method Capability in the Jeremy E. Kozdon Spectral Element Community Atmosphere Model Stanford University Geophysics Grid refinement of the Community Atmopshere Model [email protected] (CAM) creates new algorithmic challenges including coupled nonlinear dynamics, physics, and chemistry, multiple disparate time scales, and scalability requirements. In ad- Margot Gerritsen dition, new capabilities to analyze model sensitivities are Dept of Petroleum Engineering desired. Solution methods that address these issues are Stanford University becoming increasingly important. A fully implicit (FI) so- [email protected] lution method is applied to the shallow water and primitive equations within the spectral element dynamical core PP1 (CAM-HOMME) and early results are presented. FI provides a coherent nonlinear solution to all dependent vari- Sensitivity of Co2 Storage Formation Pressuriza- ables and allows relatively large time steps to be taken sta- tion and Migration to Uncertainty in Fault Zones bly without subcycling and with demonstrated accuracy. and Reservoir Properties: a Case Study. The solver implementation is occurring through the de- We investigate here the potential impact of geologic carbon velopment of a Fortran interface package for the Trilinos sequestration in a partially compartmentalized sandstone project that has been applied to several components of the basin in the Southern San Joaquin Valley in California, Community Earth System Model. USA. Uncertainty about fault behavior is addressed by as- Katherine J. Evans sessing four distinctive fault property scenarios. A sys- Oak Ridge National Laboratory tematic sensitivity study is conducted for each scenario to [email protected] identify near- and far-field key hydrogeological parameters and processes affecting pressure buildup and brine migration. PP1 Andrea Cortis Simulation of Supercritical Carbon Dioxide Seep- Earth Sciences Division, 90-1116 age from An Injection Well Lawrence Berkeley National Laboratory We present a numerical model that simulates flow and [email protected] transport of CO2 into a multi-layered subsurface system. The model uses state-of-the-art multi-threaded finite ele- Jens T. Birkholzer ment methods and unstructured adaptive mesh refinement Lawrence Berkeley National Laboratory scheme. Several scenarios spanning from a homogeneous (LBNL) single layered reservoir to heterogeneous multi-layered sys- [email protected] tems, which including cap-rock with embedded fractures, have been simulated under different operations of CO2 136 GS11 Abstracts

leaking conditions. Results show the impact of leakage PP1 rates impact on the evolution of the CO2 spread. Application of Fractal Geometry in Evaluation of Plagioclase Mineralization: Case Study Igneous Souheil M. Ezzedine,IlyaLomov,LeeGlascoe,Tarabay Rocks in Moshiran Area, Nw Iran Antoun LLNL It is widely accepted that many of Minerals show scale in- [email protected], [email protected], [email protected], variance, i.e. they are self-similar within a large range of [email protected] scales. In this paper, fractal dimension of Plagioclase crystals in Basaltic, Andesitic rocks from Moshiran area in NW of Iran have calculated using box-counting method. Im- PP1 age analysis techniques are applied and fractal dimension Simulation and Upscaling of Nonaqueous Phase varies between 1.5 to 1.85 that correspond with geochem- Liquid Dissolution in Three Dimensional Saturated ical modeling of magma mixing Coupled fractal analysis Porous Media and geochemical data reveal that D increases as the degree of magma interaction and show that homogenization We present an integrated experimental and computational paterns increases in magma. An other hand this study approach aimed at quantitatively investigating the role of indicated that present of zoning structures in Plagioclase pore structure, entrapped DNAPL distribution and hydro- crystals have relation between fractal geometry functions dynamic conditions on core-scale mass transfer rates. A .fractal geometry can help to interpretation of varies kind numerical model was developed using adaptive mesh re- texture in rocks. finement finite elements method. The numerical model solves simultaneously Navier-Stokes flow and transport Mohammad Fadaeyan with state-of-the art embedded interface tracking scheme. Payame Noor University Of Ardebil The model was used to derive upscaled mass transfer rates m [email protected] for different soil types.

Souheil M. Ezzedine PP1 LLNL An Alternative Splitting for Two-Phase Flow with [email protected] Capillary Pressure

Russell Detwiler A subset of problems in two-phase groundwater flow fea- UC Irvine ture diffusive capillary pressure terms that balance the ad- [email protected] vective motion of the fluid. One numerical method designed to solve these advection-diffusion PDEs is a split Walter McNab method where the advective and diffusive parts are solved Lawrence Livermore National Lab separately. This works well when either advection or dif- [email protected] fusion dominates; however, when these terms are supposed to balance, this splitting can lead to a severe time-step re- Lee Glascoe striction. We propose a variation of this method that pre- LLNL serves the balance between the two effects while enabling a [email protected] larger time-step that is based on an f-wave decomposition of the flux. We show results from this formulation for a groundwater flow problem. PP1 Kirsten M. Fagnan Application of Fractal Geometry in Evaluation of Lawrence Berkeley National Laboratory Plagioclase Mineralization: Case Study Igneous [email protected] Rocks in Moshiran Area, Nw Iran

The area under study is situated in North-west of Iran. George Pau This area contains volcanic rock sequences from Basaltic LBNL to Andesitic composition related to volcanic processes in [email protected] Eocene. Plagioclase were analyzed by statistical methods to test for fractal behavior. The analysis shows that self- John B. Bell affine fractal geometry can be used to characterize the zon- Lawrence Berkeley National Laboratory ing patterns of this minerals. Generally low abundance of [email protected] small plagioclase crystals increases to 5-15% with some as large as 12 mm long. The crystal size distributions of these crystals mostly plot as almost straight lines on a classic PP1 CSD diagram. fractal dimension of Plagioclase crystals in Direct Simulations of Dynamic Interfaces in Com- this area have calculated using fractal geometric methods plex Geometry such as box-counting. we can from this studies results conclude that factors operating on scales much larger than the Multiphase flow in porous media is dictated by the be- local interface processes are most important in controlling havior of fluid-fluid interfaces, which affects phase distri- the zonation. bution through hysteresis and instability. To investigate these phenomena, we perform direct numerical simulations Mohammad Fadaeyan of a 2D two-phase system. The full Navier-Stokes equa- Payame Noor University Of Ardebil tions are solved in the pore space and the Volume of Fluid m [email protected] method is used to track the interfaces. Particular attention is paid to interfacial energy and to the effects of the GS11 Abstracts 137

velocity on phase distribution. Oregon State University [email protected] Andrea Ferrari, Riccardo Maniero Institute of Geophysics Malgorzata Peszynska University of Lausanne Department of Mathematics [email protected], [email protected] Oregon State University [email protected] Ivan Lunati University of Lausanne [email protected] PP1 Vertical Equilibrium Simulation with 3D Near-Well Modeling PP1 Comparison of Preconditioning Techniques for Op- Lack of vertical resolution may cause 3D simulations of timizing a Nonhydrostatic, Parallel Tsunami Sim- CO2 sequestration to be inaccurate. To increase accuracy ulation Model and reduce computational cost, a thin CO2 plume can be approximated in terms of its thickness to obtain a 2D sim- The Tsunami Modelling Group at Alfred-Wegener- ulation model. However, the corresponding assumption of Institute has developed a tsunami simulation tool with a NC vertical equilibrium is not fulﬁlled near an injecting well. P1 − P1 Finite Element discretization on unstructured Herein, we therefore develop a method in which a verti- grids and a Leapfrog time-stepping scheme. For higher cal equilibrium formulation is coupled with a standard 3D accuracy a set of equations similar to the shallow water discretization near the well. equations has to be solved. The major percentage of the resources is required by the computation of several large, Ingeborg Ligaarden, Halvor Nilsen sparse systems of equations. By comparison of miscella- SINTEF neous preconditioning techniques their individual capabil- [email protected], [email protected] ities of optimization are presented.

Annika Fuchs PP1 Alfred-Wegener-Institute for Polar and Marine Mimetic Finite Diﬀerence Methods for Modeling [email protected] Subsurface Flows

Stephan Frickenhaus, Wolfgang Hiller, Rakowsky Natalja Mimetic finite difference (MFD) methods mimic important Alfred-Wegener-Institute for Polar and properties of underlying PDEs, such as conservation laws, Marine Research symmetry and positivity of a solution, and fundamental [email protected], [email protected], na- identities of the vector and tensor calculus. This poster [email protected] will summarize our progress in development and analysis of MFD methods as well as they usage in applied projects for modeling subsurface flows on distorted unstructured PP1 polyhedral grids. Synthetic 3D Simulations from Real Models with Topography Konstantin Lipnikov Los Alamos National Laboratory I show finite-difference discretizations of (visco-)elastic [email protected] wave equations including free surface topography boundary conditions, using an exact transform from a vertically curved (stretched) grid to a rectangular (computational) PP1 grid. I simulate real areas of 3D models covered by to- Seismic Processing of Diffractions pography. Qualitative effects are shown of prominent free surface topography on wavefields, comparing and isolat- A main task in seismic data interpretation is the identifica- ing effects of using real and homogeneous interior media, tion of sharpened objects in the subsurface, such as faults as well as assessing effects of adding viscoelasticity to the or channels. When these structures are small enough, they results. diffract the energy emitted by the acquisition process. We propose a method that optimize the traditional seismic pro- Stig O. Hestholm cessing, by considering the diffractions as information in- ExxonMobil Upstream Research Company stead of noise, to locate points at the velocity model where [email protected] diffractions are made, and thus generating better images of the subsurface.

PP1 Susanne R. Maciel A-Priori Estimates for Non-Equilibrium Systems Universidade de Brasilia [email protected] We discuss extensions and applications of a-posteriori analysis for a coupled linear system of PDEs known in multi- Ricardo Biloti scale analysis as Warren-Root model. Its structure extends Universidade Estadual de Campinas readily to nonlinear models of non-equilibrium adsorption, [email protected] Enhanced CoalBed Methane Recovery, and other kinetic models. In this poster we show numerical results for the a-posteriori analysis and for the applications. PP1 Reducing Hurricane Storm Surge Model Error Us- Viviane Klein 138 GS11 Abstracts

ing the Ensemble Kalman Filter structured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries Error is inherent in every dynamical model and in observations of the model solution. Given both, data assimilation Spontaneous rupture models are becoming increasingly methods are used to compute the best estimate of state. used to study scenario earthquakes and to assess seis- The Ensemble Kalman Filter is an advanced data assim- mic hazard. High-order numerical methods are ideally ilation method for nonlinear problems. Here it is applied suited for these problems, but stable, accurate, and effi- to the Advanced Circulation (ADCIRC) model to better cient methods are needed to incorporate the nonlinear fric- predict hurricane storm surge using water elevation mea- tion laws. We present our latest developments on the use surements. of summation-by-parts finite difference methods and the simultaneous approximation term method for such prob- Talea L. Mayo lems, with a focus on using unstructured grids. The University of Texas at Austin [email protected]. Ossian Oreilly Department of scientific computing uppsala PP1 [email protected] Tectonic Evolution at Rift Zones: Geodynamics and Numerical Modeling Jeremy E. Kozdon Stanford University Tectonic evolution at rift zones is commonly considered Geophysics symmetric along mid-ocean ridges, when modeling with [email protected] relative plate motions and steady-state processes. How- ever, the bathymetry of rift zones is generally asymmetric. Adopting an absolute frame of reference, we performed Eric M. Dunham simulations using FEM: the mantle is modeled as a viscous Department of Geophysics non-newtonian fluid, and its dynamics is described by the Stanford University Stokes equations. Results show an asymmetric thickening [email protected] of plates along the ridge, as suggested by the observations. Jan Nordström Mathematics Marco Cuffaro Linköping University Istituto di Geologia Ambientale e Geoingegneria [email protected] CNR marco.cuff[email protected] PP1 Carlo Doglioni Porescale Benchmark: Call for Participation UniversitàLaSapienza [email protected] [Organizers; M. Peszynska, Dorthe Wildenschild, Oregon State University]. We propose to define a set of benchmarks in porescale modeling organized by a group of re- Edie Miglio searchers involved in the computational and experimental Politecnico di Milano (Italy) modeling at porescale. We define the goals, propose the MOX, Dept. of Mathematics online venue, and outline the directions, applications, tech- [email protected] niques, as well as timeline. In particular, we include single and multiphase flow, biofilms and reactive transport modeling, and a variety of techniques including continuum to PP1 discrete computations. This poster is intended as a call for A New Adaptive Multiscale Fem Applied to Inter- participation in this benchmark. face Problems Malgorzata Peszynska We introduce a new adaptive multiscale finite element Department of Mathematics method (AMsFEM) that greatly improves convergence Oregon State University whilst still being conforming. AMsFEM is an extension of [email protected] the adaptive local-global multiscale finite element method by Durlofsky et al. The idea is to keep the mesh fixed and instead iteratively adapt the shape of the basis func- PP1 tions in the approximation space. This allows fine scale Testing Nonhydrostatic Sound-Proof Equations As data to be incorporated in to local problems for the ba- Prospective Governing Pde for Regional Weather sis functions whilst still having a coarse global system to Prediction solve. We present applications of this to structural optimization problems but they can be applied to groundwater The nonhydrostatic anelastic model EULAG, for research flow problems also. of multiscale atmospheric flows, is considered as a prospective dynamical core of a future operational regional nu- Ray Millward merical weather prediction (NWP) model of the European Dept of Mathematical Sciences COnsortium for Small scale Modeling (COSMO), antici- University of Bath pated to operate at kilometer- and sub-kilometer horizontal [email protected] resolutions. Results of dry and moist idealized and semi- idealized tests are summarized and supplemented with examples of realistic sub-kilometer NWP-like simulations of PP1 Coupled High-Order Finite Difference and Un- GS11 Abstracts 139

the Alpine ﬂows. namics

Zbigniew P. Piotrowski We present energy estimates for the partial differential National Center for Atmospheric Research equations of mantle dynamics, in a somewhat simplified [email protected] form. We show that the fluid pressure blows up as the melt is lost. Therefore the fluid pressure variable cannot Marcin Kurowski, Bogdan Rosa be approximated in any simple way in a finite element and Institute of Meteorology and Water Management other approximation method. [email protected], [email protected] Abraham L. Taicher University of Texas at Austin Andrzej Wyszogrodzki [email protected] NCAR MMM [email protected] Todd Arbogast Dept of Math; C1200 University of Texas, Austin Michal Ziemianski [email protected] Institute of Meteorology and Water Management [email protected] Marc A. Hesse University of Texas PP1 Department of Geological Sciences The Impact of Single-Phase Upscaling on Polymer- [email protected] Flooded Reservoirs Upscaling of geological data to reservoir models is com- PP1 mon practice in reservoir simulation. However, reducing Coupling of the Evolution of Pore Pressure and the the number of grid blocks introduces errors in the simula- Retrogressive Slope Failure During Breaching tion due to computational discretization and loss of reservoir heterogeneity. Typically upscaling studies focus on Breaching is a type of slope failure that, due to the pore Newtonian fluid injection, e.g. water flooding, whereas the pressure response, produces retrogressive sediment release. effects of upscaling on non-Newtonian fluid flow behavior We study the connection between the pore pressure dis- are not well understood. In this study, we examine the sipation and the retrogressive slope failure through flume effect of upscaling polymer-floodings. experiments and numerical modeling. We find the erosion rate of breaching is proportional to the coefficient of con- Potcharaporn Pongthunya, Peter King solidation, and the spatial distribution of pore pressure is Imperial College London self-similar through time. [email protected], [email protected] Yao You Jackson School of Geosciences The University of Texas at Austin PP1 [email protected] An Alternative to Streamlines for Flow Diagnostics on Structured and Unstructured Grids Peter B. Flemings The University of Texas at Austin In this paper, we investigate finite volume methods as an Jackson School of Geosciences alternative to traditional streamline-based methods for ob- pfl[email protected] taining flow diagnostic information. Given a computed flux field, we solve the stationary transport equations for tracer David Mohrig and time of flight on a fixed grid to partition the reservoir Jackson School of Geosciences into injector-producer pairs and to assess the heterogene- The University of Texas at Austin ity of the reservoir. We show that a multi-dimensional [email protected] upstream weighting scheme is able to reduce the numerical diffusion associated with the method. PP1 Mohammad Shahvali Model of Mineralization of Rainwater Passing Stanford University Through a Rock [email protected] Geochemical interactions of rainwater passing through a Bradley Mallison rock was modelled. The main chemical components and Chevron Energy Tech. Co the governing equlibrium and kinetic chemical reactions [email protected] were identified. Sensitivity analysis of some parameters of the model was done to better understand the model. Herve Gross The model was used to inverse modelling - calibration of Chevron Energy Technology Company several parameters of a real-world problem - using mea- [email protected] surement data published before. Acknowledgement: This result was realized under the state subsidy of the Czech Republic within the project No. 1M0554 PP1 Energy Bounds for the Equations of Mantle Dy- Ivan Bruský Institute of Novel Technologies and Applied Informatics Technical University of Liberec 140 GS11 Abstracts

[email protected]

Jan Semberaˇ The Institute of Novel Technologies and Applied Informatics Technical University of Liberec [email protected]

PP1 Calibration of Rainfall-Runoﬀ Hydrological Model and Flood Simulation Using Data Assimilation

This work focuses on the calibration of a distributed par- simonious event-based rainfall-runoff model using data assimilation. In the present work, a BLUE filtering technique was used to calibrate the initial water deficit and the velocity travel for each flood event assimilating the first available discharge measurements at the catchment outlet. The assimilation algorithm was applied on two Mediterranean catchment areas of different size and dynamics: Gardon d’Anduze and Lez. On both catchments, it was shown over a significant number of flood events, that the data assimilation procedure improves the flood peak forecast. The improvement is globally more important for the Gardon d’Anduze catchment where the flood events are stronger. The peak can be forecasted up to 36 hours head of time for some events. Such results are obtained assimilating very few observations (up to 4) during the rise of the water level. For multiple peaks events, the assimilation of the observations from the first peak leads to a significant improvement of the second peak simulation. It was also shown that the flood rise is often faster in reality than it is represented by the model. In this case and when the flood peak is under estimated in the simulation, the use of the first observations can be misleading for the data assimilation algorithm. The careful estimation of the observation and background error variances enabled the satisfying use of the data assimilation in these complex cases even though it does not allow the model error correction.

Sophie ricci, Sophie ricci CERFACS [email protected], [email protected] andrea piacentini, Olivier Thual Cerfacs [email protected], [email protected] mathieu coustau HSM [email protected]