46 GS09 Abstracts

IP1 vanced numerical computation and (2) field and laboratory The Use of Geophysical Methods to Characterize experimental results with a properly validated and verified Hydrogeologic Systems simulation tool for prediction. This result is a necessary prerequisite for wide-spread acceptance of computational There is growing use of geophysical methods to obtain in- simulation and enhancement of computer driven discov- formation about subsurface properties and processes in hy- ery and innovation in the geosciences, and, ultimately, in drogeologic systems. Critical to advancing this use is the geo-engineering. A fundamental difficulty in understanding need to better understand the link between measurements and predicting large-scale fluid movements in porous media made remotely of geophysical parameters and the prop- is that these movements depend upon phenomena occur- erties and processes governing fluid flow and contaminant ing on small scales in space and/or time. The differences in transport. Captured in the geophysical data is informa- scale can be staggering. Aquifers and reservoirs extend for tion about hydrogeologic systems across a range of scales thousands of meters, while their transport properties can from the pore scale to the facies scale. Laboratory ex- vary across centimeters, reflecting the depositional and dia- periments best reveal the complex relationships between genetic processes that formed the rocks. In turn, transport geophysical parameters and various physical and chemical properties depend on the distribution, correlation and con- properties/processes at the pore scale. Field studies best nectivity of micron sized geometric features such as pore reveal the relationship between geophysical images and the throats, and on molecular chemical reactions. Seepage and larger facies-scale hydrogeologic structure. At all scales of even pumped velocities can be extremely small compared measurement we need to develop a quantitative framework to the rates of phase changes and chemical reactions. The that allows us to accurately characterize hydrogeologic sys- coupling of flow simulation with mechanical deformations tems using data acquired with geophysical methods. is also important in addressing the response of reservoirs located in structurally weak geologic formations. An ex- Rosemary Knight ample of a subsurface grand challenge is the sequestration Stanford University of carbon in saline aquifers. Here one needs to accurately [email protected] predict the fate of injected carbon dioxide in conditions governed by multiphase flow, rock mechanics, multicomponent transport, thermodynamic phase behavior, chemi- IP2 cal reactions within both the fluid and the rock, and the Decision and Control with Uncertainty: What coupling of all these phenomena over multiple time and Problems Should We Aim to Solve? spatial scales. In this presentation we will discuss several multiscale and multiphysics approaches for addressing the There are four basic types of activity involving combina- modeling and simulation of complex subsurface phenomena tions of uncertainty and optimisation: * Uncertainty prop- such as carbon sequestration. agation where the problem is to predict the behaviour of an uncertain system, where the uncertainty is in the initial Mary Wheeler state of the system or factors, such as properties, influenc- The University of Texas at Austin ing the system evolution. * Data assimilation, also known [email protected] as history matching, system identification or inverse problems. * Decision making. Here a choice must be made between competing courses of action. For each choice of IP4 action the outcome is uncertain. * Optimal control of an Junior Scientist Award Lecture: Geologic Stor- uncertain system. A system is only known in a probabilis- age of Carbon Dioxide: A Challenge for the Geo- tic way. One has to design a control policy that optimises sciences the system. The problem is particularly difficult when optimisation of the measurement system is included in the Geologic storage of CO2 presents the geosciences commu- problem. These problems are closely related to one an- nity with a renewed challenge in terms of spatial and tem- other. However, the subject of decision theory is perhaps poral scales, non-linearly interacting physical processes, the most fundamental and well developed theory as it has data uncertainty, and urgency of answers to key regulatory a firm axiomatic basis and an extensive literature. In this questions. In this talk, we will outline the development talk we will examine the formulation of the problems and and implementation of a modeling approach to CO2 stor- then discuss the matter of how close we are to solving any age. We discuss dominant processes and temporal scales, of these problems in a satisfactory way. The main points properties of numerical methods and analytical solutions, that will be defended are (i) we should always optimise and design of new solution approaches. In the context of our expected utility and (ii) sequential formulations are applications to real datasets we conclude by opening a dis- the most fruitful for practical progress. cussion on whether simulating CO2 storage is a well posed challenge. Chris L. Farmer Oxford Centre for Collaborative Applied Mathematics Jan M. Nordbotten University of Oxford Department of Mathematics [email protected] University of Bergen [email protected] IP3 Career Awardees Talk: Challenges in Modeling IP5 Subsurface Complex Phenomena Multiple Scales Analyses for Atmospheric Flows

Today we are witnessing the beginnings of an ongoing in- Asymptotic techniques generalize the classical approach of tellectual paradigm shift in that computational simulations scale analysis in theoretical meteorology. Through, e.g., are being (1) included routinely in scientiﬁc analyses and matched asymptotic and multiple scales expansions they (2) used to make engineering design decisions. These devel- allow us to systematically study interactions across sepa- opments involve the merging of (1) high performance, ad- rated length and times scales. This will be demonstrated GS09 Abstracts 47

drawing from recent work on hurricane-like concentrated able mobility ratio between injected and displaced fluids vortices and on cloud–internal wave interactions. Whereas leads to a more uniform sweep of the aquifer leading to a the classical theory of anelastic mostions by Ogura and higher storage efficiency than injecting CO2 alone. This Phillips (1962) is naturally captured in an asymptotics- design was demonstrated through one-dimensional simula- based framework, its subsequent extensions, e.g., by Dut- tions that were verified through comparison with analytical ton and Fichtl (1969), Lipps and Hemler (1982), Bannon solutions. We then performed simulations of CO2 storage (1996), as well as Durran’s pseudo-incompressible model in a North Sea aquifer. We then extended our study to (1989,2008) pose a particular challenge. I will show that oil fields. We propose to inject more water than the tra- their systematic theoretical justification will require tech- ditional optimum that maximizes only oil recovery. This niques that go beyond scale analysis and single or multiple causes the CO2 to remain in the reservoir, increases the scales expansions. field life and leads to improved storage of CO2 as a trapped phase. Again, a short period of chase brine injection at the Rupert Klein end of the process traps most of the remaining CO2. Potsdam Institute for Climate Impact Research Free University of Berlin Martin Blunt [email protected] Dept. Earth Science and Engineering Imperial College London [email protected] IP6 Sea Ice Modelling CP1 On the geophysical scale sea ice is a thin, broken layer on A Lagrangian-Averaged Air-Water Coupled Sys- the polar oceans which is modified in thickness and com- tem for Wind-Driven Sea Surface Waves pactness by dynamic and thermodynamic processes. Sea ice represents the boundary between the two much larger Based on the Lagrangian-averaging modeling concept we geophysical fluids, the atmosphere and the ocean, and, formulate equations for the generation of wind-driven sea therefore, influences their interaction considerably. Sea ice surface waves. The equations are an air-water coupled is described as a two-dimensional deformable solid mate- system which includes viscosity and the surface tension. rial with a specific geophysical rheology. The presentation We apply the system to simplified two-dimensional lam- will focus on the optimization of sea ice dynamics, and on inar flows, and compare the results with those from the model verification using satellite data and buoy trajecto- models based on the exact Navier-Stokes equations. Es- ries. Applications to past and current sea ice anomalies pecially, we discuss its stability with laminar base profile. will be shown, including the interaction with atmosphere Growth rate, the zones of amplification and zones of decay and ocean. with respect to different wave lengths and wind speeds are found. Peter Lemke Alfred Wegener Institute Bong-Sik Kim [email protected] Mathematics Division, George Mason University - RAK, U.A.E. [email protected] IP7 Modeling Hurricane Waves and Storm Surge using Integrated Tightly Coupled Scalable Computations CP1 Parameterization of Turbulent Transport in Ran- In the wake of recent Gulf of Mexico hurricanes (Katrina, dom Vortex Models Rita, Gustav and Ike), efforts to accurately model storm surge in the Gulf of Mexico have intensified. A modeling We employ homogenization theory to develop a systematic system has been developed that simulates hurricane winds, parameterization strategy for quantifying the transport ef- wind-waves, storm surge, tides and river flow in this com- fects of mesoscale coherent structures in the ocean which plex region. This is accomplished by defining a domain and cannot be well resolved by large-scale weather and climate computational resolution appropriate for the relevant pro- simulations. We work from the ground up with simple cesses, specifying realistic boundary conditions, and imple- kinematic models and study in particular how the effective menting accurate, robust, and highly parallel unstructured diffusivity depends on the governing parameters, such as grid algorithms for both the wind waves and the long wave Strouhal number and Peclet number, in a class of dynam- current/storm surge/tide model. ical random vortex flows. Joannes Westerink Banu Baydil Department of Civil Engineering and Geological Sciences Dept. Mathematical Sciences University of Notre Dame Rensselaer Polytechnic Institute [email protected] [email protected]

Peter R. Kramer IP8 Rensselaer Polytechnic Institute Design of Carbon Dioxide Storage Department of Mathematical Sciences [email protected] We propose design strategies for CO2 injection to maximize storage in aquifers and to maximize both CO2 storage and enhanced oil recovery (EOR) in oil reservoirs. We Shafer Smith propose a carbon storage strategy where CO2 and brine Courant Institute are injected into an aquifer together followed by brine in- Center for Atmosphere Ocean Science jection alone. This renders 80-95% of the CO2 immobile [email protected] in pore-scale droplets within the porous rock. The favor- 48 GS09 Abstracts

CP1 Université de Rennes 1 Modeling Wave Breaking and Its Dissipative Ef- [email protected] fects on Planetary-Scale Wave-Current Interac- tions Jocelyne Erhel INRIA-Rennes, France The equations for basin scale currents and waves are mod- [email protected] ified to include wave breaking via velocity perturbations of random strength at random locations. The acceleration Jean-Raynald De Dreuzy field of individual perturbations is parametrized as to fit Géosciences Rennes, UMR6118 CNRS observations. The statistics of the perturbations are de- Université de Rennes 1 rived from realizations of a Gaussian ocean surface. Sim- [email protected] ulated wave groups are tracked and their growth rate of wave group energy is computed as a predictor of the onset of wave breaking. CP2 Jorge Ramirez Some Results Concerning a Model for Fractures Mathematics Department with Forchheier Flow University of Arizona Flow of a single phase, incompressible fluid in a porous [email protected] medium with a fracture is usually modeled using a conservation law together with Darcy’s law both in the fracture Juan Restrepo and in the surrounding rock matrix. However for some Departments of Mathematics and Physics fractures in which the flow is more rapid, the flow in the University of Arizona fracture is more accurately described using Forchheimer’s [email protected] equation. Here we are interested in a model in which the fracture is treated as an interface between two subdomains Michael L. Banner of rock matrix and in which the flow in the fracture, is School of Mathematics governed by Forchheimer’s equation, while that in the sur- University of NSW rounding matrix is governed by Darcy’s law. We show [email protected] existence and uniqueness of the solution of the resulting system. Some numerical results are also presented. James McWilliams Atmospheric Sciences Jean E. Roberts UCLA INRIA Paris-Rocquencourt [email protected] France [email protected]

CP2 Peter Knabner A Weak Solution and a Numerical Solution of the Universitat Erlangen-Nurenberg Coupled Navier-Stokes and Darcy Equations. Department of Mathematics [email protected] In this work we propose a multi-numerics scheme for modeling the coupling of the Navier-Stokes and Darcy Najla Frih, Ali Saada equations using the continuous finite element method in ENIT-LAMSIN the incompressible flow region and discontinuous Galerkin Tunis, Tunisia method in the porous medium region. We first show exis- [email protected], [email protected] tence and uniqueness of a weak solution. We then prove convergence of the numerical scheme and show some numerical simulations. CP2 Coupling Multi-Component Porous Media Flow Prince Chidyagwai, Beatrice Riviere with Free Flow Rice University Department of Computational and Applied Math Up to now, the coupling of free flow with porous media flow [email protected], [email protected] has been often considered only for a single-phase system. We extend this classical concept to two-component non- isothermal flow with two phases inside the porous medium CP2 and a single phase inside the free flow region. Our model On the Simulation of Flow in Large-Scale Fractured also takes into account evaporation and condensation pro- Media cesses. We discuss the coupled model and its iterative solution by means of several numerical examples. We propose to simulate flow within fractures lying in an impervious rock matrix. Each fracture is modeled by an Iryna Rybak ellipse of random distribution of eccentricity, length, posi- Universitaet Stuttgart, IANS tion and orientation. For efficiency purpose and easy mesh [email protected] refinement, fractures are meshed independently. The challenge comes then to guarantee the continuity of the fluxes Bernd Flemisch and heads at the fracture intersections by the means of a University of Stuttgart, Germany Mortar method for any crossing configurations of the frac- bernd.fl[email protected] tures. Géraldine Pichot Rainer Helmig Géosciences Rennes, UMR6118 CNRS IWS, University of Stuttgart, Germany GS09 Abstracts 49

Institut fur Wasserbau show characteristic anisotropies for different rock blocks in [email protected] the study areas. The results were applied in analysing the relative movements of rock blocks and, especially, in 3D Toon Leijnse modelling of discontinuous ore bodies. Wageningen University [email protected] Eevaliisa Laine Geological Survey of Finland eevaliisa.laine@gtk.fi Klaus Mosthaf Universitaet Stuttgart, IWS [email protected] CP3 On Semivariogram Fitting by TLS Adjustment Barbara Wohlmuth with a New Weighting Scheme for Aeromagnetic University of Stuttgart Data [email protected] In order to fit a nonlinear mathematical model to the empirical semivariogram values that belong to a set of spa- CP3 tially distributed data, the Total Least-Squares (TLS) ad- Downscaling of Pressure and Saturation Maps for justment method is employed with a new extended weight- An Improved Modelling of 4D Seismic Data ing scheme. In contrast to the standard Least-Squares (LS) method, TLS approximation is particularly suited in this History-matching workflows usually use pressure and sat- case since it treats the lag distance and the empirical semi- uration maps provided by fluid-flow simulations to com- variogram values symmetrically, assuming random errors pute 4D-seismic attributes. Unfortunately the resolution in both variables. Beside the development of a (simplified) of these maps is often too coarse to represent precisely the weighting scheme, proper measures for goodness of fit are fluid displacements at the geological scale. We introduce also considered in this more general case, the applicabil- here downscaling algorithms which compute fine pressure ity and performance of the relatively new method will be and saturation maps from geological data and reservoir- demonstrated by using a set of aeromagnetic data. simulation results. These algorithms are fast, conservative and improve significantly the 4D-seismic response of the Burkhard Schaffrin reservoir model. School of Earth Sciences The Ohio State University Guillaume Enchery aschaff[email protected] Institut Francais du Petrole [email protected] Frank Neitzel, Sibel Uzun School of Earth Sciences, The Ohio State University CP3 Columbus, Ohio, USA [email protected], [email protected] Finite Difference Modeling the Acoustic Logging in Porous Media CP4 A finite-difference time-domain (FDTD) algorithm is proposed to simulate the axisymmetric acoustic logs in fluid- Evolution of Rotation of a Satellite with Cavity saturated porous formation. In this algorithm, different Filled with a Viscous Fluid under the Action of forms of acoustic wave equations in fluid, solid and porous Light Pressure Torque media are unified as the form of Biots equations governing We investigate fast rotational motion of dynamically asym- wave propagation in poroelastic media. The algorithm is metric satellite with cavity filled with viscous fluid under validated by the comparisons with the analytical method. the action of gravitational and light pressure torque. This Simulations of the acoustic logging in radial layering and problem is similar to the motion of the planet composed horizontally layering porous formations are given by the of a liquid core and rigid mantle. The system obtained af- algorithm. ter averaging with respect to Euler–Poinsot motion is ana- Wei Guan, Hengshan Hu lyzed. Numerical analysis shows that the kinetic energy is Harbin Institute of Technology, China monotonically decreasing. Analytical analysis is conducted [email protected], [email protected] in neighboring of axial motion. Dmytro D. Leshchenko CP3 Odessa State Academy of Civil Engineering and Architecture A Geostatistical Study of Geophysical Data In- leshchenko [email protected] side Rock Blocks Bordered by Brittle Structures in Crystalline Bedrock Leonid D. Akulenko Interpolated gravity and magnetic maps are used together Institute for Problems in Mechanics RAS with elevation models in the interpretation of large geo- [email protected] logical structures such as folds and faults in crystalline bedrock. In the present study, geophysical data from study Yanina S. Zinkevich, Alla L. Rachinskaya sites in southern and eastern Finland were analysed and in- Odessa State Academy of Civil Engineering and terpolated to maps inside bedrock blocks bordered by frac- Architecture ture zones which were defined by using geological observa- [email protected], [email protected] tions and elevation models. The geophysical data consisted of gravity, magnetic and seismic surveys. As a result, geostatistical measures such as different kinds of variograms 50 GS09 Abstracts

CP4 paction, non-Newtonian behaviour of salt and sedimentary On Resolving Exponentially Large Viscosity Vari- rocks, basement evolution (due to isostasy and/or tectonic ations in Convective Mantle Flow with High Order movements) and fault induced displacements. Some syn- Discontinuous Galerkin Methods thetic and real application examples are used to validate and demonstrate the robustness of the approach. The equations governing planetary mantle convection involve a strongly temperature dependent viscosity co- Matteo Longoni, Cristiano Malossi efficient in the elliptic problem for the fluid velocity. MOX, Department of Mathematics; Politecnico di Milano The viscosity is typically Arrhenius or more generically Via Bonardi 9, Milan, Italy exp(f(T(x))) and needs to be resolved accurately in order [email protected], to calculate the correct velocity and temperature fields. An [email protected] analytic discussion showing how viscosity influences numerical calculations is followed by some numerical examples Paolo Ruffo, Giovanni Scrofani of convective mantle flow solved with the discontinuous Eni, E&P Div. - GEBA Dept Galerkin formulation on unstructured meshes. Via Emilia 1, S. Donato Mil.se (MI), Italy paolo.ruff[email protected], [email protected] Daniel T. Paulsen Brown University Andrea Villa Division of Applied Mathematics Universita’ degli Studi di Milano daniel [email protected] Department of Mathematics [email protected] Jan S. Hesthaven Brown University Division of Applied Mathematic CP5 [email protected] A Local Discontinuous Galerkin Discretization for Incompressible Hydrostatic Flows with Free Sur- Marc Parmentier face Using σ-Transformed Coordinates Brown University Geological Sciences The Local Discontinuous Galerkin (LDG) method is a em [email protected] higher order discretization method for advection-diffusion equations. In this talk we present a conservative LDG method for the simulation of incompressible hydrostatic CP4 free surface flows using σ-transformed coordinates. The Generation, Retention and Expulsion of Hydrocar- time-dependent computational domain representing the bons fluid region is transformed onto a domain that is fixed in time. The advantage of solving the resulting transformed Hydrocarbon generation and expulsion are strictly interre- system of partial differential equations is that unlike in lated processes and at a first approximation it is reasonable moving mesh strategies there is no need to smooth the dis- to assume a Darcy flow description of the expulsion pro- crete surface elevation for grid adaptation. cess. The proposed modelling combines a two-phase Darcy flow, with time dependent porosity, with a set of Ahrrenius Christoph Gersbacher reactions to describe hydrocarbon generation and cracking Division of Applied Mathematics and with a differential retention process in kerogen that af- University of Freiburg fects petroleum fractionation. The modelling approach has [email protected] been compared and validated with laboratory experiments results. Andreas Dedner Division of Applied Mathematics Anna Scotti University of Freiburg, Germany Politecnico di Milano [email protected] [email protected]

Alberto Consonni, Danilo Dolci, Loredana Caldiero CP5 Eni, E&P Div. - GEBA Dept Representation of Linear Terrain Features in a 2D [email protected], [email protected], Flood Model with Regular Cartesian Mesh [email protected] The failure of water control infrastructures leads to poten- Paolo Ruffo tially destructive floods. Accurate numerical simulation Eni, E&P Div. - GEBA Dept of such flows is fundamental in performing risk analyses Via Emilia 1, S. Donato Mil.se (MI), Italy and planning for emergency management. This paper de- paolo.ruff[email protected] scribes a cut-cell boundary approach to represent subgrid linear features (dams, rivers,...) inside a 2D structured FV code; a special version of this method is developed to CP4 represent river flows allowing the coupling of 1D and 2D Applications of Full Three-Dimensional Dynamic computations to simulate levee overtopping floods. Structural Modelling Edie Miglio An innovative full three-dimensional dynamic structural Politecnico di Milano (Italy) modelling software has been developed in order to model MOX, Dept. of Mathematics basin geological evolution. The proposed approach is able [email protected] to mimic the principal geological processes: sediment com- GS09 Abstracts 51

Mustafa Altinakar, Marcus McGrath, Yavuz Ozeren [email protected] NCCHE - University of Mississippi [email protected], Thierry Gallouet [email protected], [email protected] Université de Provence [email protected] CP5 Sylvie Pegaz-Fiornet Nonlinear Shallow Water Equation in Polar Coor- IFP dinates sylvie.pegaz-fi[email protected] An interaction of two water waves in a circular basin is studied within quadratic approximation. When the polar CP6 coordinates are used, the usual perturbation techniques in separation of variables method inevitably lead to a series Outflow Boundary Conditions in Porous Media of overdetermined systems of linear algebraic equations for Flow Equations unknown coefficients (in contrast with the Cartesian coor- To model the flow in porous media one typically uses ei- dinates). However, if we formally introduce a new function ther the Richards equation if the flow can be described satisfying the first system of this series, all these overdeter- effectively by one phase, or the two-phase flow equations mined systems become compatible (remaining overdeter- if two phases must be modeled. Due to the wide range mined) for the special case of the nonlinear shallow water of applications, the interest in these two systems is enor- equation. Using the new function and quadratic polyno- mous. Rigorous analytical results became available in the mials of the Bessel functions of radius, we explicitly ex- 80ies, when strong nonlinearities in time-dependent prob- press the coefficients of the resulting harmonics. It gives lems were treated systematically. In most contributions solutions describing the two-waves interaction which are on the subject, the analysis is simplified by restricting to found with the same accuracy as the nonlinear shallow Dirichlet boundary conditions, even though a physically water equation is derived. As a consequence, a general more appropriate boundary condition is the outflow con- boundary problem can be explicitly solved in these terms. dition. After motivating and explaining this condition we Alexander Shermenev present the corresponding qualitative analytical problems, Russian Academy of Sciences a regularization technique and existence results. [email protected] Ben Schweizer TU Dortmund CP6 Fakultät für Mathematik [email protected] Numerical Simulation of Multiphase Flows in Porous Media with a Degenerate Parabolic System CP6 In this work is introduced a numerical scheme for solving degenerate parabolic systems for porous media flow by Formulation of Compressible Immiscible Two- means of mixed ?nite elements formulation when a dis- Phase Flow Model by Means of Global Pressure tinct number of ?uid phases ?ows in distinct ?ow regions We consider a compressible immiscible two-phase flow in the physical domain. By means of an operator splitting model in porous media formulated in terms of a global pres- and domain decomposition techniques conformity condi- sure. Two possible definitions of global pressure are con- tions were obtained to bypass such degeneracy in order to sidered: a simplified one which is a generalization of incom- obtain a non-singular system for their numerical solution. pressible flow global pressure, and based on an approxima- Eduardo Abreu, Duilio Conceio tive calculation of mass densities, and a new one introduced Instituto Nacional de Matematica Pura e Aplicada - by B. Amaziane and M. Jurak which does not assume any IMPA approximation. We present analytical and computational [email protected], [email protected] comparison of the two models. Brahim Amaziane CP6 Universite de Pau [email protected] A Comparison of Two Numerical Models for Sec- ondary Oil Migration and Entrapment Mladen Jurak In this work, we compare the solutions obtained by two Department of Mathematics different methods for a synthetic trapping scenario with University of Zagreb realistic input parameters. The first method is an invasion [email protected] percolation model based on the following assumptions : oil migration is a rapid process limited by oil generation rate Ana Zgaljic-Keko and capillary pressure barriers. The second method is a University of Zagreb, Croatia two phase flow finite volume method with a flux definition [email protected] based on local extended pressure continuity conditions. Anthony Michel CP7 IFP Numerical Modelling of Dispersion in Complex [email protected] Systems

Clément Cancès We consider dispersion processes taking place in complex ENS Cachan Antenne de Bretagne systems where particles can be transported over large dis- tances by the fluctuations of the velocity field (e.g. turbu- 52 GS09 Abstracts

lent flows) or the heterogeneity of the of system (e.g. sub- come a matter of considerable concern. For proper ground- surface hydrology). For such situations, dispersion models water management, it is necessary to model the contam- based on Ficks law might not be accurate. These models ination mathematically in order to assess the effects of implicitly assume that the particles are following a Brow- contamination and predict the transport of contaminants. nian motion, where the dispersion of a cloud of particles Several deterministic models have been proposed and nu- is only driven by the local interactions between particles. merical procedures developed. Because of aquifer hetero- Such a model prevents random displacements of large am- genity, the the spatial variation of flow properties is er- plitude that could result from external forcings or hetero- ratic. Therefore a stochastic model of flow regime and geneities. A more accurate dispersion pattern can be ob- transport processes is more realistic. In this talk we use tained by assuming that random fluctuations follow a Levy a new method (A. Beskos and G.O. Roberts), Exact sim- distribution, which results in so-called Levy flights. In that ulation of diffusions, The Annals of Applied Probability case, the distribution of particles is no longer the solution 2005, vol. 15(4), 2422-2444) for modelling contaminant of a second-order diffusion equation. Instead, it can be transport. Furthermore we adress sensivity analysis of ex- shown that it is the solution of a fractional-order equation ceedance probabili- ties with respect to variations of the whose exponent is generally comprised between 1 and 2. transmissivity field, porosity and dispersivity Fractional-order differential operators are global differential operators in the sense that they take the whole behav- Franz Konecny ior of the function into account and not just the local value BOKU-University of Natural Resources and Applied of the slope or convexity. In this work, we discuss numerical Life Sciences, Vienna methods to solve the fractional-order dispersion equation. [email protected] Numerical methods like the finite difference and finite element methods are not well suited to solve this equation as they are generally of low order and thus require a lot CP7 of grid points to obtain an accurate solution. For local Models for Transport in Porous Media differential operators, this results in large sparse matrices that can be handled easily. However, for global differen- Tracer transport is most commonly described with the ad- tial operators, like the ones considered here, the resulting vection/dispersion equation (ADE). However even in sim- matrix is full since the global behavior of the function has ple experiments on homogenous systems, the ADE may to be taken into account. High-order, global numerical demonstrate incorrect behavior. In context of a specific methods like the spectral method therefore appear to be a experiment, data is compared with numerical solutions better choice to solve this problem as they naturally take of advection/dispersion and dual-permeability models. A the global behavior of the solution into account and use pore scale network model introduces a numerical labo- a limited number of degrees of freedom. Both approaches ratory for transport in homogeneous porous media with will be compared in terms of accuracy and computational time dependent boundary conditions. Finally we discuss a efficiency. model based on the continuous transport that covers general transport phenomena in porous media. Emmanuel Hanert UCLouvain Leonid Vasilyev Department of Environmental Sciences and Land Use Research Fellow Planning [email protected] [email protected] Jan M. Nordbotten Rachel Pritchard Department of Mathematics Swansea University University of Bergen [email protected] [email protected] Hua Chen CP7 PhD candidate Attractor for Random Boussinesq-Glover Equation [email protected] with Colored Noise

We consider the random Boussinesq-Glover equation with CP8 monotone operators in Banach or Hilbert spaces, driven Ensemble Kalman Filter (enkf) for An Oregon by a colored noise and with random initial condition. The Coastal Transition Zone (octz) noise is defined as stationary solution of a stochastic differential equation in finite dimensional (or Hilbert) spaces. A primitive-equation numerical ocean model is used to Under suitable assumptions, we prove the existence of study the upwelling circulation of OCTZ where shelf flows global attractor. This attractor is independent on proba- interact with the northern California Current. The present bilitary variable. Similar results arise in random reaction- OCTZ simulation results show realistic features such as diffusion equations. coastal jet separation and eddy formation offshore of Cape Blanco. An Ensemble Kalman Filter is formulated to im- Fejzi Kolaneci prove forecasts and representations of the flow, and to University of New York, Tirana study sensitivities to uncertainty in forcing and boundary [email protected] conditions.

Sangil Kim, Samelson Roger CP7 Oregon State University The Simulation of Contaminant Transport in [email protected], Groundwater and Environmental Risk Assessment [email protected]

The problem of assessing groundwater pollution has be- Chris Snyder GS09 Abstracts 53

Mesoscale and Microscale Meteorology Division Connections between them are also made. NCAR [email protected] Montri Maleewong Department of Mathematics, Faculty of Science Kasetsart University CP8 [email protected] Uncertainty Quantification for An Oregon Coastal Transition Zone Ocean Model CP8 We explore the practical effect of perturbing the bound- On Some Models of the Equipotential Gravity Sur- aries and wind forcing in a realistic-grid model of the Ore- faces in the Coastal Areas. gon Coastal Transition Zone, a region in which mesoscale eddies play an important role. The shelf flow is strongly This presentation deals with mathematical models of the wind-driven, and dynamically balanced perturbations of geoid equipotential surfaces in the coastal areas. At this the boundary data produce different solutions in various moment the greatest errors in the local (small scale) Geoid perturbed model simulations. Integrated effects on the determination are either in the complex mountain terrains simulation results are assessed, and the predictability and or in the coastal areas, and it is quite important to eval- uncertainty are quantified both in a Bayesian framework uate precise Geoid in the short wavelength (small scale) and by other standard statistical quantities. for the local communities in the coastal areas as to predict impacts of tropical storms and floods. Recent studies and Sangil Kim, Samelson Roger models of the Geoid demonstrated that the greatest errors Oregon State University in the Geoid surface have been made in the coastal area [email protected], where there are border lines between two huge volumes of [email protected] masses with rather different densities. In this presentation of the ongoing research we are considering some statistical Chris Snyder models based on the observed anomaly data as well as the Mesoscale and Microscale Meteorology Division model based on the Stokes-Helmert integral for the poten- NCAR tial of the gravitational field in the neighborhood of the [email protected] shoreline, namely, we consider some ideal boundary of the water and the land masses. We have used MatLab software to simulate some models and to visualize equipotential sur- CP8 faces. Effect of Island Shape on Oceanic Wake Formation Alexey L. Sadovski Numerical studies using Regional Ocean Modeling System Texas A&M University-Corpus Christi are presented. We investigate the formation of oceanic Dept of Comp & Math Sciences wakes, generated by obstacle of the shape of Madeira Is- [email protected] land without consideration of bathymetry (i.e., with vertical sides). The results are compared with ones, obtained Natalia Warner, Hong-Zhi Song, Yelena Nevel by [Dong, McWilliams, Shchepetkin, 2007: Island Wakes in Texas A&M University-Corpus Christi Deep Water. J. Phys. Oceanogr., 37, 962-981] where they [email protected], [email protected], ele- investigate the formation and evolution of wakes around [email protected] an idealized cylindrical island. Euclides A. Luis CP9 CEMAT (Center for Mathematics and its Applications) – Using Energy Minimizing Basis Functions As a IST, Multiscale Method, with Applications to Multigrid Technical University of Lisbon, Portugal and Domain Decomposition Solvers [email protected] We demonstrate the applicability of energy minimizing ba- Dmitri Boutov sis functions for two-phase flow simulations, and we high- Institute of Oceanography, Faculty of Sciences, light their numerous benefits. We show how they can be University of Lisbon implemented to obtain efficient serial (algebraic multigrid) [email protected] and parallel (Additive Schwarz with coarse space correction) linear solvers for large-scale heterogeneous problems. Moreover, they possess the same advantages of other mul- CP8 tiscale techniques, but without the need of constructing a Numerical Method for Solving the Unsteady coarse mesh, and they are well-suited for adaptive algebraic Gravity-Capillary Wave Problem coarsening.

The Boundary Integral Equation Method (BIEM) based Olivier Dubois on the Mixed-Eulerian-Lagrangian (MEL) appraoch is pre- IMA sented in this talk. We apply the method to numerically [email protected] solve the unsteady free surface flows in water of finite depth. Here, the fluid is assumed to be inviscid and in- Ilya D. Mishev compressible, while the flow is irrotational. The gravity ExxonMobil Upstream Research Company and surface tension effects are included in the dynamic Department Technical Software Development boundary condition. The main propose is to study the [email protected] stability of steady gravity-capillary waves. Some numerical results for both steady and unsteady flows are shown. Ludmil Zikatanov Pennsylvania State University 54 GS09 Abstracts

[email protected] scale Modeling and Simulation 4 (2005) 1, 88 - 114. Patrick Henning CP9 University of Münster, An Unfitted Discontinuous Galerkin Finite Ele- Institut für Numerische und Angewandte Mathematik ment Method for Numerical Upscaling in Porous [email protected] Media

Porescale simultations usually requirer a trade-off between CP9 computational costs, simplification of the modell or the ge- A Multiscale Mass Conservative Domain Decompo- ometry. A new scheme is presented, avoiding most of these sition Preconditioner for Solving Elliptic Problems draw-backs. It combines the idea of Unfitted Finite Ele- on Perturbed Grids ments with Discontinuous Galerkin methods. The minimal number of unknowns is not determined by the shape of the We present a multiscale mass conservative domain decom- domain, still a maximum of the geometric information is position preconditioner for solving elliptic problems on per- accounted. The method is verified by computing the perturbed grids. An important feature for the multiscale meability for a domain with known properties. methods, is the localisation approximations, for reducing the size of the global problem. We study different proper- Christian Engwer ties of the fine scale solution. We have looked at lack of IWR, University of Heidelberg monotonicity on the coarse scale, and studied circulations [email protected] in fine scale velocity field. Andreas Sandvin CP9 University of Bergen, CIPR Iterative Multiscale Finite Volume Method for [email protected] Compressible Multiphase Flow in Porous Media Ivar Aavatsmark We introduce an iterative MSFV (i-MSFV) method for Center for Integrated Petroleum Research parabolic problems arising from compressible multiphase University of Bergen flow in porous media as an extension of recently pub- [email protected] lished i-MSFV method for incompressible (elliptic) problems. Convergence studies are presented including appli- Jan M. Nordbotten cations for multiphase flow. We show that only a few itera- Department of Mathematics tions per time step are sufficient in order to obtain good re- University of Bergen sults; even for highly anisotropic heterogeneous reservoirs. [email protected] In any case, however, the resulting solution is conservative at the fine scale. CP10 Hadi Hajibeygi, Patrick Jenny Institute of Fluid Dynamics Hybrid Method for Low-Frequency Electromag- ETH Zurich netic Scattering from a Resistive Underground Tar- [email protected], [email protected] get We present a fast and accurate hybrid method for comput- CP9 ing low-frequency electromagnetic scattering from a resistive underground target. The method consists of solving a The Heterogeneous Multiscale Finite Element finite volume problem in a localized region containing the Method for Advection-Diffusion Problems with target, and using the integral equation (IE) method to ob- Rapidly Oscillating Coefficients and Large Ex- tain the field outside that region. The hybrid method thus pected Drift replaces the dense-matrix part of the rigorous IE method In this contribution we analyze a new version of the het- by sparse-matrix calculations based on an approximation erogeneous multiscale finite element method (HM-FEM; of Maxwell’s equations. originally introduced by E and Engquist [1]) for solving Shaaban A. Bakr multiscale advection-diffusion problems. These types of PH.D. researcher, centre for Integrated Petroleum problems have a variety of applications in geoscience, es- Research pecially in modelling transport of solutes in groundwater [email protected] and surface water. We give a-priori and a-posteriori error estimates for the method and provide corresponding numerical experiments that underline the analytical results. Trond Mannseth For details see [2,3,4]. [1] W. E and B. Enquist. The het- Centre for Integrated Petroleum Research erogeneous multiscale methods. Commun. Math. Sci. University of Bergen, Norway 1 (2003), no. 1, 87–132. [2] P. Henning, M. Ohlberger. [email protected] The heterogeneous multiscale finite elements method for advection-diffusion problems with rapidly oscillating coef- CP10 ficients and large expected drift. Münster University, in preparation. [3] P. Henning, M. Ohlberger. The heteroge- Impact of Time-Lapse Seismic Data on Permeabil- neous multiscale finite element method for elliptic homog- ity Estimation enization problems in perforated domains. Münster Uni- Time-lapse pseudo-seismic (saturation) data are integrated versity, Preprint 01/08 - N. [4] M. Ohlberger. A-Posteriori with production data to estimate the permeability field. error estimates for the heterogeneous multiscale finite ele- We investigate the impact of pseudo-seismic data with ment method for elliptic homogenization problems. Multi- fairly large uncertainty on the final estimates by apply- GS09 Abstracts 55

ing an error analysis to a particular estimation technique. S. Lambot, J. Vanderborght Numerical experiments show that the over-parametrization Institute of Chemistry and Dynamics of the Geosphere problem is more due to measurement errors than represen- Forschungszentrum Jülich tation bias. A quantity is derived to study the impact of [email protected], [email protected] perturbations in different types of measurements on the estimate. CP10 Tao Feng Recovery of Active Faults from Surface Displace- Centre for Integrated Petroleum Research ment Fields. [email protected] The goal of this research project is to process measure- Trond Mannseth ments of surface displacements in such a way to use them Centre for Integrated Petroleum Research as data for the inverse problem consisting of locating faults University of Bergen, Norway and portraying their geometry. Our research is also aim- [email protected] ing at determining whether a measured displacement field on the surface is indicative of the onset of a destabilization phase. We have already entirely solved a two dimen- CP10 sional problem associated to the strike slip model, which Locating Point Diffractors in Layered Media by essentially reduces displacement fields to two dimensional Spatial Dynamics scalar fields. Deriving the inversion method involved a rigorous mathematical eigenvalue asymptotic analysis, lead- We present a new approach to the problem of detecting ing to closed form inversion formulas. Those formulas were point diffractors from active source surface seismic data. then tested for robustness in numerical simulations. As We formulate an optimization problem in the configura- the strike slip model is limited in scope (it captures only tion space of possible collections of scatterers and con- one of the textbook examples of faults), we have worked struct a birth-and-death spatial dynamic, which converges on extending our results to fully three dimensional fault to the optimal solution. By design, this dynamic does problems. In this much more difficult case, we have al- not have resolution limits typical of migration based tech- ready obtained very promising closed form formulas (valid niques, which allows for subwavelength sensing. for the dominant part of the asymptotic behavior), and we have tested their use on numerical data. Nonetheless, a Oleg V. Poliannikov complete mathematical analysis of the eigenvalue problem Massachussetts Institute of Technology obtained by studying destabilization is still being inves- [email protected] tigated. This is joint work with I. R. Ionescu, with the support of NSF grant DMS 0707421. CP10 Darko Volkov Non-Invasive Methods and Modelling Approaches Worcester Polytechnic Institute to Study the Impact of Subsurface Structures on [email protected] Flow and Transport Ioan Ionescu Geophysical methods may play an important role in Universite Paris 13 - Institut Galilee managing our terrestrial environment and in maintaining [email protected] ecosystem functioning and services. Especially, the application and further development of hydrogeophysical methods combined with mathematical models seem very promis- CP11 ing to maintain and protect soil and groundwater quality. An Experimental Setup of Ground-Based and Air- Hydrogeophsical methods may help to improve our control borne Systems to Study Spatio-Temporal Struc- on storage, filter and buffer functions of soils and ground- tures in Atmosphere-Land Surface Energy, Water water systems. Moreover, methods are needed that will and Co2 Exchange help us to bridge the gap between the scale of measurements and observations and the scale at which manage- Exchange processes between land surface, vegetation and ment of terrestrial systems takes place. In this presenta- atmosphere over structured, inhomogeneous regions are in- tion several examples will be presented showing how hydro- vestigated in an experimental approach. For that purpose geophysical research can contribute in meeting these chal- ground-based long-term monitoring and dedicated cam- lenges and may be used to characterize subsurface water paigns are combined within the Rur catchment, Germany. flow and transport. Four campaigns covering different vegetation periods have been performed with instrumentation ranging from leaf Harry Vereecken level gas exchange, eddy correlation, scanning remote sen- Insitute of Chemistry and Dynamics of the Geosphere sors to aircraftobservations. Synergistic data analysis shall Forschungszentrum Jülich reveal spatio-temporal structures in the exchange processes [email protected] and their relation to external parameters.

J.A. Huisman Susanne Crewell, Jan Schween Institute of Chemistry and Dynamics of the Geosphere Institute for Geophysics and Meteorology Forschungszentrum J¨ulich Cologne University [email protected] [email protected], [email protected]

J. van Der Kruk Heiner Geiss, Uwe Rascher, Anke Schickling Institute of Chemistry and Dynamics of the GEosphere FZ J¨ulich Forschungszentrum J¨ulich [email protected], [email protected], [email protected] [email protected] 56 GS09 Abstracts

Christoph Selbach the least computer time. Institute for Geophysics and Meteorology Cologne University David L. Williamson [email protected] National Center for Atmospheric Research [email protected]

CP11 One-Shot Parameter Optimization in Climate CP12 Modeling A Priori Convergence Analysis of a Coupled Ge- omechanics and Reservoir Flow Model with Stress- We present an iterative method to solve data assimilation Dependent Permeability problems to identify parameters of parts of the climate system as for example ocean or atmospheric models. The goal We consider the numerical solution of a coupled geome- is to obtain feasibility and optimality by simultaneously up- chanics and ?a stress-sensitive reservoir flow model.? We dating the state, adjoint and parameter values. Numerical combine a ? mixed finite element for Darcy flow and results are shown on the basis of a least-squares fit of the Galerkin finite element for elasticity. ? ?This work fo- Rahmstorf North Atlantic THC box model to given data. cuses on deriving ?convergence results for the numerical solution of this nonlinear partial differential system. The Claudia Kratzenstein, Thomas Slawig CG/mixed method produces optimal convergence rates Christian-Albrechts-Uni Kiel with respect to regularity. The theoretical error estimates Department of Computer Science we derived include the possibility for the displacement and [email protected], [email protected] the flow variables being calculated on different grids. We perform numerical experiments for verifying our theory and Andreas Griewank modeling some engineering applications. HU Berlin, MATHEON Research Center, Germany [email protected] Silvia Barbeiro Department of Mathematics, University of Coimbra CSM, ICES, University of Texas at Austin CP11 [email protected] Three-Dimensional Dynamics in Non-Parallel Shear Stratified Flows Mary Wheeler The University of Texas at Austin The instabilities of non-parallel flows such as those in- [email protected] duced by polarized inertia-gravity waves embedded in a stably stratified environment are analyzed in the context of the 3D Euler-Boussinesq equations. We derive a suf- CP12 ficient condition for shear stability and a necessary con- Large Deformation in Viscoelastic Solid Bodies – dition for instability in the case of non-parallel velocity Numerical Simulation of Salt Migration. fields. Three dimensional numerical simulations of the full nonlinear equations are conducted to characterize the re- We consider instability of a two layered solid body of a spective modes of instability, their topology and dynamics, denser material on top of a lighter one. This problem is and subsequent breakdown into turbulence. We investi- widely known to geophysicists in sediment-salt migration gate three-dimensional characteristics and present compu- as salt diapirism. In the literature, this problem has often tational results on Lagrangian particle dynamics. been treated as Raleigh-Taylor instability in viscous fluids instead of solid bodies. In this presentation, we propose Alex Mahalov a successive incremental method for large deformation in Department of Mathematics viscoelastic solids as a model for salt migration. Arizona State University [email protected] I-Shih Liu Instituto de Matemática Mohamed Moustaoui Universidade Federal do Rio de Janeiro dept. of mathematics and statistics [email protected] Arizona State University, Tempe, AZ 85287 [email protected] Rolci Cipolatti Instituto de Matematica Universidade Federal do Rio de Janeiro CP11 [email protected] Evaluation of Numerical Schemes Intended for Global Atmospheric Climate Models Mauro A. Rincon Instituto de Matemática (DCC/IM) The products of climate models are temporal statistics Universidade Federal do Rio de Janeiro based on a calculated evolution of an atmosphere model [email protected] in a forced-dissipative equilibrium. Evaluation techniques beyond deterministic test cases are needed. Because of un- certainties in the nonlinear, interactive forcing, absolute er- CP12 rors of the statistics are difficult to attribute to the dynam- An Asymptotic Model of Carbon Dioxide Dissolu- ics. However comparative statements can be made which tion and Mineral Carbonation Kinetics address the question: from a set of schemes which produce the same quality statistical solution, which requires We formulate a nonlinear o.d.e. model that describes the kinetics of the dissolution of carbon dioxide in water, and subsequent chemical reactions through to the formation of GS09 Abstracts 57

calcium carbonate, a process central to CO2 sequestration. of the coupled elliptic-hyperbolic system is used for such An asymptotic analysis reveals seven diﬀerent timescales optimization. We show that global and local optimization within this system, and approximate expressions for the procedures yield better results than with equidistant steps. evolution of each species on each timescale. These approximations are used to derive uniformly valid composite ex- Nikolay Andrianov pressions for the evolution of the system to equilibrium. Schlumberger [email protected]

Mark J. Mitchell, Oliver Jensen, Andrew Cliffe, Mercedes Maroto-Valer CP13 The University of Nottingham An Efficient Algorithm for Modelling Dynamic [email protected], [email protected], Drainage [email protected], [email protected] The high computational cost involved in modelling viscous effects in multiphase flow simulations using large pore net- CP12 work models comes from the requirement to solve a new The Riemann Solution for the Injection of Super- large linear system every time one phase displaces another critical Carbon Dioxide and Steam in a Porous from a pore. To address this problem, we propose the use Medium of an algorithm that performs a low-rank sparse Cholesky update. This direct sparse solver is faster than the pre- We solve a model for flow of CO2, vapor and water in conditioned conjugate gradient (PCG) iterative solver, and porous media, neglecting compressibility, heat losses and eliminates the slowing down associated with the PCG in capillary effects. We study the dynamics of CO2 seques- the case of adverse viscosity ratios. We apply the method tration in brine aquifers assuming constant pressure and to a simple description of two-phase dynamic drainage in temperature, emulating long time scale scenarios. Due to unstructured pore network models. high pressures and temperatures, CO2 appears in supercritical state. To solve the Riemann Problem, we analyze Dick Kachuma mathematical structures such as rarefactions, shock waves Geoscience Research Centre, Total E&P UK and their bifurcations. [email protected]

Helmut Wahanik Dur´an, Dan Marchesin Igor Bondino Instituto Nacional de Matematica Pura e Aplicada Geoccience Research Centre, Total E&P UK [email protected], [email protected] [email protected]

Johannes Bruining Delft University of Technology CP13 [email protected] Central Schemes for Porous Media Flow We discuss the development of a new, genuinely multi- CP12 dimensional second order semi-discrete central scheme for Capillary Effects on the Dynamic Sequestration of solving hyperbolic conservation laws arising in the simula- Co2 tion of multiphase flow problems in heterogeneous porous media. The scheme produces accurate solutions, partic- We present a series of models of the dynamics of a plume ularly in the presence of high permeability flow channels, of CO2 being sequestered in a confined inclined permeable which lead to strong restrictions on the time step selection. rock. We describe the effects of capillary retention in the Numerical simulations are presented and discussed for ap- pore spaces both on the advancing CO2 front and, in the plications in CO2 sequestration and oil reservoir simula- late stages, on the receding CO2 front. We also discuss tion. the role of capillary forces in controlling the entry pressure of CO2 into a neighbouring, lower permeability layer, and Felipe Pereira how this can enhance the lateral dispersion of the flow as Department of Mathematics it thins. Simplified analytical models are presented along University of Wyoming with numerical solutions of the governing equations to il- [email protected] lustrate the key effects. Frederico C. Furtado Andy Woods University of Wyoming BP Institute for Multiphase Flow Dept of Mathematics University of Cambridge [email protected] [email protected] Marcos Mendes CP13 Department of Mathematics University of Wyoming On An Optimal Number of Time Steps For a Se- [email protected] quential Solution of An Elliptic-Hyperbolic System

We are interested in eﬃcient sequential solution of the Simone Ribeiro pressure-saturation formulation of two-phase ﬂow equa- Department of Mathematics tions in porous media. We estimate an optimal number Universidade Federal Fluminense, Brazil of pressure updates in sense of saving computational ef- [email protected] forts at given accuracy. An analytical solution to a special initial boundary value problem for the 1D formulation 58 GS09 Abstracts

CP13 Instituto Nacional de Matematica Pura e Aplicada Testing Nonlinear Solver Techniques on Difficult (IMPA) Finite Element Problems in Unsaturated Flow in [email protected] Porous Media Johannes Bruining Discritizations of unsaturated flow in porous media create Delft University of Technology extremely difficult nonlinear systems of equations to solve. [email protected] This presentation will show results of testing combinations of Newton only and Newton with Picard nonlinear itera- Dan Marchesin tions with bisection, quadratic, and forcing function only Instituto Nacional de Matematica Pura e Aplicada line searches. A three-dimensional research groundwater [email protected] finite element computer program written for the parallel environment was used for the testing. Results for both an analytical solution and a laboratory test problem will be CP14 presented. Rarefaction Waves for Flow in Porous Media with Fred T. Tracy Mass Transfer Between Phases Engineer Research and Development Center Using singular perturbation methods, we study the long Waterways Experiment Statiuon time behavior of rarefaction waves appearing in stiff non- [email protected] hyperbolic system of balance laws modelling thermal flow in porous media for several chemical species and phases. CP14 By enforcing thermodynamical equilibrium laws, they reduce to systems of conservation laws, where non-isothermal Finite Volume Approximation of evaporation or condensation rarefactions appear. However a Multi-Component Multi-Phase Reservoir Model under thermodynamical equilibrium there should be no with Heat Transfer mass transfer between phases: we discuss here the contra- In order to interpret recorded temperatures, we are in- dictory existence of these mass transfer rarefaction waves. terested in the thermal simulation of a multi-component, multi-phase (oil, gas and water) flow in petroleum reser- Dan Marchesin voirs. To do, we have extended an existing isothermal Instituto Nacional de Matematica Pura e Aplicada simulator (GPRS : General Puropse Reservoir Simulator) [email protected] by adding an exhaustive energy equation and corresponding thermodynamics. Finite volumes are employed for the space discretization and the nonlinear system obtained is Wanderson Lambert solved by Newton-Raphson’s method. Numercal tests in- IMPA cluding real test-cases will be presented. [email protected]

Layal Lizaik Hans Bruining 64000 Delft University of Technology [email protected] [email protected]

Mohamed Amara Universite de Pau et des Pays de l’Adour CP14 Laboratoire de Mathematiques Appliquees Mathematical Modelling of Crown Forest Fire Ini- [email protected] tiation Mathematical model of forest fire was based on an anal- Daniela Capatina ysis of known experimental data and using concept and LMA Laboratoire de mathématiques appliquées methods from reactive media mechanics. The forest and UniversitédePau combustion products are considered as a homogeneous two [email protected] temperatures, reacting, non - deformed medium. The research is done by means of mathematical modeling of physi- Peppino Terpolilli cal processes. It is based on numerical solution of Reynolds Total CSTGF equations for chemical components and equations of en- [email protected] ergy conservation for gaseous and condensed phases. The boundary-value problem is solved numerically. As a result of mathematical modeling the fields of temperatures, CP14 mass concentrations of components of gaseous phase, vol- Analysis of Spontaneous Ignition in Porous Media ume fractions of components of solid phase, as well as vec- torial fields of velocity at different instants of time with Stability of combustion in a porous medium is studied in taking into account mutual influence of the layer of atmo- a simplified model that takes into account the balance be- sphere and a crown fire on each other was obtained. tween heat generation with temperature dependence given by Arrhenius law and heat losses due to conduction to the Valeriy A. Perminov rock formation. The system evolution is described by in- Belovo Branch of Kemerovo State University finitely many nonlinear modes. Its long time behavior is p [email protected] dictated by the two dominant modes, whose phase diagram contains two attractors and a saddle, as in classical chemical engineering. CP14 Nonlinear Operator Splitting for Thermal Multi- Pablo Castaneda GS09 Abstracts 59

Phase Multi-Component Displacements CP17 Maximum Likelihood Parameer Estimation by The characteristics associated with temperature and com- Ensemble-Based Filters positions are closely related in thermal-compositional flow problems. However, use of a tie-line based Compositional The maximum likelihood (MLE) parameter estimation is Space Parameterization (CSP) approach, these character- a mathematically rigorous and practically robust method, istics can be separated at the nonlinear level with appropri- and ensemble-based filters can be an efficient tool for MLE ate assumptions. For more than two phases, tie-simplexes parameter estimation. These filters calculate the like- (tie-triangles for three-phase) can be used for the parame- lihood function of the observations. I will discuss the terization. We demonstrate that for thermal-compositional MLE method, its implementation for ensemble-based fil- simulations, we can employ an efficient sequential coupling ters, and advantages and disadvantages. I will also present scheme, thus avoiding a fully coupled strategy. the results of estimating the noise strength of a stochastic PDE model that conceptually represents an Atlantic Ocean Denis Voskov, Hamdi Tchelepi Thermohaline Circulation. Energy Resources Engineering Department Stanford Univeristy Sangil Kim [email protected], [email protected] Oregon State University [email protected] CP15 A Numerical Method for System of Wave, Current, CP17 and Seabed Morphology in Coastal Processes Estimation of Non-Gaussian Random Fields with the Ensemble Kalman Filter and Kernel Principal In order to accurately simulate multi-physics coastal ocean Component Analysis processes, the wave action equation, the shallow-water equations, and the Exner equation are coupled in a simulta- Because history matching is an ill-posed problem with non- neous manner. A flux-limited version of the Roe scheme is unique solutions, additional prior information, usually in derived to discretize the coupled system for high-resolution the form of geological constraints on the history match- solutions. Numerical examples and prediction of actual ing problem, is generally required to obtain geologically problems will also be presented to demonstrate the per- realistic history matched models that have good predic- formance in comparison with convention approaches and tive capability. However, history matching is a computa- interaction among wave, current, and seabed morphology. tionally intensive process, especially for large scale simulation models, as it usually requires numerous simulations Hansong Tang to obtain a history matched solution. Towards this end, Dept. of Civil Eng., City College of NewYork, CUNY the ensemble Kalman filter (EnKF) has recently gener- [email protected] ated significant attention as an efficient approach for as- similating dynamic data. Although the EnKF has many Timothy Keen advantages such as ease of implementation and efficient un- Oceanography Div.,Naval Research Lab. certainty quantification, it is technically appropriate only [email protected] for random fields (e.g., permeability) characterized by two- point geostatistics (multi-Gaussian random fields). Real- istic systems however are much better described by non- CP15 Gaussian random fields characterized by multipoint geo- Morphodynamics Discontinuous Galerkin Mod- statistics, which is capable of representing key geological elling with Applications to Stratigraphy structures such as channels. History matching algorithms that are able to reproduce realistic geology provide en- Morphodynamics is the study of the time-dependent inter- hanced predictive capacity and can therefore lead to better action and adjustment of the seafloor (or riverbed) topog- reservoir management. In this work, we apply kernel prin- raphy and hydrodynamic processes. To deal with problems cipal component analysis (KPCA) to parameterize non- in which complex domains and a range of scales between Gaussian random fields characterized by multipoint geo- the physical processes are involved, the application of ro- statistics. By using high order polynomial kernels, ker- bust numerical methods is of paramount importance. In nel PCA enables preserving arbitrarily high-order statis- this work, we introduce a discontinuous Galerkin method tics of non-Gaussian random fields, thereby providing the to solve the hydrodynamics and the seafloor evolution and capability to reproduce complex geology. The KPCA pa- apply it to stratigraphy modelling. rameterization in then applied in conjunction with EnKF, Pablo A. Tassi which allows dynamic data assimilation while ensuring that CERMICS - ENPC the prior geological characteristics of the updated random [email protected] fields (such as channels) are retained during the Kalman update. Furthermore, the KPCA parameterization dramatically reduces the number of state variables on which Alexandre Ern the EnKF is applied, thereby improving the efficiency of Universite Paris-Est the EnKF. The overall procedure is then applied to several CERMICS, Ecole des Ponts synthetic examples. The approach is shown to better re- [email protected] produce complex geology, which leads to improved history matches and better predictions, while retaining reasonable Serge Piperno computational requirements. Cermics Ecole des Ponts, ParisTech Pallav Sarma [email protected] Chevron Energy Technology Company San Ramon CA [email protected] 60 GS09 Abstracts

Wen Chen Anke Richter Chevron ETC Forschungszentrum Dresden-Rossendorf [email protected] [email protected]

Tina Scharge CP17 Gesellschaft für Anlagen- und Reaktorsicherheit mbH Wavelet Kernel Anova [email protected] A new response surface method called Wavelet Kernel ANOVA, is proposed for uncertainty propagation and sen- Wolfgang Voigt sitivity analysis of an expensive multiphase flow reservoir TU Bergakademie Freiberg simulator. The method is based on a wavelet Reproduc- [email protected] ing Kernel Hilbert Space (RKHS) technique. An adaptive experimental design method is also proposed to iteratively Stefan Wilhelm improve the accuracy of the response surface. The perfor- AF-Colenco Ltd mance of the method are compared with a similar approach [email protected] based on kriging on a realistic reservoir model. Thomas Willms Samir Touzani, Daniel Busby Gesellschaft für Anlagen- und Reaktorsicherheit mbH IFP [email protected] [email protected], [email protected] Georgia Wollmann Anestis Antoniadis TU Bergakademie Freiberg University of Joseph Fourier [email protected] [email protected]

CP18 CP18 Mathematical Issues in Subsoil Bioventing Mod- THEREDA A elling and Optimal Design Thermodynamic Reference Database for Nuclear Waste Disposal in Germany Oxygen is required in bioventing to improve the activity of bacteria to biodegrade contaminants in the subsoil and THEREDA provides consistent thermodynamic datasets thus air is inflated through wells. The mathematical model to assist the long-term safety assessment of nuclear waste describes the bacteria population dynamics and the dy- repositories. It meets specific German requirements (high namics of a multiphase, multicomponent fluid in porous salinities and temperatures). THEREDA is build on a re- media. A critical point of the design problem is to choose lational SQL-database. The application of referential in- well positions and air flow rates to optimise the biodegra- tegrity, thermodynamic dependencies, alternative datasets dation process. Several approaches are possible: minimis- and uncertainty estimates allows to deliver tailor-made pa- ing the costs, maximising the instantaneous biodegrada- rameter files for use in geochemical modelling software like tion rate, maximising oxygen concentration, subsoil air flow EQ3/6, GWB and ChemApp covering law-of-mass-action evaluation and so on. and Gibbs-energy-minimization codes. Filippo Notarnicola Sven Gester Istituto Applicazioni Calcolo, I.A.C. - CNR, Bari Forschungszentrum Dresden-Rossendorf [email protected] [email protected]

Marcus Altmaier CP19 Forschungszentrum Karlsruhe Application of a Coupled VF/EF Multi-Scale [email protected] Method to Cement Media Homogenization

Vinzenz Brendler We present here the results of a work on a multiscale res- Forschungszentrum Dresden-Rossendorf olution method using both Finite Volums and Elements in [email protected] the field of numerical homogenization. Our method rely upon the coupling of two grid scales: a coarse one and a fine one. The trick is to build a Finite Element basis on Sven Hagemann, Horst-Jürgen Herbert the coarse grid from problems solved on the fine one. In Gesellschaft für Anlagen- und Reaktorsicherheit mbH previous work on this subject, the Finite Element method [email protected], [email protected] was used in both the fine and coarse scales, whereas, in our approch, the fine scale simulations are made via Finite Christian Marquardt Volums. This way, we hope to increase the stability of the Forschungszentrum Karlsruhe method in view of strong discontinuities and anisotropy of [email protected] the studied media. Our application exemple is a model of cement media, where very important variations of diffusiv- Helge C. Moog ity occur. Gesellschaft für Anlagen- und Reaktorsicherheit mbH [email protected] Thomas Abballe CEA Saclay Volker Neck [email protected] Forschungszentrum Karlsruhe [email protected] Grégoire Allaire GS09 Abstracts 61

CMAP CP20 France Modern Techniques of Software Development for [email protected] Simulation of Complex Applications – A Selection of Recent Development in the Contextof the Dune Philippe Montarnal Framwork CEA Saclay France In this paper we present software techniques as well as re- [email protected] cent development of the software package DUNE [1], [2] and in particular of the module DUNE-FEM [3]. For sev- Eli Laucoin eral test problems as well as for more complex applica- CEA Saclay tions, such as the simulation of fuel cells, we present nu- Francve merical results. These results have been obtained using [email protected] modern simulation techniques such as higher order continuous and discontinuous Galerkin methods (also in a stabilized version [4]) in combination with local grid adaptiv- CP19 ity. The parallelization of the code has been taken into Subdomain Time Stepping for Transport in Porous account which is in combination with local grid adaptivity Media a non-trivial part since dynamic load balancing has to been done. References [1] P. Bastian, M. Blatt, A. Dedner, In many problems concerning transport in heterogeneous C. Engwer, R. Klöfkorn, M. Ohlberger, and O. Sander. A porous media the simulation domain can be divided into generic grid interface for parallel and adaptive scientific several subdomains with different hydrogeological proper- computing. I: Abstract framework. Computing, 82(2- ties. These different properties imply different time scales 3):103–119, 2008. [2] P. Bastian, M. Blatt, A. Dedner, that we would like to take into account by using differ- C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, and ent time steps in the different subdomains. This leads to O. Sander. A generic grid interface for parallel and adap- space time domain decomposition. We discuss various for- tive scientific computing. II: Implementation and tests in mulations of this domain decomposition method using the DUNE. Computing, 82(2-3):121–138, 2008. [3] A. Ded- Schur complement formulation or the Schwarz waveform ner, A. Klöfkorn, M. Nolte, and M. Ohlberger, DUNE- relaxation method. FEM – the fem module, http://www.mathematik.uni- freiburg.de/iam/research/projectskr/dune/, Mathematis- Jerome Jaffre ches Institut, Universität Freiburg, 2008. [4] A. Ded- INRIA-Roquencourt ner and R. Klöfkorn. A generic stabilization approach 78153 Le Chesnay cedex France for higher order discontinuous galerkin methods for con- Jerome.Jaff[email protected] vection dominated problems. Preprint Nr. 8 (sub- mitted to SIAM Sci. Comp.), Mathematisches Insti- Caroline Japhet tut, Universität Freiburg, http://www.mathematik.uni- Paris 13 university, France freiburg.de/IAM/homepages/robertk/postscript/dedner kloefkorn limiter.p [email protected] 2008. Robert Kloefkorn Michel Kern University of Freiburg INRIA [email protected] [email protected]

Jean E. Roberts CP20 INRIA Paris-Rocquencourt Nonlinear Solution Strategies for Compositional France Simulation [email protected] We present a simulation framework based on automatic differentiation that provides wide flexibility in choosing the CP19 nonlinear formulation and selecting primary and secondary Upscaling Fast Reaction in Stratified Aquifers variables. The behavior of new and existing nonlinear formulations for compositional simulation is analyzed. Fully We analyze the irreversible bimolecular reaction A+B-¿C implicit formulations are considered, where the full Jaco- in a stratified random porous medium. In case of fast bian in terms of both the primary and secondary variables reaction, the problem can be solved in terms of a single is constructed. The behaviors of the Newton iterations advection-dispersion equation for the mixing ratio (Z). We are analyzed for different variable sets, equation alignment, compute the reactants concentrations expected values by and nonlinear updating strategies. using the probability density function (pdf) of Z. We assume the pdf of Z to be beta-distributed with mean and Denis Voskov variance computed by semi-analytical solutions Energy Resources Engineering Department Stanford Univeristy Marco Massabo [email protected] CIMA Research Foundation [email protected] Hamdi Tchelepi Petroleum Engineering Department albert j valocchi, Albert J. valocchi Stanford University Department of Civil & Environmental Engineering [email protected] University of Illinois at Urbana-Champaign [email protected], [email protected] 62 GS09 Abstracts

MS1 Smagorinsky models can only provide a marginal improve- Model Reduction of Oceanic Flows ment over under-resolved simulations, while both dynamic Smagorinsky and AD models lead to significant improve- Both accurate and computationally efficient simulations ments in mixing accuracy. The primary accomplishment of turbulent flows are needed to understand and predict of this study is that it is shown that the hybrid approach oceanic flows. Reduced-order models represent natural attains the best agreement with the mixing curve from choices in these applications. The fundamental challenge is DNS, while being computationally approximately a thou- to retain the physics of the underlying turbulent flow while sand times faster. keeping the computational cost at a minimum. In this talk, we will present reduced-order modeling strategies synthe- Tamay Ozgokmen sizing ideas originating from proper orthogonal decomposi- University of Miami/RSMAS tion and large eddy simulation of turbulent flows. In partic- [email protected] ular, we will present approaches based on the variational multiscale and dynamic subgrid-scale methods. Analysis Traian Iliescu and numerical illustrations of our methodology will also be Virginia Tech. presented. [email protected] Traian Iliescu Paul F. Fischer Virginia Tech. Argonne National Laboratory [email protected] fi[email protected] Jeff Borggaard Virginia Tech MS1 Department of Mathematics Resolution and Scale Dependence of Relative Dis- [email protected] persion in a Hierarchy of Ocean Models

Zhu Wang We examine a hierarchy of ocean models, ranging from sim- Virginia Polytechnic Institute and State University ple 2D turbulence simulations to North Atlantic HYCOM [email protected] output, to determine the effect of Eulerian spatial model resolution on the two particle statistics of synthetic drifter trajectories. In each case, particle dispersion at large time MS1 and space scales is found to be controlled by hyperbolic Numerical Simulation of Population Balance Sys- structures produced by identifiable meso-scale features of tems the flow. In all cases, time-distance graphs given in terms of computed Finite Size Lyapunov Exponents show an in- The talk will describe a numerical approach for simulating crease in the extent of exponential scaling with increasing population balance systems which is mainly based on finite spatial smoothing of the velocity field and scaling of the element methods. It will address the following topics: limiting exponent with resolved hyperbolicity. • the simulation of the turbulent background flow, Andrew Poje • the simulation of transport–dominated equations Mathematics without spurious oscillations in the computed solu- CUNY-Staten Island tions, [email protected] • the impact of using different schemes for solving the Angelique Haza higher–dimensional equation for the population bal- MPO, RSMAS, University of Miami ance. [email protected] The numerical simulations will consider a precipitation process. Tamay Ozgokmen, Marcello Magaldi University of Miami/RSMAS Volker John, Adela Kindl, Michael Roland, Ellen [email protected], Schmeyer, Carina Suciu [email protected] FR 6.1 - Mathematik Universitaet des Saarlandes [email protected] MS2 sb.de, [email protected], [email protected], Modeling of Multi-Phase Flow Processes in Heated [email protected], [email protected] Fracture-Matrix Systems

Analysis of the proposed underground repository for ra- MS1 dioactive waste at Yucca Mountain, Nevada, requires pre- Large Eddy Simulation of Mixing in the Lock- diction of water-vapor flow processes in unsaturated frac- exchange Problem tured rock at elevated temperatures near and above the boiling temperature of water. This constitutes a challeng- LES of a 3D lock-exchange problem are presented, which ing modeling problem. We elaborate on these challenges contains shear-driven mixing, internal waves, interactions and present possible conceptual and solution approaches, with boundaries and convective motions, while having a with specific focus on the respective roles of fractures and simple domain, initial and boundary conditions, and forc- matrix and their interaction. ing. Two general classes of LES models are tested, namely eddy viscosity models based on constant-coefficient and dy- Jens T. Birkholzer namic Smagorinsky models, and an approximate deconvo- Lawrence Berkeley National Laboratory lution (AD) model. It is found that constant-coefficient GS09 Abstracts 63

(LBNL) MS2 [email protected] An Interfacial-area Based Approach for Modeling Degassing Processes in Fractured Porous Media

MS2 In the vicinity of radioactive waste disposal sites, degassing Massively Parallel Discrete Fracture and Matrix might occur in fractures which is to be avoided as it allows Simulations - A Route to Faster and More Real- radioactive substances to reach the ground surface rela- istic Predictions tively quickly. The degassing in the fracture is highly dependent on the interfacial area separating the fluid phases We present a new massively parallel algorithm for discrete which cannot be taken into account by classical models. fracture and matrix simulations which is based on finite ele- Therefore, we present a new approach based on interfacial ment finite volume discretisations and hierarchical solvers. areas and derive constitutive equations for fractures from We observe linear scaling for up to 64 processors on mod- a micro-scale model for single fractures. els containing several million degrees of freedom. This now allows us to resolve the non-linear coupling of small scale Jennifer Niessner capillary – viscous and large scale gravitational – viscous Institut fuer Wasserbau (IWS) processes adequately for realistic high-resolution represen- Universitaet Stuttgart, Germany tations of fractured reservoirs. [email protected]

Sebastian Geiger Philipp Nuske, Benjamin Faigle Heriot-Watt University University of Stuttgart Edinburgh [email protected], [email protected] [email protected]

Qi Huangfu, Fiona Reid Rainer Helmig University of Edinburgh IWS, University of Stuttgart, Germany Edinburgh Parallel Computing Centre Institut fur Wasserbau [email protected], [email protected] [email protected]

Stephan Matthai Majid Hassanizadeh Montan University of Leoben University of Utrecht Department of Minearl Resources and Petroleum [email protected] Engineering [email protected] MS3 Dim Coumou Production Optimization and Reservoir Inverse Potsdam Institute for Climate Impact Research Modeling Using Principal Component Analysis Earth System Analysis [email protected] Principal Component Analysis (PCA) is the basis of powerful model order reduction procedures for optimization within the oil industry. By PCA a high-dimensional linear MS2 space is optimally projected onto another space of much Complex Gas–Water Processes in Discrete lower dimension. These spaces can represent state vari- Fracture–Matrix Systems ables (pressure and saturation) and reservoir properties (permeability and porosity). In this talk I will explain the Degassing effects may occur in fractures in the vicinity of fundamentals of PCA and illustrate its use in optimization deep radioactive-waste-disposal sites as a result of a pres- by examples from production optimization and reservoir sure drop. These effects play an important role e.g. in the model inversion. investigation of the hydraulic conditions in the near field of the disposal sites. The aim of this presentation is to David Echeverria-Ciaurri, Marco Cardoso, Matthieu contribute to the understanding of non-isothermal behav- Rousset, Louis J Durlofsky ior of water–gas systems in the near field of atomic waste Department of Energy Resources Engineering disposal sites in fractured porous media. For the simula- Stanford University tion on the laboratory scale we use a percolation model. [email protected], [email protected], To transfer the information from the laboratory scale to [email protected], [email protected] the field scale we use a renormalization scheme. Tapan Mukerji Rainer Helmig Department of Geophysics IWS, University of Stuttgart, Germany Stanford University Institut fur Wasserbau [email protected] [email protected]

Insa Neuweiler MS3 University of Hannover Identiﬁability, Controllability and Observability in neuweiler @hydromech.uni-hannover.de Hydrocarbon Reservoir Models

Jennifer Niessner Over the past few years systems and control concepts have Institut fuer Wasserbau (IWS) been applied in reservoir engineering, e.g. optimal control, Universitaet Stuttgart, Germany Kalman ﬁltering, model reduction. The success of these [email protected] applications is determined by the identiﬁability, controlla- 64 GS09 Abstracts

bility and observability properties of the reservoir model ground nuclear waste repository, we derive a new compo- at hand. In this presentation the controllability and ob- sitional model of compressible multiphase flow and trans- servability properties of single-phase and multi-phase flow port in porous media, with interphase mass transfer.This reservoir models are analyzed and interpreted. Addition- new unified modeling of fully and partially water saturated ally, it is shown how to determine and use approximate porous materials makes possible a unified numerical treat- model structures with identifiable parameterizations. ment of both fully and partially water saturated situations. Existence of solutions, is proved under adequate assump- Jorn F.M. van-Doren tions,and numerical simulations showing the efficiency of Shell International Exploration & Production this modeling are presented. [email protected] Alain Bourgeat Maarten J. Zandvliet Université Lyon1 Shell International E&P UMR CNRS 5208 [email protected] [email protected]

Jan Dirk Jansen MS4 Delft University of Technology/ Shell International E&P Phase Exchange in Two-phase Flow in Porous Me- [email protected] dia and Complementary Problems Two-phase flow with phase exchange is modeled as a set Paul M.J. Van den Hof, Okko H. Bosgra of time dependant nonlinear partial differential equations Delft Center for Systems and Control with nonlinear complementary conditions. Such a formula- Delft University of Technology tion allows appearance and disappearance of a phase as well [email protected], [email protected] as the use of some laws which are widely used as Henry’s law. We discretize the problem with cell-centered finite volumes method or mixed finite elements and discuss ap- MS3 propriate solvers for the solution of the resulting nonlinear Model Reduction via Multiscale Methods: Appli- complementary problems. cation to Water Flooding Optimization Jerome Jaffre In this talk we discuss the use of a multiscale mixed finite INRIA-Roquencourt element method (MsMFEM) for model order reduction in 78153 Le Chesnay cedex France reservoir engineering optimization problems. We illustrate Jerome.Jaff[email protected] the use of the methodology for finding optimal rates and well-placement in water-flooding examples. We also discuss Ibtihel Ben Gharbia, Jean Charles Gilbert pros and cons for the MsMFEM approach compared to e.g., INRIA-Rocquencourt PCA (principal component analysis)-based techniques. ibtihel.ben [email protected], [email protected] Stein Krogstad SINTEF ICT Amel Sboui [email protected] EDF LaMSID, Clamart, France [email protected]

MS3 Reducing Model Order by the Deﬁnition of a Ran- MS4 dom Function From a Given Set of Model Realiza- Fully Coupled HMFE Approximation for Two- tions phase Flows in Porous Media

In this talk we provide a novel framework for geostatis- For modeling CO2 underground storage, two-phase, two- tics/spatial modeling. We establish a method for defin- component flow with possible diappearance of each phase ing a random function from a set of generated/measured and phase-exchange is considered. By neglecting tem- realizations, typically associated with uncertainty analy- perature variations the model is reduced to a system of sis processes. This function reduces drastically the order two time-dependent partial differtial equations. The un- of the model. Once the random function is available, we knowns are quantities derived from saturations, composi- show how consistent sets of new realizations, with struc- tions and pressures,with relations independent of time and tural properties similar to the initial set, can be generated space. The discretization ansatz is a mixed finite element without re-running the algorithm or consulting the gener- method, not necessarily of lowest order. For the chosen ating source. discretization fluxes are explicitely eliminated and condensation leads to a nonlinear equation in terms of Lagrange Celine Scheidt, Jef Caers multipliers at each time step. Department of Energy Resources Engineering Stanford University Peter Knabner [email protected], [email protected] Universitat Erlangen-Nurenberg Department of Mathematics [email protected] MS4 Gas Migration in a Nuclear Waste Repository; a Estelle Marchand, Torsten Mueller Unified Modelling of Fully and Partially Saturated University of Erlangen-Nuremberg Porous Materials Department of Mathematics [email protected], Motivated by modelling the gas migration in an under- [email protected] GS09 Abstracts 65

MS4 tainty Quantifcation in Elliptic Equations Principle of Equivalence and Method of Negative Saturations for Multicomponent Flow with Phase In this talk, we present a Generalized Spectral Decomposi- Transitions Through Porous Media tion method for probabilistic uncertainty quanti?cation in elliptic equations. The decomposition aims at approach- We analyse the flow with phase transitions when the two- ing the stochastic solution on reduced bases (stochastic phase fluid can be alternated with the zones occupied by and deterministic), similar to the Polynomial Chaos ex- single-phase non-equilibrium fluid. The principle of equiv- pansions, except that the expansion bases are not selected alence is poved which says that a non-equilibrium single- a priori but constructed and adapted to the problem equa- phase fluid is hydrodynamically equivalent to an imagi- tions and parameters uncertainty. Di?erent algorithms nary two-phase equilibrium fluid having specificic physical are considered for the construction of the reduced bases properties called the equivalence conditions. One of these (Power-type and Arnoldi-type iterations), and compared conditions necessarily implies that the saturation of one on a test problem related to steady linear and non-linear imaginary phase is negative. We prove the consistence the- ground water ?ow simulations (Darcy equations). Per- orem which shows that such equivalence conditions do not formance and implementation aspects are discussed with contradict to fundamental thermodynamic principles. The regard to the classical stochastic ?nite element method, equivalence theorem allows for developing an efficient nu- and we discuss the extension of the Generalized Spectral merical method of modeling these processes, by applying Decomposition method to large unsteady problems arising the uniform two-phase flow equations for all the flow do- in nuclear waste disposal simulations. main, but different thermodynamic constitutive conditions for single-phase and two-phase zones. The moving inter- Olivier Le Matre face between these zones is detected automatically once Laboratoire d’Informatique pour la Mécanique et les the saturation becomes negative. The method is tested on Sciences one-dimensional analytical solutions. The numerical ex- LIMSI-CNRS ample of solving two-dimensional flow problems with ir- [email protected] regular shape of the interface are obtained. The advanced version of the method is developed for the cases of diffu- Anthony Nouy sion, adsorption and chemical reactions, when the inter- Université de Nantes face between zones is detected as the surface of the week Institut de Recherche en Génie Civil et Mécanique (GeM) discontinuity of the saturation field. The simulated exam- [email protected] ples concerns oil displacement by partially miscible gas and CO2 injection in an aquifer. Lionel Mathelin Laboratoire d’Informatique pour la Mécanique et les Mikhail Panfilov Sciences LEMTA-UMR 7563 LIMSI-CNRS Institut National Polytechnique de Lorraine - France [email protected] mikhail.panfi[email protected]

Anahita Abadpour MS5 LEMTA-UMR 7563 Efficient Iterative Solvers for Stochastic Ground- Nancy Universite France water Flow Problems [email protected] We consider finite element discretizations of PDEs with a stochastic differential operator arising in groundwater flow MS5 simulations. We report on the design of efficient itera- Gaussian Process Emulators for Groundwater Flow tive solvers for the resulting large coupled linear system of equations. In particular we present a new approach for We explore the application of Gaussian process emula- preconditioning such linear systems which takes advantage tors to uncertainty analysis of groundwater flow models. of the special Kronecker product structure of the Galerkin Emulators statistically approximate the output of com- matrix. We demonstrate the efficiency of our techniques puter models and can be used as cheap substitutes for the on selected model problems. model. A model of groundwater flow through the Culebra Dolomite at the Waste Isolation Pilot Plant site is chosen Elisabeth Ullmann as a test case to illustrate the methods. The uncertainty in TU Bergakademie Freiberg the output of the model given the uncertainty in the inputs [email protected] is quantified. Oliver G. Ernst Kenneth A. Cliffe, Ian Dryden, Nicola Stone TU Bergakademie Freiberg University of Nottingham Fakultaet Mathematik und Informatik andrew.cliff[email protected], [email protected] [email protected], [email protected] MS5 Jeremy Oakley Efficient Numerical Methods for Stochastic Com- University of Sheffield putations j.oakley@sheffield.ac.uk Numerical algorithms for effective incorporation of uncertainty into differential equations are discussed. The un- MS5 certainty is modeled as functions of random variables, and Generalized Spectral Decomposition for Uncer- the governing equations are treated as stochastic. By using generalized polynomial chaos (gPC) expansion, the solu- 66 GS09 Abstracts

tions are expressed as convergent series of orthogonal poly- Artem Myasnikov, Kyrre Bratvedt nomials in terms of the random variables. Based on gPC, Schlumberger Moscow various numerical schemes can be designed, via either a [email protected], [email protected]field.slb.com stochastic Galerkin (SG) approach or a stochastic colloca- tion (SC) approach. In this talk we discuss and compare the strength and weakness of gPC based SG and SC meth- MS6 ods. The focus is on their accuracy and efficiency. We Tie-simplex Based Parameterization for Thermo- will also demonstrate the clear connection between these dynamical Equilibrium Computations of Multi- methods and the classical deterministic spectral methods component Systems with Arbitrary Number of and their applications to inverse problems such as param- Phases eter estimation. We present a general framework for the computation of Dongbin Xiu thermodynamic equilibrium of multi-component systems Purdue University that form an arbitrary number of phase. We parame- [email protected] terize the high-dimensional compositional space using tie- simplexes (tie-triangles for three-phase) to represent the multi-phase regions. The tie-simplex computation and MS6 interpolation procedure complement the parameterization Interfacial Momentum Balance Between Non- and form a complete mathematical framework. We demon- equilibrium Phases strate the efficiency of the method for several multi-phase equilibrium problems of practical interest that include The net stress on a flat interface is not zero during a phase both equilibrium flash calculations and multi-phase, multi- change. A net stress is needed to balance the jump in mo- component flow problems. mentum experienced by the molecules as they cross the interface; a stress-free interface introduces an error in the Denis Voskov solution for the velocity field. This work presents an ex- Energy Resources Engineering Department pression for interfacial momentum balance between non- Stanford Univeristy equilibrium phases and investigates the equilibration pro- [email protected] cess in the presence of natural convection. Hamdi Tchelepi Kjetil Haugen, Abbas Firoozabadi Petroleum Engineering Department Yale University Stanford University [email protected], abbas.fi[email protected] [email protected]

MS6 MS7 Numerical and Mathematical Aspects of Multi- Geological Storage as a Carbon Mitigation Option phase/Component Solubility in Water Abstract not available at time of publication. The numerical and mathematical aspects of multi-phase /component solubility in water are considered where ther- Michael Celia modynamically consistent three-phase behavior is coupled Princeton University with nonlinear transport in porous media. In this model, Dept of Civil Engineering several hydrocarbons are allowed to dissolve in the aque- [email protected] ous phase while all other components expect water exist in the oil and gas phases. The proposed computation of any gas solubility in the aqueous phase is based on EOS frame- MS7 work. The numerical simulation results are presented and On the Use of Streamlines and Front Tracking for discussed. Compressible Flow

Alexander Lukyanov We investigate the use of streamline methods and front Schlumberger Geoquest tracking for compressible flow. Operator splitting is used [email protected]field.slb.com to incorporate gravity effects. We apply this method for the injection phase of CO2 storage and point out in which J. Berge, A. Desitter, A. Priestley, S. Hurter, D. situations the method has advantages and when other ap- Labregere proaches should be considered. Schlumberger [email protected], [email protected], [email protected], Halvor M. Nilsen [email protected], [email protected] SINTEF Oslo [email protected] MS6 Front Tracking Technique for Three Component Knut-Andreas Lie Two Phase Incompressible Flows SINTEF ICT, Dept. Applied Mathematics [email protected] Abstract not available at time of publication.

Nikolay Belov MS7 Schlumberger Moscow An Eﬃcient Upscaling Based on a Uniﬁed Fine- IPM RAS [email protected] GS09 Abstracts 67

scale Multi-physics Model breaking problem in the context of Boussinesq approximation, see Ozg¨¨ okmen et al. (2007) and this is one of the The main challenge in modeling fluid flow through motivations for our work. Moreover, the analysis of fluids naturally-fractured carbonate karst formation is how to with very different viscosity coefficients in the horizontal address various flow physics in complex geological archi- and vertical direction is motivated also by the study of Ek- tectures due to the presence of caves which are connected man layers, see for instance the introduction of Chemin et via fracture networks at multiple scales. In this paper, al. (2000), Desjardins and Grenier (2000) and Pedlosky we present an efficient upscaling process that is based on (1979). a unified fine-scale multi-physics model which adaptively couples Stokes-Brinkman with discrete fracture network Luigi C. Berselli models. The underlying idea is to use Stokes-Brinkman Dipartimento di Matematica Applicata ”U. model to represent flow through rock matrix, void caves Universita’ di Pisa and intermediate flows in high permeability regions and to [email protected] use discrete fracture network model to represent flow in fracture network. This unified approach adaptively treats fractures as lower dimensional geometries with permeabil- MS8 ities assigned according to their apertures. Consequently, A Goal-Orientated Mesh Adaptive and Dual- various numerical solution strategies can be efficiently ap- Weighted Pod for Data Assimilation into Ocean plied to greatly improve the computational efficiency in Modelling flow simulations. A novel dual weighted POD method for adapting mesh, Guan Qin, Linfeng Bi order reduction and 4D-Var data assimilation is presented University of Wyoming here. The aim is to (1) optimise the reduced bases , thus [email protected], [email protected] improving the quality of reduced ocean models representation of the goal; (2) design an error measure to guide an adaptive meshing algorithm. The goal functional for opti- MS7 mising reduced bases and meshes has been designed to be On Eulerian-Lagrangian Formulations and Their consistent with that for 4-D Var data assimilation. Analyses Michael Navon We present optimal-order error estimates for a class of Florida State University Eulerian-Lagrangian methods for advection-diffusion equa- [email protected] tions, which are uniform with respect to the vanishing parameter epsilon. The estimates depend on the given ini- Fangxin Fang tial, boundary, and right side data but not on the true Department of Earth Science and Engineering solution. We also discuss optimal-order error estimates Imperial College London, U.K. for Eulerian-Lagrangian methods for the coupled system in [email protected] porous medium flow. These results justify the strength of Eulerian-Lagrangian methods. Numerical results are presented to verify the analysis. MS8 On a LES-deconvolution Model for the Ocean with Hong Wang a Fixed Wind University of South Carolina Department of Mathematics We model the oceanic flow by using the Navier-Stokes [email protected] equations together with the rigid lid assumption, which yields flux conditions for the velocity at the surface, that KaiXing Wang couple the ocean to the atmosphere. We stay here in the School of Mathematics, Shandong University case of a fixed atmospheric wind. We start by showing Jinan, Shandong 250100, China how to adapt the periodic Leray-Alpha model to the case [email protected] of those realistic boundary conditions. We next turn to the Layton-Lewandowski deconvolution model, based on the Van Cittert algorithm. This model cannot be adapted MS8 like this to the case of the ocean. We observe that the Van Analysis of a Scale Similarity LES Model Designed Cittert algorithm is in fact nothing but a finite difference for Certain Stratified Flows scheme of a certain evolution equation. This yields a new LES deconvolution model adjusted to the ocean, for which We propose and give some mathematical analysis results we prove the existence and the uniqueness of a smooth so- for a Large Eddy Simulation model which involves regu- lution. We also prove the convergence of those solutions larization only in the horizontal variables. The method we to a dissipative solution to the Navier-Stokes equations consider, which fits into the class of scale similarity models, when the deconvolution parameter goes to infinity. This is similar to the “Simplified Bardina model’ introduced by research work has been initially performed by A.-C. Ben- Layton and Lewandowski (2006). We are able prove that nis, R. Lewandowski and E.-S. Titi. R. Lewandowski is our new model has good mathematical properties (exis- supported by the ANR project 08FA300-01. tence and uniqueness in appropriate Sobolev space). The mathematical foundation is one of the first steps for the Roger Lewandowski validation, even if numerical experiments on realistic prob- IRMAR, UMR 6625 lems will be the necessary further step. Universite Rennes 1 [email protected] The idea of considering extra-viscosity (sub-grid-scale terms) acting only in the horizontal variables is well dif- fused in the community, especially for the mixing dam 68 GS09 Abstracts

MS8 MS9 Three-Dimensional Dynamics in Non-Parallel Development of Model Concepts for Flow in Shear Stratiﬁed Flows Macro-porous Media on Diﬀerent Scales

The instabilities of non-parallel flows such as those in- The fast infiltration of heavy rainfalls in macro-porous hill- duced by polarized inertia-gravity waves embedded in a slopes is one of the key processes which triggers fast infil- stably stratified environment are analyzed in the context tration, saturuation and pressure increase and thus defor- of the 3D Euler-Boussinesq equations. We derive a suf- mation processes. A so-called cascade model concept has ficient condition for shear stability and a necessary con- been developed for macropore infiltration based on condition for instability in the case of non-parallel velocity trolled laboratory experiments and it is implemented in the fields. Three dimensional numerical simulations of the full framework of a two-phase flow model concept for porous nonlinear equations are conducted to characterize the re- media. The exchange parameters which are determined by spective modes of instability, their topology and dynamics, this tool will be transfered to a double continuum model and subsequent breakdown into turbulence. We investi- concept which is then applied on the field scale. gate three-dimensional characteristics and present computational results on Lagrangian particle dynamics. Reinhard Hinkelmann TU Berlin Alex Mahalov [email protected] Department of Mathematics Arizona State University Leopold Stadler [email protected] TU Berlin, Germany [email protected] Mohamed Moustaoui dept. of mathematics and statistics Kai Germer, Juergen Braun Arizona State University, Tempe, AZ 85287 University of Stuttgart [email protected] kai.germer @iws.uni-stuttgart.de, [email protected] stuttgart MS9 Asymptotic and Numerical Modelling of Flows in MS9 Fractured Porous Media with Finite Volume Meth- Deformation Band Populations in Fault Damage ods Zones - Impact on Fluid Flow

We study some asymptotic models used to compute the Fault damage zones in highly porous reservoirs are flow outside and inside fractures in 2-D heterogeneous dominated by deformation bands that generally have porous media. The flow is governed by the Darcy law with permeability-reducing properties. Due to an absence of large discontinuities in the permeability tensor. The frac- sufficiently detailed measurements and the irregular distri- tures, supposed to have a small aperture with respect to the bution of deformation bands, a statistical approach is ap- macroscopic length scale, are then asymptotically reduced plied to study their influence on flow. A stochastic model to immersed fault interfaces. A cell-centered finite volume of their distribution is constructed, and band density, dis- scheme on general polygonal meshes fitting the interfaces tribution, orientation and flow properties are chosen based is derived to solve the set of 2-D/1-D equations with the on available field observations. The sensitivity of these dif- additional differential transmission conditions linking both ferent parameters on the upscaled flow is analyzed. The pressure and normal velocity jumps through the interfaces. influence of a heterogeneous permeability distribution was We prove the convergence of the FV scheme and derive ex- also studied by assuming the presence of high permeabil- istence and uniqueness of the solution to the asymptotic ity holes within bands. The fragmentation and position of models proposed. Various numerical results are reported these holes affects significantly the block effective perme- showing different kinds of flows in the case of impermeable ability. Results of 1D and 2D local upscaling are compared or partially/highly permeable immersed fractures. These and qualitatively similar results for the flow characteristics numerical solutions of the asymptotic models are validated are obtained. Further, the procedure of iterative local- by comparing them to the solutions of the global Darcy global up scaling is applied to the problem. model or to some analytic solutions. Dmitriy Kolyukhin Philippe Angot CIPR LATP Université de Marseille Bergen, Norway Marseille, France [email protected] [email protected] Sylvie Schueller Franck Boyer CIRP, Bergen, Norway LATP now at IFP, Rueil-Malmaison, France Université d’Aix-Marseille III, France [email protected] [email protected] Magne S. Espedal Florence Hubert Department of Mathematics,University of Bergen, Norway LATP [email protected] Université de Provence, Marseille, France [email protected] Haakon Fossen Centre for Integrated Petroleum Research University of Bergen, Norway [email protected] GS09 Abstracts 69

Alvar Braathen MS10 Centre for Integrated Petroleum Research Hybrid Optimization Methods for Simulation Bergen, Norway Based Problems [email protected] Simulation based optimization is increasingly important for hydraulic application problems, especially the need to han- MS9 dle real-valued as well as integer-valued variables is emerg- Preferential Flow in Fissure Systems ing. Hybrid optimization methods applied in a well suited framework can help to solve arising problems with less sim- The asymptotic analysis of Darcy flow near a very thin ulations calls if they are well adapted for the underlying highly-permeable fissure is revisited. The limiting problem problems. In this talk we will discuss mixed-integer non- is Darcy flow in the region coupled to tangential Darcy flow linear simulation based optimization using surrogate func- through the lower-dimensional interface approximation of tions for efficient derivative free optimization. the fissure. Stokes flow in the fissure leads to Brinkmann flow in the interface model. For a fine-scale periodic struc- Thomas M. Hemker ture of highly-permeable fissures of width decreasing at TU Darmstadt twice the rate of the periodic scale, we obtain the homog- Dept. of Computer Science enized limit and establish the two-scale convergence. (pre- [email protected] liminary report)

Ralph Showalter, Fernando Morales MS10 Department of Mathematics Groundwater Calibration with POD Oregon State University [email protected], We demonstrate a POD (proper orthogonal decomposi- [email protected] tion) tool for calibration of models for saturated flow in porous media. POD was developed for flow control and builds a global basis from “snapshots’ taken from a dy- MS10 namic simulation. In our steady-state context we build the Particle Swarm Optimization with Surrogate Func- basis from the sensitivities. The advantages of POD are tions for Water Management Problems that matrix assembly and factorization for the finite element simulation are moved out of the optimization loop. We provide a framework to improve the efficiency of the We show three-dimensional results that indicate that the particle swarm optimization method by using surrogate performance of the optimization using POD is essentially functions. For water resources management problems, this the same has that for the much more expensive optimiza- helps alleviate the burden of costly simulation calls re- tion using the full finite element simulator. We may also quired to model groundwater flow and transport that are show results for global optimization using POD as the sur- embedded in the objective function. We present results rogate model. on a hydraulic capture problem posed as a mixed-integer nonlinear problem in determining the number of wells, well Tim Kelley, Corey Winton rates, and locations to minimize clean up costs. North Carolina State University [email protected], [email protected] Kathleen Fowler Clarkson University Owen J. Eslinger Department of Mathematics US Army Corps of Engineers [email protected] Information Technology Laboratory [email protected] Matthew Parno Clarkson Univeristy Jackie Pettway [email protected] ERDC [email protected] MS10 Tailoring Hybrid Optimization Methods for Water Stacy Howington Resources Management US Army Engineer Research and Development Center [email protected] Hybridizing optimization methods has emerged as highly promising. However, the effectiveness of this approach may be compromised if the methods combined are not suited to MS11 one other or to the application of interest. In this talk, Coupling Discontinuous Galerkin Discretizations we will discuss hybrid optimization in the context of water Using Mortar Finite Elements for Advection- resources management. We will focus on the characteristics Diffusion-Reaction Problems of the problem domain and of some optimization techniques and present numerical results demonstrating the efficacy of We investigate DG-DG domain decomposition coupling tailoring hybrids. using mortar finite elements to approximate the solution to general second-order partial differential equations. Genetha Gray This class of equation includes second-order elliptic and Sandia National Laboratories parabolic equations, advection-reaction equations, as well [email protected] as problems of (mixed) hyperbolic-elliptic-parabolic type. In the formulation, we consider the upwinded flux for the advective flux and provide the matching condition by weakly imposing continuity of the total flux on the inflow boundary part of the interface and continuity of the total 70 GS09 Abstracts

flux and the solution on the characteristic boundary part merical results indicate second-order convergence for pres- of the interface via mortar finite elements. The subdomain sures at the cell centers and first-order convergence for sub- grids need not match and the mortar grid may be much face fluxes if the grids are sufficiently regular. Second-order coarser, giving a two-scale method. The diffusion coeffi- convergence for face fluxes is also observed numerically. cient is allowed to be degenerate. Convergence results in terms of the fine subdomain scale h and the coarse mortar Ross Ingram scale H are then established. If the interface lies in the Univeristy of Pittsburgh advection-reaction regime, with proper choice of h and H, Department of Mathematics optimal convergence rates are achieved. A non-overlapping [email protected] parallel domain decomposition algorithm reduces the coupled system to an interface mortar problem. The properties Mary Wheeler of the interface operator are discussed. The University of Texas at Austin [email protected] Mi Young Kim Inha University Ivan Yotov [email protected] Univeristy of Pittsburgh Department of Mathematics Mary Wheeler [email protected] The University of Texas at Austin [email protected] MS12 Homogenization of Porous Media by the Periodic MS11 Unfolding Method Analysis of MPFA Convergence on General Ge- ometries We consider the Stokes and the Navier-Stokes problems in a perforated domain. The holes are periodically distributed The similarities between the multi-point flux approxima- with a period e, their size is of the order de. Both d and tion (MPFA) methods and the mimetic finite difference e are small parameters. Our aim is to give the asymptotic method can be used to prove convergence of the MPFA behavior of the velocity and of the pressure of the fluid, methods on general grids in 2D and 3D. We examine the as these two parameters go to zero. We first discuss the assumptions needed for convergence of the MPFA meth- cased=1corresponding to the classical homogenization ods, with particular attention to the limitations posed by (cf. [3] and [4]). For the the general cased=ea(i.e., the the analysis and how the theory compares to the numerical case of small holes), we derive several limit problems, corre- convergence results. sponding to different values of a. These limit problems are either the Darcys law, or a Stokes problem or the Bringman Annette Stephansen law. Finally, we study the case of partially perforated do- Unifob Petroleum mains. The proofs use the periodic unfolding method (see, Centre for Integrated Petroleum Research for instance [1] and [2]) which avoiding the introduction of [email protected] extension operators, allows us to treat complex geometries of domains. References [1] D. Cioranescu, A. Damlamian, Runhild Aae Klausen G. Griso, Periodic unfolding and homogenization, C. R. CMA, University of Oslo Acad. Sci. Paris S er. I Math. 335 (2002), 99-104. [2] A. [email protected] Damlamian, An Elementary Introduction to Periodic Un- folding, GAKUTO International Series Math. Sci. Appl. 24 (2005), 119-136. [3] E. Sanchez - Palencia, Non ho- MS11 mogeneous Media and Vibration Theory, Lecture Notes in Modeling Multiphase Flow Coupled with Biogeo- Physics 127, Springer Verlag (1980). [4] L. Tartar, Incom- chemistry in Porous Media pressible fluid flow in a porous medium- convergence of the homogenization process. Appendix in [3]. Abstract not available at time of publication. Doina Cioranescu Mary Wheeler Laboratoire Jacques-Louis Lions The University of Texas at Austin Université Pierre et Marie Curie [email protected] [email protected]

MS11 MS12 A Multipoint Flux Mixed Finite Element Method Multiscale Models for Processes with Evolution of on Hexahedra Microstructures

We present a mixed finite element (MFE) method for Many problems in science and engineering involve time- Darcy flow on hexahedral elements, which reduces to cell- varying microstructures. Important examples are phase centered finite differences and performs well for discontin- transitions with microstructures of dendritic or eutec- uous full tensor coefficients. Motivated by the multipoint tic type, or processes in porous media, where deposi- flux approximation (MPFA) method where sub-face fluxes tion/resolution may change the geometry of pores. In such are introduced, we introduce an enhanced version of the cases the application of standard homogenization does not lowest order Brezzi-Douglas-Marini (BDM) MFE space in- lead to a purely macroscopic model as in more traditional volving four velocity degrees of freedom per face. A special examples, but to multiscale models. We address the deriva- quadrature rule is employed that allows for local velocity tion and analysis of such models and their use in simula- elimination and leads to a symmetric and positive definite cell-centered system for the pressures. Theoretical and nu- GS09 Abstracts 71

tions. Hydrated Materials Christof Eck Charged hydrated materials exhibit internal coupling Institut für Angewandte Analysis und Numerische mechanisms stemming from the intrinsic characteristics of Simulation the constituents. In this content, the model under consid- University of Stuttgart eration consists of a fluid-saturated solid matrix carrying [email protected] volume-free fixed negative charges, while the pore fluid is given by a mixture of a liquid solvent and the cations and anions of a dissolved salt. Based on the well-founded The- MS12 ory of Porous Media (TPM), use is made of the assump- Upscaling of Differential Equations Modelling the tion of quasi-static processes. The governing equations are Reactive Flow Through a Deformable System of given by the volume balance of the fluid mixture governed Biological Cells by the hydraulic pressure, the concentration balance governed by the cation concentration, the overall momentum We consider a system of model equations coupling fluid balance governed by the solid displacement and the electri- flow, deformation of solid structure and chemical reactions cal continuity equation governed by the electrostatic force. in biological tissue. Our goal is to obtain the upscaled Furthermore, the mechanical solid extra stress is described system modeling reactive flow through biological tissue on by an extended neo-Hookean material law, while the vis- the macroscopic scale, starting from a system on the cell cous fluid flow follows an extended Darcy’s law, which in- level. The novelty of the upscaled model is that it includes cludes the gradients of the ion concentrations and the elec- Biot’s equations from the soil consolidation theory, coupled trical potential. Furthermore, the ion diffusion is described with reactive transport. (Joint work with W. Jaeger and by an extended Nernst-Planck equation. Finally, the model M. Neuss-Radu) is implemented into the FE tool PANDAS by use of a mixed finite element scheme. The presented examples proceed Andro Mikelic from boundary conditions depending on internal variables Institut Camille Jordan, UFR Mathématiques such that certain stabilisation techniques are needed. Universite Claude Bernard Lyon 1 [email protected] Wolfgang Ehlers Institute for Mechanics University of Stuttgart MS12 [email protected] Crystal Dissolution and Precipitation in Porous Media MS13 We propose a pore scale model for crystal dissolution and Ionic Multi-Species Transport in Porous Materials precipitation in a porous medium. As a result of the precip- with Account to Surface Charge Phenomena itation and dissolution the pore geometry may change. Us- ing the proposed model we derive upscaled effective equa- A set of macro level Nernst Planck Poisson type of equations on the Darcy scale via a formal homogenization pro- tions are derived, describing the diffusion of ionic species cedure. Numerical simulations show that solutions of the in the pore water of a porous material with charged pore upscaled model match the averaged solutions of the pore- walls, using the electroquasistatic hybrid mixture theory. scale model very well. The effect of the surface charge on the global ionic diffusion is studied by a separate microscopic tentative approach Tycho L. van Noorden based on ionic double layer formations. A numerical so- Department of Mathematics & Computer Science lution technique based on the finite element approach is TU Eindhoven formulated. [email protected] Bjorn Johannesson Dept Civil Engineering MS13 University of Denmark Osmotic, Swelling, and Disjoining Pressures at [email protected] Multiple Scales

In swelling porous media, pressures commonly used include MS13 disjoining pressure, osmotic pressure, and swelling pres- Passive Measurements of Electrical Potential as a sure. These are attributed to microscopic forces such as Non-intrusive Method to Determine and Locate electrostatic forces, Van der Waals forces, and surface hy- Hydromechanical Disturbances dration. Here we discuss the definitions of these different pressures and examine the relationship between them and A pore scale model of transport of ions in a charged porous microscale forces within the framework of two upscaling material is developed using a volume averaging operator approaches for swelling porous materials: hybrid mixture applied to the Nernst-Planck and Stokes equations that theory and homogenization. couple Maxwell and Biot equations. The macroscopic equations are solved with a finite element method. We Lynn Bennethum present results of the forward and inverse modeling. The Dept Mathematical and Stat inverse modeling is developed inside a Bayesian framework Sci. Univ Colorado Denver using MCMC samplers. Different applications are shown [email protected] in hydrogeophysics and volcanology. Andre Revil MS13 Dept of Geophysics Electro-chemical and Swelling Behaviour of Active Colorado School of Mines [email protected] 72 GS09 Abstracts

MS14 [email protected] Corrected Operator Splitting for Two-phase Flow with Gravity Forces in Porous Media Seong H. Lee Chevron ETC In this talk, we apply the corrected operator splitting [email protected] (COS) algorithm for two-phase flow including gravity in porous media, combining the characteristics method with the finite volume method. The motivation is to gain the MS14 computational efficiency from the hyperbolic solver and a Multi-scale Multi-physics Models for Flow and good handling of the non-linear flux term with a more accu- Transport in Porous Media rate shock width using large time step. The methodology of the COS algorithm is described and numerical results Physical processes generally take place on different tem- are given. poral and spatial scales. Also, on the same scale, they may vary in space. A standard approach would solve for Yufei Cao the most complex processes occurring in the domain of in- IANS, University of Stuttgart, Germany terest on the finest relevant scale. This is unnecessarily [email protected] expensive. Therefore, we discuss multi-scale multi-physics approaches which allow to take the space and time depen- Magne S. Espedal dence of processes into account, thus reducing the required Department of Mathematics,University of Bergen, Norway amount of data and computing time. [email protected] Jennifer Niessner Rainer Helmig Institut fuer Wasserbau (IWS) IWS, University of Stuttgart, Germany Universitaet Stuttgart, Germany Institut fur Wasserbau [email protected] [email protected] Rainer Helmig Barbara Wohlmuth IWS, University of Stuttgart, Germany University of Stuttgart Institut fur Wasserbau [email protected] [email protected]

MS14 MS15 Mixed Multiscale Finite Element Methods for Reduced-Order Models for Time-Periodic Dynam- Porous Media Flows Using Limited Global Infor- ics in Ocean Flows mation A number of phenomena in ocean flows exhibit time- In this talk, I will describe multiscale methods for fluid- periodic dynamics. These may arise due to diurnal forcing structure interaction. This is a highly nonlinear problem or are inherent flow features such as breaking waves or that involves coupling Stokes equations with elasticity. We Langmuir cells. In this talk, we discuss the adaptation of propose several multiscale methods and their analysis. Nu- reduced-order model development based upon proper or- merical results are presented. This is a joint work with thogonal decomposition (also known as empirical orthogo- Peter Popov and Yuliya Gorb. nal functions) to include sensitivity variables. The resulting dynamical systems exhibit better long time integration Yalchin Efendiev behavior. This improvement is preserved as parameters in Dept of Mathematics the model are varied. Texas A&M University [email protected] Jeff Borggaard Virginia Tech Department of Mathematics MS14 [email protected] On Taking Large Time Steps for Transport

A major advantage of multi-scale methods compared to MS15 classical upscaling consists in their ability to reconstruct Chemical Data Assimilation: Computational Tools fine-scale velosity fields, which can be used to solve for and Applications phase transport. Here, the stability of an implicit fractional flow formulation is investigated and an analysis of the clas- The task of providing an optimal analysis of the state of sical Newton-Raphson scheme explains the well known, se- the atmosphere requires the development of novel compu- vere time step size restriction for S-shaped flux functions. tational tools that facilitate an efficient integration of ob- Then, a simple, unconditionally stable modification is de- servational data into models. We discuss several new com- vised. putational tools developed for the assimilation of chemical data into atmospheric models. The distinguishing feature Patrick Jenny of these models is the presence of stiff chemical interac- Institute of Fluid Dynamics tions. The variational tools presented in this talk include ETH Zurich automatic code generation of chemical adjoints, properties [email protected] of adjoints for advection numerical schemes, calculation of energy singular vectors and their use in placing adaptive Hamdi Tchelepi observations. Data assimilation results using the 4D-Var Petroleum Engineering Department method are shown for several real test problems to illus- Stanford University GS09 Abstracts 73

trate the power of the proposed methods. voirs from Well Tests Adrian Sandu Geologically-realistic models of fractured reservoirs are Virginia Polytechnic Institute and constructed via a workflow involving the integration of State University various data. However these data are often incomplete [email protected] and uncertain, such that the model parameters cannot be fully characterized. The Covariance Matrix Adaptation- Evolution Strategy has been used to estimate identifiable MS15 fracture sets conductivities from well tests data. The global Some Mathematical Problems in Geophysical Fluid sensitivities of the conductivities are computed during op- Dynamics timization from a response surface methodology and the Sobol decomposition technique. Abstract not available at time of publication. Arnaud Lange,Jèrèmie Bruyelle, Marius Verscheure Roger Temam Institut Francais du Petrole Inst. f. Scientific Comput. and Appl. Math. [email protected], [email protected], Indiana University [email protected] [email protected]

MS16 MS15 A Linear Finite-element Node-centered Finite- Dynamic Transitions in Thermohaline Circulation volume Method Including Jump Discontinuities Applied to 2-phase Fracture / Matrix Flow Abstract not available at time of publication. Using operator-splitting, we compute pressure / velocity Shouhong Wang with the FEM and 2-phase transport with the FVM. At Indiana University material interfaces, where saturation can become discon- [email protected] tinuous, we enrich this discretisation with as many degrees of freedom as materials are joined. Additional functional- MS16 ity computes sector-to-sector fluxes, retaining higher-order accuracy, and pressure on the enriched mesh. An implicit Simulation of Flow and Transport Processes in a calculation of nonlinear diffusive transfer processes across Discrete Fracture Matrix System I.Geostatistical fracture-matrix interfaces complements our new method. Generation of Fractures on an Aquifer Analogue Scale Stephan Matthai Montan University of Leoben The critical step for the discrete fracture model approach Leoben, Austria is the generation of a representative fracture network. In [email protected] this study, we will show a geostatistical fracture generator which integrates statistical geometries and spatial characteristics in terms of a standardized variogram, neighbor- Hamid Maghami-Nick hoods and a fracture cell density. Later the flow and trans- Imperial College London port behavior of a fracture matrix system is investigated, [email protected] where the fracture matrix system is represented by the generated fracture network embedded in a porous rock matrix. MS16 A. Assteerawatt, Rainer Helmig Flow simulation in 3D Discrete Fracture Networks IWS, University of Stuttgart, Germany Institut fur Wasserbau The simulation of flow in discrete fractured media leads to [email protected], solve very large linear systems. Those systems are sparse [email protected] and with a specific shape due to the underlying physical problem. In order to solve efficiently this type of systems, different solvers have been tested. We used both direct Hakon Haegland and iterative ones. The iterative solvers were based on a University of Bergen, Norway multigrid method or a conjugate gradient with various pre- Department of mathematics conditionings. Sequential and parallel versions were tested [email protected] on clusters.

Andras Bardossy Baptiste Poirriez IWS, University of Stuttgart, Germany INRIA Rennes Institut fur Wasserbau University of Rennes 1 [email protected] [email protected]

Helge K. Dahle Jocelyne Erhel University of Bergen, Norway INRIA-Rennes, France Department of mathematics [email protected] [email protected] Jean-Raynald de Dreuzy Geosciences Rennes, UMR6118 CNRS MS16 Universit´e de Rennes 1 Automated Characterization of Fractured Reser- [email protected] 74 GS09 Abstracts

MS17 MS17 An Inverse Prob- Simulation-based Nonlinear Least Squares Fitting lem for Coupled Heat-Groundwater Transport in the Shallow Subsurface In this talk we will discuss the development of a trust region-based derivative-free optimization solver for nonlin- In an effort to improve synthetic thermal imagery for re- ear least squares problems. Our emphasis is on achieving mote sensing technologies, a suite of closely coupled numer- rapid decrease of the residuals since the simulation-based ical simulators has been developed. This computational objectives of interest to us are computationally expensive testbed includes thermal and moisture transport finite el- and rarely allow for many evaluations. The central issue ement models, coupled with solar and vegetation models. is managing the set of models as the evaluation history It is well suited for simulations of specific scenarios, which grows. We will illustrate the algorithm on a variety of sci- otherwise might be difficult and time consuming to repro- entific applications. duce in the field. This talk will focus on the inverse problem related to determining material properties. Stefan Wild Argonne National Laboratory Owen J. Eslinger [email protected] US Army Corps of Engineers Information Technology Laboratory Jorge J. Moré [email protected] Argonne National Laboratory Div of Math & Computer Science [email protected] MS17 Forecasting Subsurface Model Performance During Simulation-based Optimization MS18 Quasi-Positive Families of Continuous Darcy-Flux In subsurface transport models, constraint violations may Finite Volume Schemes occur before complete simulation of the remediation time- frame. A new approach exploits this behaviour by monitor- Families of continuous Darcy-flux control-volume dis- ing remediation constraints during simulation. For a given tributed (Multi-point flux Approximations) CVD(MPFA) function evaluation, simulation is pre-empted (terminated finite volume schemes are presented for the general full- early) if infeasible results are forecasted. A demonstration tensor porous media pressure equation. These schemes problem is presented involving the design of a barrier sys- maintain flux and pressure continuity while only depending tem constructed from sorptive materials. Results suggest on a single degree of freedom per control-volume. The new that model pre-emption can significantly reduce computa- families of schemes are compared with earlier formulations tional cost without affecting solution quality. in terms of quadrature range, numerical convergence and stability for challenging problems involving high full-tensor L. Shawn Matott, Bryan Tolson anisotropy. University of Waterloo [email protected], [email protected] Michael G. Edwards Swansea University School of Engineering MS17 [email protected] Inverse Modeling for Non Linear Groundwater Sys- tems with Local RBF and Global Optimization Algorithms with Application to a Large Chinese MS18 Aquifer Fully Conservative Streamline Methods for Two- phase Flow We present new optimization algorithms for identifying parameters in nonlinear partial differential equation models Linear transport of a tracer in an ambient fluid can be of groundwater aquifers. The approach incorporates both approximated by a fully conservative characteristic or La- local and global optimization methods. It includes the use grangian method in which both fluids are conserved locally. of response surfaces of the objective function in order to Nonlinear two-phase flow is a similar transport problem, reduce the number of times the computationally expensive except that streamlines and characteristics no longer coin- PDE model must be computed. The method is applied to cide. We extend linear characteristic methods to two-phase data from a large (456 sq km) aquifer that supplies water streamline methods in one space dimension, preserving the to Beijing, China. masses of both fluids. Our method is effective with time- steps that are several times the CFL step. Christine Shoemaker Cornell University Todd Arbogast [email protected] Dept of Math; C1200 University of Texas, Austin Jiahua Wei [email protected] Tsinghua University Beijing, China Chieh-Sen Huang [email protected] ational Sun Yat-sen University Kaohsiung, Taiwan Stefan M. Wild [email protected] Cornell University School of Operations Research & Thomas F. Russell IE US National Science Foundation [email protected] [email protected] GS09 Abstracts 75

MS18 comparison to experimental results is made. Control Volume Mixed Methods and Relationships to MPFA Hans Bruining Delft University of Technology The control volume mixed finite element method (CVM- [email protected] FEM), applied to flow equations in porous media, is a vari- ant of the RT0 mixed method in which finite-volume vector Karl-Heinz Wolf, Hamidreza Salimi velocity test functions yield a discrete Darcy law on control TU-Delft volumes, in addition to the usual cell-by-cell conservation. k.h.a.a. [email protected], [email protected] The talk will discuss new results on superconvergence for CVMFEM on distorted quadrilaterals, analysis of CVM- FEM with mortar couplings, and schemes that combine MS19 features of CVMFEM and multipoint flux approximation Modelling Microbial Clogging in Porous Media on (MPFA). the Darcy Scale Thomas F. Russell A concept is presented to model biomass accumulation in National Science Foundation the subsurface on the Darcy scale. It accounts for bacterial USA growth, deposition of bacteria on the porous medium, de- [email protected] tachment, decay, and the effects of biofilm growth on the hydraulic properties of the porous medium. The intended Mary Wheeler application is the simulation of the plugging of damaged The University of Texas at Austin or fractured cap-rock in injection well vicinity in a CO2 [email protected] storage reservoir and the protection of well cement against corrosion using biofilms. Ivan Yotov Anozie Ebigbo Univeristy of Pittsburgh Institut für Wasserbau Department of Mathematics Universität Stuttgart [email protected] [email protected]

MS18 Rainer Helmig A Mortar Multiscale Solver for Stochastic Approx- IWS, University of Stuttgart, Germany imations of Flow in Random Porous Media Institut fur Wasserbau [email protected] Recent work has shown that the construction of a multiscale basis for the mortar mixed finite element method can Holger Class greatly reduce the computational cost in solving the coarse Universitaet Stuttgart scale interface problem. We show that this multiscale ba- Scientist sis only needs to be computed for the mean of the random [email protected] field and can be reused as an efficient preconditioner for each of the subsequent stochastic realizations. Al Cunningham Center for Biofilm Engineering Mary Wheeler Montana State University The University of Texas at Austin al [email protected] [email protected]

Tim M. Wildey MS19 The University of Texas at Austin Fast-reaction Asymptotics for a Reaction-diffusion Austin, USA System with Distributed Microstructure [email protected] We investigate a reaction-diffusion process in a two-phase medium with microscopic length scale . The diffusion co- Ivan Yotov 2 Univeristy of Pittsburgh efficients in the two phases are highly different (d1/D = ) Department of Mathematics and the reaction constant k is large. First, the homogenisa- [email protected] tion limit → 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k →∞and obtain a two-scale reaction-diffusion system with a moving MS19 boundary traveling within the microstructure. This results Modeling the Pore Space in Carbonate Reservoirs are the outcome of a joint work with Sebastian A. Meier by Using Acids (Bremen, Germany).

Carbonate reservoirs can contain large fractures that can Adrian Muntean cause short circuit ﬂows leaving much oil unproduced. This Department of Mathematics paper investigates the idea of permeability reduction in the TU Eindhoven fracture by injection of a mixture of acids. A 1-D sim- [email protected] ulation shows that upstream dissolution and downstream precipitation of CaSO4 are the dominant processes. A 2-D simulation shows that downstream fractures are clogged, MS19 whereas continuously wormholes are created upstream. A Bioﬁlms in Porous Media: Theoretical and Exper- 76 GS09 Abstracts

imental Advances MS20 Reactive Transport in Porous Media: Multiple- I will discuss efforts, developed over the last 10 years, to Scale Analysis, Instability Phenomena formally upscale the transport and reaction processes associated with biofilms in porous media. Our results to date Reactive transport in porous media is of paramount impor- are multi-scale, starting from the cell scale, and currently tance in many applications. Finding the correct chemical ending (after a sequence of upscaling efforts) at the Darcy reaction scheme is one of the major modelling complexity. scale. Both local mass equilibrium and non-equilibrium However, coupling with transport brings additional diffi- models have been examined. I will also discuss recent suc- culties. Two-types of difficulties are considered in this re- cesses in imaging biofilms in porous media using x-ray to- view of recent results: (i) multiple-scale problems, with the mography. development of effective surface properties and ”homogenized” models taking into account the various scales of the Brian D. Wood pore and media geometry, as well as surface roughness and School of Chemical, Biological, & Environmental heterogeneity, (ii) hydrodynamics instabilities during dis- Engineering solution processes. Oregon State University [email protected] Michel Quintard Institut de Mécanique des Fluides de Toulouse [email protected] MS20 Coupled Hydro-Geomechanical Analysis of Fault Reactivation and Water Induced Compaction MS20 Numerical Solution to an Integro-differential Equa- Injection and production of fluids cause changes of pres- tion Modeling Swelling Porous Materials sure, temperature and saturation that affect the state of stress in oil reservoirs, resulting in porosity and per- We demonstrate the results of a discrete scheme used to meability variations. It is therefore a coupled hydro- solve a nonlinear model of a swelling porous material. The geomechanical problem. Reservoir simulation with geome- model is cast as a Volterra partial integrodifferential equa- chanical coupling, considering the appropriate constitutive tion (VPIDE) of the second kind where the dependent vari- behavior of the materials, allows realistic modeling of water able is the liquid phase volume fraction. A pseudospectral induced compaction and fault reactivation, that can influ- differentiation matrix is constructed to compute the spatial ence in the production of oil due to pressure and fluid loss derivatives and a Volterra Runge-Kutta scheme is used to in the reservoir. solve the VPIDE at each time step. Leonardo Guimaraes Keith Wojciechowski Dept Civil Engineering - Federal University of Department of Mathematical Sciences Pernambuco University of Colorado Denver Brazil [email protected] [email protected]

MS21 MS20 Setup of the MoMaS Reactive Transport Bench- Macroscopic Effects of Dissolution of Intergranular mark Contacts: A Multi-scale Analysis We will present here the definition of the reactive trans- The paper investigates dissolution/diffusion phenomena port benchmark of MoMaS. According to the interests of that occur within the intergranular contact and their in- MoMaS, the reactive transport problem should be repre- fluence on macroscopic behavior of chalk rocks. The in- sentative of the problems encountered in nuclear waste dis- tergranular interface is modelled as an evolving structure posal simulations. Moreover, we want to interest a com- in which the contact between grains takes place along a munity as large as possible: geochemistry, hydro geology, set of isolated islands surrounded by fluid. The mathe- numerical methods, applied mathematics... Nevertheless, matical description of dissolution and diffusion processes the high complexity of both transport and chemical phe- is obtained by incorporating molecular and volume aver- nomena occurring in such a system may be an obstacle aging. Extensive numerical studies of interface structure for some researcher who may not be familiar with hydro- evolution are carried out. The macroscopic description of geological and geochemical concepts. The problems pro- chemo-mechanical coupling is formulated by invoking an posed here are built on the same mathematical concepts as evolution law that employed the notion of a dual time scale real hydro-geochemical problems, but their description has associated with the intergranular contact evolution. been simplified. The difficulty for building this benchmark was also to provide a sufficient simple problem without loss Dariusz Lydzba of mathematical and numerical difficulties. The objectives Institute of Geotechnics and Hydrotechnics of this benchmark are to propose a challenging test for nu- Wroclaw University of Technology merical methods used on reactive transport modelling in [email protected] porous media. In order to focus on numerical methods, the problem presented here is on quite small size, from Stan Pietruszczak hydrodynamic and from geochemical point of view. To McMaster University obtain a really challenging test, the chemical coefficients [email protected] presented in this benchmark are not real one; but they are still realistic This benchmark consists in three independent Jian-Fu Shao parts, ranked by complexity: Easy, Medium, Hard. Each Ecole Polytech Lille part consists of a 1D and a 2D reactive transport problem. [email protected] The flow and transport phenomena are the same for the GS09 Abstracts 77

three parts. From one part to the other, some chemical Reactive Transport Problems phenomena are added increasing the difficulties. We have developed a global numerical method for reactive Jerome Carrayrou transport problems based on a robust and efficient Dif- Universite de Strasbourg, France ferential Algebraic Equations (DAE) solver. The coupled [email protected] Partial Differential Algebraic Equations (PDAE) are first discretised in space by a finite difference method. The resulting DAE are then discretised in time by a BDF method MS21 in association with a modified Newton-LU method. We Results of the GdR MoMaS Reactive Transport have used our method to simulate 2D problems, in partic- Benchmark with RICHY2D ular some of the Geochemistry MoMaS benchmarks.

In this talk the software RICHY2D for the simulation of re- Caroline de Dieuleveult active transport in porous media and computational results ANDRA for nine of the twelve MoMaS benchmark problems are pre- INRIA Rennes sented. The software is based on the one-step method. In Caroline.de [email protected] order to reduce the size of the resulting discrete problems, it uses a reformulation of the system. RICHY2D is based Jocelyne Erhel on M++ a platform for solving systems of nonlinear partial INRIA-Rennes, France differential equations with Finite Elements in parallel. Campus de Beaulieu [email protected] Joachim Hoffmann University of Erlangen-Nuremberg Department of Mathematics MS22 hoff[email protected] Data Assimilation for a Viscous Incompressible Fluid

MS21 We study the inverse problem of determining the initial Coupling Transport and Chemistry in Porous Me- state, and possibly the forcing, of a viscous incompress- dia with a Newton-Krylov Method: Application to ible fluid observed directly or indirectly over a period of the MoMaS Benchmark time. We will formulate this as a Bayesian inverse problem, giving rise to a probability measure on function space Reactive transport modelling leads to the coupling between for the initial vector field, and the forcing (or model er- a set of advection-diffusion PDE’s, and a set of algebraic ror). We will describe effective MCMC methods that allow equations. The resulting nonlinear system is solved by a us to sample from such a distribution, and present some Newton-Krylov method (which does not require storing the numerical results. jacobian matrix), using as main unkowns the total mobile and total immobile concentrations. The main advantage Simon Cotter is to keep chemistry distinct from transport, while still University of Warwick providing a globally coupled algorithm. We validate the Mathematics Institute method on the 1D and 2D MoMaS benchmark. [email protected] Michel Kern INRIA MS22 [email protected] Quantifying Robustness of Mixing Diagnostics In- ferred from Satellite Altimetry Laila Amir INRIA, France Several recent studies make use of satellite altimetry data Itasca consultants, France to infer mixing diagnostics in the global surface ocean. The laila [email protected] reliability of these diagnostics is unclear, however: in particular, the effect of unresolved scales on turbulent trans- Jean-Baptiste Apoung-Kamga port cannot be quantified. We examine a range of mixing Université Paris-Sud diagnostics in simulations of quasigeostrophic and surface [email protected] quasigeostrophic turbulence and directly probe their dependence on sampling resolution. In this way, we aim to Pascal Havé quantify the robustness of altimetry-inferred mixing diag- IFP nostics. [email protected] Shane R. Keating New York University Jean-Gabriel Houot Courant Institute of Mathematical Sciences Université de Nancy [email protected] [email protected] Shafer Smith Adrien Semin Courant Institute INRIA Center for Atmosphere Ocean Science [email protected] [email protected]

MS21 Numerical Results with a Global Method for 2D 78 GS09 Abstracts

MS22 MS23 Relative Dispersion in the Atmosphere and Ocean Patterns in Soil-Vegetation-Atmosphere Systems: Theory, Modeling and Data Assimilation A signature of Lagrangian chaos is that the separation between two particles deployed at slightly different positions The Transregio 32 is an interdisciplinary project based in a flow will grow exponentially in time. In this talk we on the hypothesis that explicit representation of patterns examine the statistics of particle pairs from in situ exper- in the soil-vegetation-atmosphere system in experimental iments in the atmosphere and ocean. There are indeed and theoretical studies will improve our understanding indications of exponential growth at smaller spatial scales, and predictions of the pertinent mass, energy, and mo- but the behavior at larger scales differs, apparently due to mentum fluxes and their interactions. We will provide the large scale circulation. an overview of the research activities at the Universities of Bonn, Cologne and Aachen and the Research Center Joseph LaCasce Jlich including the application of coupled simulation tools University of Oslo in conjunction with measured data and data assimilation Department of Geosciences techniques [email protected] Clemens Simmer Meteorological Institute MS22 Bonn University Effective Diffusivity: A Tool to Quantify Inhomo- [email protected] geneous, Instantaneous, and Irreversible Transport

When advection-diffusion of a passive tracer is described MS23 with respect to the level set of the tracer itself, it becomes Non-invasive Methods and Modelling Approaches pure diffusion with a spatially and temporally varying dif- to Study the Impact of Subsurface Structures on fusion coefficient. I will review this effective diffusivity for- Flow and Transport malism, its relationship to other metrics of statistical mechanics, its applications to quantify inhomogeneous mixing Geophysical methods may play an important role in in the ocean and atmosphere, and some ideas for parame- managing our terrestrial environment and in maintaining terization. ecosystem functioning and services. Especially, the application and further development of hydrogeophysical meth- Noburu Nakamura ods combined with mathematical models seem very promis- University of Chicago ing to maintain and protect soil and groundwater quality. Department of Geophysical Sciences Hydrogeophsical methods may help to improve our control [email protected] on storage, filter and buffer functions of soils and groundwater systems. Moreover, methods are needed that will help us to bridge the gap between the scale of measure- MS23 ments and observations and the scale at which manage- An Experimental Setup of Ground-based and Air- ment of terrestrial systems takes place. In this presenta- borne Systems to Study Spatio-temporal Struc- tion several examples will be presented showing how hydro- tures in Atmosphere-Land Surface Energy, Water geophysical research can contribute in meeting these chal- and CO2 Exchange lenges and may be used to characterize subsurface water flow and transport. Exchange processes between land surface, vegetation and atmosphere over structured, inhomogeneous regions are in- Harry Vereecken, Sander Huisman, Jan van der Kruk, vestigated in an experimental approach. For that purpose Sebastian Lambot, Jan Vanderborght ground-based long-term monitoring and dedicated cam- Insitute of Chemistry and Dynamics of the Geosphere paigns are combined within the Rur catchment, Germany. Forschungszentrum Jülich Four campaigns covering different vegetation periods have [email protected], [email protected], been performed with instrumentation ranging from leaf [email protected], [email protected], level gas exchange, eddy correlation stations, scanning re- [email protected] mote sensors to aircraftobservations. Synergistic data analysis shall reveal spatio-temporal structures in the exchange processes and their relation to external parameters. MS23 Atmospheric-land Feedbacks in Clear and Cloudy Susanne Crewell, Jan Schween Boundary Layers Institute for Geophysics and Meteorology Cologne University We investigated the effect of land surface heterogeneity on [email protected], [email protected] cloud formation using a large eddy simulation model. Our study showed that by altering the turbulent structure of Heiner Geiss, Uwe Rascher, Anke Schickling the atmospheric boundary layer, heterogeneity may create FZ Jülich conditions that are favourable for cloud formation. How- [email protected], [email protected], ever, the results of the model are sensitive to the numerics. [email protected] The choice of the advection scheme has significant influence on the transport over the interface between the turbulent Christian Selbach boundary layer and the laminar free atmosphere, which is Institute for Geophysics and Meteorology at the height at which clouds form. Cologne University [email protected] Jordi Vila Meteorology and Air Quality Wageningen University and Research Center GS09 Abstracts 79

[email protected] MS24 Time Migration Velocity Analysis by Image-wave Chiel van Heerwaarden Propagation in the Common-image Gathers Wageningen University and Research Center Wageningen, The Netherlands Image-wave propagation or velocity continuation describes [email protected] the repositioning of a migrated seismic event as a function of migration velocity. In the common-image gather (CIG) domain, it can be used for iterative migration veloc- MS24 ity analysis. Continuation of CIGs allows to detect those Analysis and Algorithms for a Regularized Cauchy velocities at which events flatten. A correction formula Problem arising from a Non-Linear Elliptic PDE translates constant flattening velocities into varying time- for Seismic Velocity Estimation migration velocities. Thus, the migration velocity model can be improved iteratively until a satisfactory result is We derive and study nonlinear elliptic PDE’s in 2D and 3D reached. connecting the Dix velocity and geometrical spreading of the image rays, and hence the true seismic velocity which is Joerg Schleicher a product of the Dix velocity and the geometrical spread- University of Campinas ing. The physical setting allows us to pose only a Cauchy Dept. Applied Mathematics problem, and hence is ill-posed. However we are still able [email protected] to solve it numerically on a long enough interval of time to be of practical use. Jesse C. Costa Federal University of Para Maria K. Cameron [email protected] New York University Courant Institute Amelia Novais [email protected] University of Campinas Dept. Applied Mathematics Sergey Fomel [email protected] University of Texas at Austin [email protected] MS25 James Sethian An Hybrid Finite Volume Method for Two Phase University of California, Berkeley Flow Problems: Formulation, and Numerical Re- Department of Mathematics sults [email protected] We will present extension of Sushi finite volume method in the case of two phase flow in porous media. The scheme MS24 uses unknowns at the centre of the cells and unknowns on Review of Recent Advances in Time-domain Seis- the interfaces. In relation with theses last unknowns, we mic Imaging have to ensure continuity of some fluxes : different choices can be retained and we will discuss this point. We will Abstract not available at time of publication. compare our results with results obtained by other methods as mixed finite elements. Sergey Fomel University of Texas at Austin Clément Chavant [email protected] EDF (Electricité de France) R&D Département AMA [email protected] MS24 Ray-theoretical Aspects of Seismic Time Migration Ophélie Angelini and Demigration EDF-LAMSID [email protected] This work is devoted to a ray-theoretical analysis of elementary wavefields inherent to time migration and demigration of seismic data. For such processes we base our- Eric Chenier selves on the standard hyperbolic traveltime approxima- Université Paris Est, tion with respect to source-receiver offset and migration Laboratoire Modélisation et SImulation Multi Echelle aperture. Essential is also the construction of two-way [email protected], surface-to-surface ray propagator matrices corresponding to normal rays, for which the slowness vector is normal Robert Eymard to the subsurface reflector, and image rays, for which the Université Paris Est slowness vector is normal to the measurement surface in [email protected] the time-migration domain. The combination of such matrices provides useful insight into the processes of seismic Sylvie Granet migration and demigration. EDF [email protected] Einar Iversen NORSAR [email protected] MS25 Cell Centered Finite Volume Schemes for CO2 Ge- 80 GS09 Abstracts

ological Storage Simulations [email protected]

In this talk, we study the near well discretization of CO2 Yan Li storage models using cell centered multipoint flux approx- Department of Mathematics, Texas A&M University imation schemes for the Darcy fluxes. The finite volume [email protected] discretization uses an hybrid mesh connecting a near well radial mesh to the reservoir mesh for a deviated well. The system of equations is a two phase two components Darcy MS26 flow model with dissolution of the CO2 component into the Dynamic Upscaling of Multiphase Flow in Porous aqueous phase. Media Via Adaptive Reconstruction of Fine Scale Roland Masson Variables Institut francais du petrole We propose an upscaling method that is based on dynamic [email protected] simulation of a given model in which the accuracy of the upscaled model is continuously monitored via indirect error- Léo Agelas, Daniele Di Pietro, Guichard Cindy, Ivan measures. If the indirect error measures are bigger than Kapyrin a specified tolerance, the upscaled model is dynamically IFP updated with approximate fine scale information that is [email protected], [email protected], reconstructed by a multi-scale finite volume method. The [email protected], [email protected] new upscaling algorithm is validated for two-phase, incompressible flow in heterogeneous porous media. Robert Eymard University Paris East Seong H. Lee [email protected] Chevron ETC [email protected]

MS25 Xiaochen Wang, Hui Zhou Discretisation Schemes for Anisotropic Heteroge- Stanford Univ. neous Problems on Near-Well Grids [email protected], [email protected]

In this work, we construct analytical solutions for near- Hamdi Tchelepi well flow which is not aligned with a radial inflow pattern. Petroleum Engineering Department These solutions resemble strongly heterogeneous, possible Stanford University anisotropic media, which is less accounted for in existing [email protected] near-well models. We compare different control volume discretisation schemes and radial-type grids for such cases, and give their convergence behavior. The results of these MS26 singlephase flow test cases are supported by multiphase Generic Global Scale-up: Advantages and Chal- flow simulations. lenges

Sissel Mundal Generic global scale-up is based on global flow solutions Centre for Integrated Petroleum Research obtained using generic boundary conditions as opposed to [email protected] well-driven boundary conditions tailored to specific flow scenarios as in other global scale-up methods. This paper Eirik Keilegavlen review some of the advantages of generic global scale-up, its University of Bergen, Norway relation with global multiscale finite element methods, and [email protected] the challenges in its practical applications. Some practical resolutions to address the challenges are also discussed. Ivar Aavatsmark Centre for Integrated Petroleum Research Xiao-Hui Wu [email protected] ExxonMobil Upstream Research Company [email protected]

MS26 Local-global Two-phase Upscaling of Flow and MS26 Transport in Heterogeneous Formations Numerical Upscaled Model of Transport with Non- separated Scales We present a local-global two-phase (LG2P) upscaling approach to generate upscaled transport functions. The We show numerical results for a new model for advection- LG2P upscaling directly incorporates global coarse-scale diffusion-dispersion in porous media in the presence of mul- two-phase solutions into local upscaling. It effectively cap- tiple scales which are not necessarily well separated. The tures the impact of global flow, while avoiding global two- model, developed theoretically in prior work and motivated phase fine-scale simulations. Local boundary conditions by experiments of Haggerty et. al., includes as special are updated with time-dependent coarse solutions, there- cases the classical homogenized model as well as the double fore capturing the global flow both spatially and tempo- porosity models, but is characterized by presence of addi- rally. Through various examples, we show that the method tional memory terms. We discuss various discretizations consistently provides accurate coarse models for both flow for the model with special attention paid to handling the and transport predictions. new memory terms. Most significant issue is how to detect which terms are important in what regimes of flow and Yuguang Chen transport and how the model compares with experimental Chevron Energy Technology Company GS09 Abstracts 81

data. displacement is time-lagged. Son-Young Yi Vivette Girault Oregon State University University of Paris 06 [email protected] [email protected]

Malgorzata Peszynska, Ralph Showalter Gergina Pencheva Department of Mathematics CSM, ICES Oregon State University The University of Texas at Austin [email protected], [email protected] [email protected] Mary Wheeler The University of Texas at Austin MS27 [email protected] A Unified Mixed Formulation Naturally Coupling Stokes and Darcy Flows Tim M. Wildey Solving Stokes-Darcy coupled flow using stable Galerkin The University of Texas at Austin formulations for both subproblems usually leads to unbal- Austin, USA anced rates of convergence. We present a stabilized mixed [email protected] FEM for Darcy flow, compatible with Galerkin stable elements for Stokes, with balanced rates of convergence for MS27 velocity and pressure. The discontinuities of the solutions on the interface of the free fluid and the porous medium are Preferential Flow and Geomechanics incorporated in the finite element approximation by linear Dynamic capillary pressure effects alter classical parabolic transformations derived from the interface conditions. models of filtration flow to those of pseudoparabolic type. Maicon Correa These effects become substantial in fast processes or at National Laboratory of Scientific Computing small scales. We consider these issues in the filtration LNCC, Brazil through elastic porous media with such pressure-saturation [email protected] relationships. Ralph Showalter Abimael Loula Department of Mathematics National Laboratory of Scientific Computing, Brazil Oregon State University [email protected] [email protected]

MS27 MS28 The Chaotic Dynamics of Anomalous Dispersion as Multi-D Upwinding for Multi-Phase Transport in Models by a Nonstationaryextension of Brownian Porous Media Motion Multidimensional methods for hyperbolic equations can Given an arbitrary mean square displacement, we show lessen the correlation of numerical errors with the com- how to construct a family of stochastic processes with this putational grid reducing bias in inherently unstable flow displacement and with independent, nonstationary incre- problems. We present a family of monotone multidimen- ments. The resultant process is used to model anomalous sional methods for two-phase flow with gravity, which is and classical diffusion. By computing the fractal dimension extendable to more general scalar hyperbolic equations. A it is shown that the complexity of the family of processes local coupling in the flux calculation is introduced through is the same as that of Brownian motion. An analytical ex- the use of interaction regions resulting in a compact stencil pression is developed for the finite-size Lyapunov exponent and extension to any grid topology. and numerical examples presented. Jeremy Kozdon John Cushman Stanford University Dept Earth Atmospheric Sciences [email protected] Purdue University [email protected]. Brad Mallison Chevron Energy Tech. Co. MS27 [email protected] Domain Decomposition for Poroelasticity and Elas- ticity with DG Jumps and Mortars Margot Gerritsen Dept of Petroleum Engineering We couple a time-dependent poroelastic model in a region Stanford University with an elastic model in adjacent regions. We discretize [email protected] each model independently on non-matching grids and we realize a domain decomposition on the interface by intro- ducing DG jumps and mortars. The unknowns are con- MS28 densed on the interface allowing the computation in each Multidimensional Upwind Schemes for Flow in subdomain to be performed in parallel. We establish error Porous Media on General Quadrilateral and Tri- estimates for an algorithm where the computation of the angular Grids Standard reservoir simulation schemes employ single-point 82 GS09 Abstracts

upstream weighting for convective flux approximation. in porous media. A number of numerical examples are pre- These schemes introduce both coordinate-line numerical sented to illustrate computational advantages of DG meth- diffusion and cross-wind diffusion into the solution that ods for porous media flow, with emphasis on the treatment is grid and geometry dependent. New locally conserva- of capillary pressure heterogeneity and the dynamic mesh tive higher-order multi-dimensional upwind schemes that modification. minimize both directional and cross-wind diffusion are presented for convective flow approximation. The schemes are Mary Wheeler coupled with full-tensor Darcy flux approximations. The The University of Texas at Austin new schemes are comprised of two steps; (a) Truly multi- [email protected] dimensional upwind approximation, which involves flux approximation using upwind information obtained by up- Shuyu Sun stream tracing along wave-vector paths where wave infor- Clemson University mation travels in multiple dimensions. Multi-dimensional [email protected] formulations using edge-based and cell-based approximations that reduce cross-wind diffusion are presented. Con- ditions on tracing direction and CFL number lead to a MS29 local maximum principle that ensures stable solutions free Stochastic Velocity Field Models for Eddy-Rich of spurious oscillations. (b) Higher-order approximation Flows that corrects the directional diffusion of the approximation. Benefits of the resulting schemes are demonstrated Recent high-resolution radar observations of surface veloc- for convective reservoir simulation test cases involving a ity have revealed submesoscale eddies in the coastal areas. range of unstructured grids and permeability fields. While By an objective estimation method, eddies are detected standard simulation methods yield relatively poor results and their parameters such as center coordinates, size, and for such cases, the new methods prove to be particularly intensity are estimated. The obtained statistics are used effective. to parametrically represent the birthdeath process of eddies via a model stochastic velocity field known as inlar Sadok Lamine flow. The model is developed further to represent the eddy Shell EP International B.V. amplitude decay more accurately. [email protected] Mine Caglar Micheal Edwards Department of Mathematics University of Wales Swansea Koc University [email protected] [email protected]

MS28 MS29 Eulerian-Lagrangian Methods for Multiphase Mul- Solving the Pressure Poisson Equation in Large- ticomponent Transport aspect Ratio Ocean-shaped Domains

Transport in porous media is often advection-dominated. A key challenge in the development of non-hydrostatic This leads to efforts to incorporate Lagrangian techniques ocean models is that the Poisson equation for pressure must into numerical schemes, in order to overcome CFL limita- be solved in a domain with extremely large aspect ratio . tions, numerical dispersion, and non-physical oscillations. This leads to a matrix with a condition number which is bounded from below by c−2 for some positive constant c In multiphase transport, these efforts are made easier by → working with an adjoint system, whose natural interpre- as 0, in the case in which Neumann boundary condi- tation is in terms of mass movement rather than wave tions are applied everywhere. Since the convergence rate propagation. The talk will explain this in the context of (required number of iterations for a given tolerance) for Eulerian-Lagrangian methods for multiphase multicompo- iterative solvers scales with condition number, this makes nent transport and will outline some recent developments. standard iterative solvers extremely slow. However, in the case in which Dirichlet boundary conditions are specified, Tom F. Russell the condition number is bounded from above by the con- National Science Foundation dition number of the matrix which one must solve for a [email protected] hydrostatic model. This motivates the preconditioner approach used by the MITgcm ocean model. However, as formulated, that approach can not easily be extended to fully MS28 unstructured meshes such as those used by the Imperial Discontinuous Galerkin Methods for Transport in College Ocean Model (ICOM). In this talk, we prove some Porous Media estimates on the condition number for finite element discretisations of the Poisson equation in the large aspect ratio Two-phase flow in porous media has important applica- limit, and suggest a new approach for preconditioning the tions for petroleum reservoir engineering and groundwa- matrix system based integrating an approximated reduced ter processes. Both applications may involve multiple system for the top surface boundary condition in a multi- time and spatial scales, long simulation time periods, and grid solver. These solvers enable previously unachievable many coupled nonlinear components. In particular, the simulations in large aspect ratio domains (such as three- advection-dominated component and the nonlinear cou- dimensional gyres) and we will present some of our latest pling of compressibility, capillary pressure and relative per- results from these simulations. meabilities often result in sharp saturation fronts, which demands steep gradients to be preserved with minimal os- Colin Cotter cillation and numerical diffusion. In this talk, we consider Imperial College London the combined method of discontinuous Galerkin (DG) and Department of Aeronautics mixed finite element (MFE) for simulating two-phase flow [email protected] GS09 Abstracts 83

Stephan Kramer tical slice model. Imperial College Applied Modeling and Computational Group Tobias Hundertmark [email protected] Universitaet Potsdam Institute for Mathematics [email protected] MS29 CABARET in the Ocean Gyres Sebastian Reich Universität Potsdam A new high-resolution numerical method is proposed for [email protected] modelling quasigeostrophic mesoscale ocean dynamics in eddying regimes. The method is based on a novel, second- order non-dissipative and low-dispersive conservative ad- MS30 vection CABARET scheme. The properties of the new Peer Methods for the Compressible Euler Equa- method are applied to the classical model of the double- tions. gyre ocean circulation. It is demonstrated that, in turbulent regimes, the new method leads to a significant acceler- A new time-splitting method for the integration of the com- ation of the numerical solution convergence, in comparison pressible Euler equations is presented. It is based on a two- to the conventional second-order method. step peer method which is a general linear method with second-order accuracy in every stage. The scheme uses Sergey Karabasov a computationally very efficient forward-backward scheme University of Cambridge for the integration of the high-frequency acoustic modes. Department of Engineering With this splitting approach it is possible to integrate sta- [email protected] bly the compressible Euler equations without any artificial damping. The peer method is tested with the dry Euler Pavel Berloff equations and a comparison with the common split-explicit Physical Oceanography Dept. second-order three-stage Runge-Kutta method by Wicker Woods Hole Oceanographic Inst. and Skamarock shows the potential of the class of peer pberloff@whoi.edu methods with respect to computational efficiency, stability and accuracy. Vasily Goloviznin Moscow Institute of Nuclear Safety (IBRAE) Stefan Jebens [email protected] Leibniz Institute for Tropospheric Research, Permoserstrae 15, D-04318 Leipzig, Germany. [email protected] MS29 Large Eddy Simulation of Sub-mesoscale Motion MS30 Due to Surface Frontal Instability Auxiliary Variables and Deferred Corrections for The behavior of ocean flows at the sub-mesoscale range is Divergence Constrained Flows poorly understood despite its importance for many practical problems, such as the short-term dispersion of pollu- A class of methods for the numerical solution of incom- tants and oils spills. Most ocean models rely on hydrostatic pressible and low-Mach number flows based on a novel dynamics, mixed-layer and subgrid-scale parameterizations combination of deferred corrections and auxiliary variables to represent these processes. In this study, large eddy sim- is presented. Temporal integration is done using spectral ulations of frontal instability are carried out and mixing deferred corrections which allow multiple terms in an equa- across the front is quantified using background potential tion to be treated either implicitly or explicitly and with energy, drifter releases to compute finite-scale Lyapunov different time steps and can easily be constructed to attain exponents and relative dispersion. high formal order of accuracy. These methods are combined with a finite volume discretization of an auxiliary Tamay Ozgokmen variable formulation of the equations of motion to produce University of Miami/RSMAS higher-order accurate flow solvers. The key idea in auxil- [email protected] iary variable methods is to formulate an equation for a variable which does not have an explicit divergence constraint but from which the desired constrained velocity can be nu- Paul F. Fischer merically extracted by the analog to the procedure used Argonne National Laboratory in projection methods. Examples from incompressible, 0- fi[email protected] Mach, and low-Mach number flows will be presented. Michael Minion MS30 University of North Carolina-Chapel Hill Improving Time Integration by Conservative Reg- Mathematics Department ularization of Atmospheric Equations [email protected] We present a conservative regularization approach to the compressible Euler equations that replaces the pressure MS30 gradient in the momentum equations by the gradient of a A Discontinuous Galerkin Hp-Adaptive and Time smoothed pressure field. The smoothing selectively slows Implicit Mesoscale Model down the fastest sound wave components only, without altering the slow dynamics and does not introduce additional Moore’s law predicts a doubling in available computing viscosity. We will present numerical results from a 2D ver- power every 18 months: at this rate a O(1km2) global 84 GS09 Abstracts

climate simulation will only be achievable 30 years from timation now with the numerical methods currently employed in atmospheric models. We explore a class of linearly implicit In statistics, semblance is related to the second moment time-stepping methods: Rosenbrock W-methods. With and in optimization, to the least-squares solution of max- preconditioning techniques, they offer an efficient way of imum signal energy as a characterization of reflection integrating the compressible Euler equations. We also di- events. We define extensions of semblance by replacing cuss a new way to reduce the cost of evaluating Jacobians. second-order by higher-order quantities. These semblance measures behave differently in the estimation of Common- Amik St-Cyr Reflection-Surface parameters by means of the hyperbolic National Center for Atmospheric Research traveltime approximation applied to multicoverage data. Institute for Mathematics Applied to the Geosciences We find improved parameter estimates using a fourth-order [email protected] semblance. Emerson Lima MS31 Universidade Catolica de Pernambuco Velocity Model Determination by Double Path- [email protected] integral Imaging Lucio Santos Path-integral imaging sums over the migrated images for University of Campinas a set of migration velocity models. Those velocities where [email protected] common-image gathers align horizontally are stationary, thus favoring these images in the sum. Thus, the image Joerg Schleicher forms without knowledge of the velocity model. By exe- University of Campinas cuting the path-integral imaging a second time using the Dept. Applied Mathematics velocity as a weight factor in the sum, the stationary ve- [email protected] locities can be extracted by a division of the two images. Joerg Schleicher Martin Tygel University of Campinas University of Campinas Dept. Applied Mathematics [email protected] [email protected] MS32 Jesse C. Costa Federal University of Para Commercial Simulation Software for Porous Media: [email protected] Capabilities and Developments In structural engineering, automotive, oil-gas or aircraft in- MS31 dustries the commercialization of computational mechanics software is fairly advanced. Today, a powerful finite ele- Unconventional Methods for Seismic Imaging ment/finite volume technology has been established there Abstract not available at time of publication. in hands of only a few big players worldwide. In contrast, however, looking to porous media, where we mainly focus Evgeny Landa on subsurface water resources, environmental, geothermal OPERA and industrial porous material problems, the situation is University of Pau rather different. Surprisingly, the water resources market [email protected] is still widely dominated by a classic finite difference program, the USGS code MODFLOW, available for free (except GUI), which stems from the eighties and possesses MS31 in the meantime a number of extensions and adaptations. Generalized Moveout Approximation for It has similarities to an open-source development project. Anisotropic Waves On the other hand, there is an increasing number of research codes at universities funded by public authorities, In this paper, we consider the hyperbolic, the shifted hy- which cover a large disciplinary spectrum ranging from perbola, the rational and the generalized traveltime ap- multi-phase flow via chemical reaction systems, fracture proximation for the qP- and qSV-waves in a homogeneous flow modeling, deformation processes to different numer- VTI medium. We also consider the qP-wave in acoustic ap- ical approaches. It suggests that most of the problems proximation. Fomel and Stovas (2009) proposed the gener- seem now solvable and those software products could sat- alized moveout approximation with other approximations isfy most desires in research and practice. Nevertheless, being the special cases. Being compared with the hyper- there are also commercial simulation software systems, for bolic, shifted hyperbola and rational approximations in few example FEFLOW, which has shown a further growing po- examples, the generalized approximation gives the best re- tential in the porous media market. In the present paper we sults. will discuss the scope and requirements for such a commercial porous media modeling system. We critically ask: who Alexey Stovas needs commercial software, for what and what are the basic NTNU requirements, advantages and challenges? Where are the [email protected] deficiencies and technological constraints? We characterize the status quo regarding the capabilities available, numerical features and inherent software technology. In develop- MS31 ing innovative and globally competitive software products Fourth-order Statistics for Seismic Parameter Es- the following guiding principles become more important: depth and breath of capabilities, completeness (modeling GS09 Abstracts 85

that works), availability and usefulness (GUI, interfaces, [email protected] service, teaching), scalability as well as adaptive architecture. From the current stage we give an outlook to future needs and progressing software developments. Examples MS32 are given for geothermal applications and large-swelling ab- Simulation of Density and Temperature Driven sorbing porous materials. Flow and Contaminant Transport in Fractured Porous Media Using d3f and r3t Hans-Jörg Diersch Groundwater Modelling Centre In this talk, we discuss the mathematical models and the DHI-WASY GmbH, Berlin, Germany numerical methods for the simulation of the density and [email protected] temperature driven flow and the contaminant transport in fractured porous media. The fractures are represented by manifolds with the reduced dimensionality. In the frac- MS32 tures, we consider the same phenomena as in the bulk Applications of Software Tools D3F and R3T for medium. The discretized PDEs for the bulk medium and Coupled Problems of Variable Density Flow and the fractures are solved as a coupled system by the Newton Transport in Porous Media method with the multigrid linear solver. We present numerical results obtained using the simulation programmes The software tools D3F and R3T can solve numerically sev- d3f and r3t extended to the case of the fractured media. eral complex applications of subsurface flow and transport problems. The tools are based on library UG (Unstruc- Dmitry Logashenko tured Grids) that enables the computations on complex Steinbeis Forschungszentrum 936 geological domains discretized by an unstructured, locally Germany adapted, multilevel grid that can be redistributed on pro- [email protected] cessors of parallel computer. The tool D3F (Distributed Density Driven Flow) solves nonlinear flow and transport Alfio Grillo equation that are fully coupled due to the dependence of University of Frankfurt a.M. fluid density on transported concentration. The tool R3T alfi[email protected] (Retardation, Reaction, Radionuclides, Transport) solves many nonlinear transport equations that are coupled due Michael Lampe to reactions (e.g., decay, slow and fast sorption, etc.) and Goethe Center for Scientific Computing where the transport is dominated by the advection deter- University of Frankfurt a.M., Germany mined from the D3F velocity field. In this talk we intro- [email protected] duce not only the most interesting features of these software tools (implicit/explicit in time discretizations, New- ton solvers with analytic linearization, level set methods, MS33 etc.), but also the experiences of a general interest con- Mixed Multiscale Finite Element Methods using cerning the development and the usage of complex software Limited Global Information tools for this type of problems. I will describe mixed multiscale finite element methods us- Peter Frolkovic ing limited global information. In particular, I will stress Department of Mathematics how multiple global information can be incorporated into Slovak University of Technology multiscale basis functions. This is a joint work with J. [email protected] Aarnes and L. Jiang. Yalchin Efendiev MS32 Dept of Mathematics Discontinuous Galerkin Method for Convection Texas A&M University Dominated Transport in Porous Media Using [email protected] DUNE

In this paper we present software techniques as well as Jorg Aarnes recent development of the software package DUNE and SINTEF, Norway. Present: DNV. in particular of the module DUNE-FEM. For several test [email protected] problems as well as for more complex applications, such as the simulation of fuel cells, we present numerical results. Lijiang Jiang These results have been obtained using modern simulation IMA, University of Minnesota techniques such as higher order continuous and discontinu- [email protected] ous Galerkin methods (also in a stabilized version) in combination with local grid adaptivity. Since we are interested in the simulation of complex problems the parallelization MS33 of the code has been taken into account. In adaptive simu- A Loosely Coupled Hierarchical Fracture Model for lations this becomes a non-trivial part since dynamic load the Iterative Multi- Scale Finite-Volume Method balancing needs to be done. Applied to different problems the code shows a very good scalability even on a high num- Recently, the multi-scale finite volume (MSFV) method for ber of processors. flow in heterogeneous porous media was combined with an efficient iterative procedure, which allows to converge so- Robert Klöfkorn lutions to the corresponding fine-scale references. Here, Mathematisches Institut, Abt. für Angewandte this iterative MSFV (iMSFV) method is extended by a hi- Mathematik erarchical fracture model, where the flow in the resolved Universität Freiburg fracture network is represented on lower dimensional manifolds. Therefore, a similar datastructure as for the well 86 GS09 Abstracts

treatment in the MSFV context is employed. [email protected]

Patrick Jenny, Hadi Hajibeygi Jean Francois Thovert Institute of Fluid Dynamics [email protected] ETH Zurich lcd/cnrs [email protected], [email protected]

MS34 MS33 Bounds of Dynamic Permeability and Related Multiscale Simulation of Fractured Reservoirs Problems

In recent years, many different (but related) methods that Transfer coefficients within porous media are assessed by attempt to capture the multiscale behavior of flow in combining the physical principles of the homogenization of heterogeneous reservoirs have been developed. Here, we periodic media and the geometrical simplifications of the extend our own previous models (variational multiscale self-consistent method. This approach provides two static mixed methods) for the simulation of flow in fractured and dynamic permeability assessments that enable to build reservoirs, in which fractures are viewed as entities of lower bounds for a wide class of media. Similarly the Klinken- dimensionality than the domain. We will conclude the pre- berg effect for rarefied fluids is estimated. As for diffusion sentation with results for realistic problems. problems, estimates of trapping coefficient and of thermal Peter Kang, Luis Cueto-Felgueroso, Ruben Juanes permeability involved in the dynamic gas compressibility MIT are given. Civil and Environmental Engineering Claude Boutin [email protected], [email protected], [email protected] Laboratoire Geomateriaux ENTPE France MS33 [email protected] A General Iterative Scheme for the Multiscale Fi- nite Volume Method MS34 In the Multiscale Finite-Volume (MSFV) method a con- How to Model Dispersion in Unsaturated Double servative velocity field is constructed from an approximate Porosity Medium? An Integrated Approach pressure field, which is obtained by superimposition of lo- Multi-scale, multi-components, multi-phases are the key cal solutions coupled by a global problem. Due to the lo- words that characterize the double porosity media subject calization assumption, the MSFV solution differs from the to geo-environmental conditions. In relation to this con- exact solution of the problem. By estimating the localiza- text we present an integrated upscaling approach which tion error, an iterative algorithm can be constructed that combines three issues: theoretical, numerical and exper- converges to the exact solution and conserves mass at any imental. A physical model was designed to imitate the iteration. double-porosity media and to enable performing the disper- Ivan Lunati sion experiments in fully controlled conditions. The mod- Ecole Polytechnique Fédérale de Lausanne elling is based on the observations and follows the logic: ivan.lunati@epfl.ch from micro towards macro. Jolanta Lewandowska MS34 Université Joseph Fourier Laboratory Sols, Solides, Structures - Risques (3S-R) Deformation of Porous Media on the Pore Scale [email protected] and Induced Variations

The deformation of porous media is calculated by solv- Tien Dung Tran Ngoc ing the elastostatic equations discretized on unstructured BRGM, Département Géothermie, 3 avenue Claude meshes made of irregular tetrahedra. The macroscopic con- Guillemin, 450 ductivity and permeability necessitate the resolution of the [email protected] Laplace and the Stokes equations on the initial and deformed meshes. Applications will be provided for a number of media either reconstructed or measured by microtomog- MS34 raphy. Results relative to the evolution of the media and of A Three-Scale Model of pH-Dependent Flows In- the macroscopic properties of the media will be presented. cluding Ion Adsorption in Kaolinite Clays A new three-scale model to describe the coupling between Pierre Adler pH-dependent flows and ion transport in kaolinite clays is Université Pierre et Marie Curie proposed. The poorus medium is characterized by three France separate nano-micro and macroscopic length scales. The [email protected] pore (micro)-scale is characterized by micro-pores saturated by an aqueous solution containing four monovalent Jasinsky Lukasz ionic species and charged solid particles surrounded by thin UPMC Sisyphe electrical double layers. The two-scale nano/micro model [email protected] is homogenized to the macroscale leading to the derivation of effective equations. Valeri Mourzenk Marcio A. Murad LCD/CNRS National Laboratory of Scientific Computation GS09 Abstracts 87

LNCC/MCT neous Porous Media [email protected] The fluid-fluid interface during immiscible displacement Sidarta Lima has a strong influence on mass transfer during the flow Federal University Rural of Rio de process in heterogeneous porous media. Important criteria Janeiro are the front roughness and the averaged saturation at the [email protected] front. Similar to the concept of dilution and dispersion in solute transport theory, these two measures differ in their relation to processes at the fluid interfaces. This presenta- Christian Moyne tion discusses predictions of large scale front behavior ob- LEMTA UMR CNRS-INPL-UHP tained theoretical methods and experimental observations. [email protected]

Didier Stemmelen Insa Neuweiler LEMTA UMR CNRS-INPL-UHP Leibniz University Hannover [email protected] Institute for Fluid Mechanics [email protected] Claude Boutin Laboratoire Geomateriaux Heiss Veronica ENTPE France Universitaet Stuttgart [email protected] [email protected]

MS35 MS35 Statistical Distributions of Conservative and Re- Global Random Walk Simulations for Sensitivity active Species Concentrations in Heterogeneous and Uncertainty Analysis of Transport Models Porous Media The global random walk algorithm (GRW) performs the We present a semi-analytical method of deriving the full simultaneous tracking on a ﬁxed grid of huge numbers of probability distribution of concentration at observation particles at costs comparable to those of a single-trajectory points or volumes, which is based on ﬁrst-order approxima- simulation by the traditional particle tracking approach. tions of one- and two-particle displacements. The resulting Ensembles of GRW simulations of a typical advection- concentration pdf approximately follows a beta distribu- dispersion process in aquifers are used to obtain reliable tion. This pdf can be mapped to the concentration pdf sof estimations of the input parameters for the upscaled trans- species that react upon mixing. Estimates of mean values port model and of their correlations, input-output correla- and standard deviations based on second-order perturbations, probability distributions, and relations between in- tion analysis rather than mapping entire pdf s are biased. put and output uncertainty.

Nicolae Suciu, Calin Vamos Olaf A. Cirpka, Ronnie Schwede Romanian Academy, University of T Tiberiu Popoviciu Institute of Numerical Analysis ”ubingen [email protected], [email protected], Center for Applied Geoscience [email protected] [email protected], [email protected] MS36 Finite Volume Schemes for Simulating Meso- and MS35 Micro-scale Atmospheric Flows Combined Deterministic and Stochastic Sensitivity Analysis - Application to Uncertainty Analysis Two different finite volume schemes for simulating meso- and micro-scale atmospheric flows are discussed in detail. For a model y=f(x), x uncertain vector, we want to 1) First an adaptation of Smolerkiewicz’s MPDATA scheme resume the influence of components of x on components on unstructured grids is presented. The second finite vol- of y, 2) use it for uncertainty analysis. We first choose ume scheme is based on flux-based wave decomposition simple o,p so, that the singular value decomposition (SVD) suggested by LeVeque. The f-waves scheme is described of (p(F(o))’(x) is almost independent of x (deterministic in detail and Euler solutions for different benchmark prob- analysis). The SVD of [cov(p(y),o(x))]inv([cov(o(x),o(x)]) lems are presented. The scheme is also compared with the fairly solves 1). We can precede the analysis with a proper National Center for Atmospheric Research’s state-of-the- orthogonal decomposition of o(x) to deal with correlated art WRF model. input components. Nash’at Ahmad Estelle Marchand Science Applications International Corporation INRIA Rocquencourt 1710 SAIC Drive, M/S 2-3-1, McLean, VA 22102, U.S.A. Projet Estime BP 105 [email protected] [email protected] MS36 MS35 A Runge-Kutta Discontinuous Galerkin Method Movement of Fluid Interfaces and Their Averaged with Time Accurate Local Time Stepping Properties During Two-phase Flow in Heteroge- Our research objectives are the construction and application of accurate and efficient schemes for unsteady flow 88 GS09 Abstracts

problems. In this talk, a recently developed explicit Runge- from semi-implicit time-stepping methods as well as from Kutta based discontinuous Galerkin discretization is pre- Lagrangian particle methods. We have implemented and sented. The focus is set on the time accurate local time studied both types of regularizations for the shallow-water stepping algorithm and an efficient implementation using equations and the ICON spherical spatial discretization ap- a mixed modal/nodal approach. To demonstrate the ac- proach. After a survey of the basic regularization concepts curacy and efficiency of the method, several test problems we will present numerical results. This is joint work with for the compressible Navier-Stokes equations are shown. Marco Restelli, Marco Giorgetta, Tobias Hundertmark and Peter Korn. The work has been funded by the German Sci- Gregor Gassner ence Foundation (DFG) under the SPP Metstroem. Institut fuer Aerodynamik und Gasdynamik [email protected] Sebastian Reich Institut für Mathematik, Universität Potsdam Frieder Loercher, Claus-Dieter Munz Am Neuen Palais 10, 14469 Potsdam, Germany, Tel.: +49 Institut fuer Aerodynamik und Gasdynamik (IAG) 331 97 [email protected], [email protected] [email protected] MS37 MS36 A Multilayer Saint-Venant System : Derivation Theory and Numerics of Sound-proof Models for and Numerical Validation Atmospheric Motions We are interested in this talk in the derivation and analysis The classical Ogura and Phillips’ (1962) anelastic model, of a multilayer model for shallow flows. The model allows subsequent extensions by Dutton and Fichtl (1969), Lipps the fluid to circulate from one layer to the connected ones. and Hemler (1982), or Bannon (1995/96), and the pseudo- The main properties (energy, hyperbolicity) of the model incompressible model by Durran (1988) will be revisited. are exhibited. A kinetic interpretation and some numerical We demonstrate that only the Ogura-Phillips model has simulations including a recirculation case with wind forcing a systematic single-scale asymptotic derivation, but that are also given. even multiple scales asymptotic techniques are incapable of yielding the extended anelastic or pseudo-incompressible Emmanuel Audusse models. In turn, we demonstrate that these models reduce, Laboratoire d’Analyse, Géométrie et Applications at small scales, to the incompressible Boussinesq approx- Université Paris 13, France imation (anelastic) and to the zero Mach number, vari- [email protected] able density flow equations (pseudo-incompressible), respectively. Thus these models are compatible with par- MS37 ticular low Mach number limits of the compressible Euler equations at least on small scales. To show that these mod- Finite Volume Simulation of the Geostrophic Ad- els do provide valid approximations to low Mach number justment in a Rotating Shallow Water System flows in the atmosphere, more advance techniques of math- We focus on the simulation of the geostrophic adjustment ematical analysis are needed. The outline of a proof that is phenomenon for rotating shallow water models by means of work in progress at the time of submission of this abstract finite volume methods. The well-balanced properties and will be provided. A Godunov-type projection method that the discrete dispersion laws of the numerical schemes play was motivated by these considerations will be summarized a fundamental role. Here we consider spatial discretization and tests involving small-scale flow with large density vari- based on a first order Roe- type method and some higher ation as well as breaking topographic internal waves will order extensions based on WENO reconstructions. The be presented. time discretization is designed in order to provide suitable Rupert Klein approximations of inertial oscillations, taking into account Potsdam Institute for Climate Impact Research the Hamiltonian structure of the system for these solutions. Free University of Berlin Some numerical experiments for 1d and 2d problems will [email protected] be shown. Carlos Pares Didier Bresch University of Málaga, Spain UniversitédeSavoie [email protected] [email protected]

MS37 MS36 A Roe-type Scheme for Two-phase Shallow Gran- Implementation of Pressure and Velocity Regular- ular Flows over Variable Topography ized Equations We consider a depth-averaged two-phase model for gravity- Numerical modeling of atmospheric flows is a multiscale driven flows made of solid grains and fluid, moving over problem for which the treatment of turbulence and scale variable basal surface. In particular, we are interested in separated phenomena is essential. Our approach consists applications to geophysical flows such as avalanches and in studying both phenomena by means of regularizations debris flows. We numerically solve the model equations by of the underlying model equations. We have in particu- a high-resolution finite volume scheme based on a Roe-type lar studied velocity (α-Euler models) and pressure regu- Riemann solver. Well-balancing of topography terms is larizations. While the concept of velocity regularization is obtained via a technique that includes these contributions well-known from incompressible Navier-Stokes equations, into the wave structure of the Riemann solution. the extension of velocity regularizations to compressible flows is non-trivial. Pressure regularizations arise naturally Marica Pelanti, Franois Bouchut GS09 Abstracts 89

ENS Paris, France dient [email protected], [email protected] Channelized melt flow due to reactive infiltration in a Anne Mangeney porous medium has been proposed as a mechanism for melt Institut de Physique du Globe de Paris extraction in the Earths mantle. We present analytical and Universite Paris 7 numerical results from an extended mathematical formula- [email protected] tion for melt migration in a deforming mantle column that undergoes steady upwelling. To study the spatial distribution of the channels, we explicitly track the abundance of a MS37 dissolving mineral in the otherwise nonreactive solid. We High Order Well-balanced Finite Volume Schemes present approximate analytic solutions for steady upwelling for Systems of Balance Laws columns, and study their stability to small perturbations using linear stability analysis. The height of the upwelling A new family of high-order well-balanced schemes for the column is larger that the compaction length of the sys- numerical solution of hyperbolic systems of balance laws is tem, and therefore compaction is stabilizing the system proposed. The schemes are designed with use of two sets more than previously acknowledged. Upwelling, porosity of variables, conservative and equilibrium ones. We dis- dependence of the bulk porosity, and increasing disequi- cretize the equations in the conservative variables, while for librium also stabilize the system. These linear results are reconstruction we use the equilibrium ones. We construct in good agreement with high-resolution numerical simula- well-balanced schemes up to the fourth order and apply our tions at early times. Although the system studied is stable technique to the shallow water equation and nozzle flow. to initial perturbations in the range of parameters of geological interest, sustained perturbations of the porosity at Giovanni Russo the inflow boundary lead to localization. Melt flow into University of Catania the channel is limited by the formation of a compacting Department of Mathematics boundary layer, not previously observed. If boundary per- [email protected] turbations are sustained long enough the dissolving mineral is exhausted in regions of high melt flow and the channel Alexander Khe splits due to compaction. Upward branching of channels is Lavrentyev Institute of Hydrodynamics expected in the upper part of the upwelling column, in con- 630090 Novosibirsk, Russia trast to the inverted cascade obtained in previous studies. [email protected] In summary, it is more difficult to localize melt flow than previously thought and sustained perturbations are necessary to force melt localization. The presence of mantle MS38 heterogeneity in the upwelling mantle might provide such The Solidification of An Ideal Ternary Alloy in a sustained perturbations. This may provide a link between Mushy Layer source heterogeneity and the distribution of dunite bodies in the mantle section of ophiolites. We examine a model for the solidification of a ternary alloy in a mushy layer. The effects of species diffusion are in- Alan Schiemenz cluded along with heat diffusion in order to investigate the Department of Applied Mathematics possibility of double-diffusive and other modes of convec- Brown University tion in this system common in many geophysical systems. alan [email protected] We investigate the properties of non-convecting base state solutions for this ternary system and then present linear Marc A. Hesse stability results that reveal convective modes of instability. Dept. of Geological Sciences Brown University marc [email protected] Daniel Anderson Department of Mathematical Sciences George Mason University MS38 [email protected] Open Melt Conduits in Mantle Undergoing Decom- pression Melting Sam Coriell Metallurgy Division We examine the dominating physicial processes for an open NIST channel of melt within a partially molten viscous matrix. [email protected] Melting of the residual rock is fundamentally driven by the rate that heat is transported from the hotter mantle Geoffrey McFadden beneath; in an open conduit this is mostly provided by the National Institute of Standards and Technology motion of melt rather than matrix. Large melting rates [email protected] keep channel walls open against viscous closure due to the reduced channel pressure, which is essentially magmostatic. Bruce T. Murray Department of Mechanical Engineering Ian J. Hewitt SUNY at Binghamton Oxford University [email protected] [email protected]

MS38 Andrew Fowler Oxford University Stability of Upwelling Mantle in a Solubility Gra- Mathematical Institute [email protected] 90 GS09 Abstracts

MS38 along wells. Traditional numerical methods are computa- Reactive Channelization in Mushy Layers and the tionally expensive for large complex geological systems and Mantle with large numbers of wells. The VESA model combines vertically-averaged governing equations with a subscale an- The formation of chimneys in a mushy layer and the for- alytical model for wellbore flow. CO2 injection is solved nu- mation of dunite channels in the mantle both occur by the merically on a coarse grid, capturing the large-scale injec- reactive infiltration instability. In both cases, fluid flow tion problem, while the embedded analytical model elimi- is driven by buoyancy through a permeable, reactive ma- nates expensive grid refinement around wells. trix up a solubility gradient, leading to matrix dissolution and channelization of flux. The theory and experiments Sarah Gasda used to study these two systems have been developed inde- University of North Carolina at Chapel Hill pendently and yet much can be learned by a comparative [email protected] study. For example, theory for the reactive-convective instability in a mushy layer assumes chemical equilibrium Jan M. Nordbotten between crystals and brine, while the theory for magmatic Department of Mathematics systems is based on disequilibrium and linear reaction ki- University of Bergen netics. New simulations of magmatic flow beneath a mid- [email protected] ocean ridge demonstrate the power of a computational implementation based on equilibrium thermodynamics and Michael Celia the Enthalpy Method. New experiments on mushy layers Princeton University suggest that disequilibrium and kinetics are important in Dept of Civil Engineering explaining new phenomena. This talk will examine simi- [email protected] larities and differences between reactive channelization in mushy layers and the mantle. It will weigh the motivations and benefits of assuming thermodynamic (dis)equilibrium MS39 in theoretical descriptions of the two systems. Investigation of Numerical Methods for CO2 Injec- tion Richard F. Katz University of Oxford This talk will focus on numerical methods for the bench- [email protected] mark problem. We investigate methods utilizing methods specially suited for advection dominated flow and gravity segregation and use operator splitting to combine this MS39 methods. In the investigation of several methods for the Simulation of a Benchmark - Solutions and Error given benchmark problem, we focus on methods which eas- Estimates ily can be extended to more complicated geometry. In particular we investigate streamline methods and reordering Geological storage of carbon dioxide in deep saline aquifers methods. is considered as a means to reduce greenhouse gas emissions. Different storage mechanisms play a role in this con- Halvor M. Nilsen text. In our contribution, we are concerned with the mech- SINTEF anisms of residual- and dissolution trapping. We present Oslo 2D- and 3D numerical results related to a model of an ex- [email protected] tended sloping aquifer and investigate the effect of the men- tioned trapping mechanisms and their proper time scales. The results of the 2D- and the 3D simulations are com- MS39 pared, as well as various types of boundary conditions. Overview of Modeling Choices for CO2 Storage The results are also compared to semi-analytical solutions by Hesse et al (2008) where a sharp interface and no dis- This talk will give an overview of the proposed benchmark solution is assumed. problem for this minisymposium. Recognizing that despite the simplicity of the benchmark, it poses severe computa- Maria Elenius tional challenges. The talk will discuss available modeling Bergen Center of Computational Science choices that may be applied to reduce the computational University of Bergen load, and assess these modeling choices in the context of [email protected] the benchmark.

Klaus Johannsen Jan M. Nordbotten University of Bergen, Norway Department of Mathematics [email protected] University of Bergen [email protected] Jan M. Nordbotten Department of Mathematics MS40 University of Bergen [email protected] Homogenization-based Multiscale Finite Elements for Heterogeneous Porous Media

MS39 Multiscale methods are used to solve flow problems with heterogeneous permeability. We show that a popular mixed Vertically Integrated Approaches to Large Scale multiscale finite element fails to reproduce constant flow CO2 Storage fields, and so fails to converge in any meaningful way. The problem arises for anisotropic permeability. We expect the Models of CO2 injection into geological formations must capture both the large-scale plume and small-scale leakage same for isotropic permeability when the microstructure GS09 Abstracts 91

leads under upscaling to a tensorial homogenized perme- ing why heterogeneity and inertia seem to diminish each ability. A modiﬁed method based on homogenization is other’s impact, as well as handling anisotropy emerging shown to converge with respect to this microstructure. from upscaling are the main issues of this talk. Todd Arbogast Malgorzata Peszynska Dept of Math; C1200 Department of Mathematics University of Texas, Austin Oregon State University [email protected] [email protected]

MS40 MS41 Sparse Finite Element Method for Periodic Multi- Analysis of Immiscible Two-phase Flows in Porous scale Nonlinear Monotone Problems Media with Discontinuous Capillarities

In this talk, I will present a sparse tensor product Finite El- We consider a simplified model for two-phase flows in ement (FE) method for the high-dimensional limiting prob- porous media made of different rocks. We focus on the lem obtained by applying the multiscale convergence to a effects of the discontinuity of the capillarity field. We first multiscale nonlinear monotone problem in Rd. The limit- consider a model with capillarity within the rocks. Then ing problem is posed in a product space, so tensor prod- we look for the asymptotic problem for capillarity forces uct FE spaces are used for discretization. This sparse FE remaining only at the interface. We propose a simple mod- method requires essentially the same number of degrees of eling of oil-trapping by the mean of non-classical shocks at freedom to achieve essentially equal accuracy to that of a the interface. standard FE scheme for a partial differential equation in Rd. It is proved that for the Euler-Lagrange equation of Clément Cancès a two scale convex variational problem in a smooth and ENS Cachan Antenne de Bretagne convex domain, the solution to the high-dimensional limit- [email protected] ing equation is smooth. An analytic homogenization error is then established, which together with the FE error provides an explicit error estimate for an approximation to the MS41 solution of the original multiscale problem. Without this A Phase-field Model of Unsaturated Flow – Stabil- regularity, such an approximation always exists when the ity Analysis and the Development of Gravity Fin- meshsize and the micro scale converge to 0, but without a gers rate of convergence. Infiltration of water into homogeneous dry soil often leads Viet Ha Hoang to preferential flow in the form of fingers. The canonical Nanyang Tech. University model for unsaturated flow, known as Richards equation, Singapore is totally stable and therefore unable to reproduce this be- [email protected] havior. We use this physical problem to introduce a new class of models of multiphase flow in porous media, which account for the presence of a macroscopic interface (the MS40 wetting front), and explain why and how fingering occurs. A Multiscale Mixed Finite-element Method for the Stokes-Brinkman Equations Luis Cueto-Felgueroso, Ruben Juanes MIT We present a multiscale mixed finite-element method for Civil and Environmental Engineering detailed modeling of free-flow and porous regions in vuggy [email protected], [email protected] and naturally-fractured reservoirs. The method uses a standard Darcy model to approximate flow on a coarse grid and captures fine-scale effects through basis functions MS41 computed numerically by solving local Stokes-Brinkman Outflow Boundary Conditions in Porous Media flow problems on the underlying fine-scale grid. Flow Equations Knut-Andreas Lie To model the flow in porous media one typically uses ei- SINTEF ICT, Dept. Applied Mathematics ther the Richards equation if the flow can be described [email protected] effectively by one phase, or the two-phase flow equations if two phases must be modeled. Due to the wide range Astrid Fossum Gulbransen of applications, the interest in these two systems is enor- SINTEF ICT mous. Rigorous analytical results became available in the Dept. Applied Mathematics 80ies, when strong nonlinearities in time-dependent prob- [email protected] lems were treated systematically. In most contributions on the subject, the analysis is simplified by restricting to Dirichlet boundary conditions, even though a physically MS40 more appropriate boundary condition is the outflow con- Upscaling Inertia Effects in Flow dition. After motivating and explaining this condition we present the corresponding qualitative analytical problems, We discuss upscaling of inertia effects in heterogeneous a regularization technique and existence results. porous media. From lab scale to reservoir scale we consider non-Darcy flow model; we present recent analytical Ben Schweizer and numerical results extending work with C. Garibotti. TU Dortmund A separate project with Trykozko is on upscaling from Fakultät für Mathematik porescale to lab scale. Connecting these scales, explain- [email protected] 92 GS09 Abstracts

MS41 Pavia, Italy Non-linear Interface Models for Multi-phase Flow [email protected] Problems in Heterogeneous Media

We consider two extensions to standard capillary pressure MS42 relationships for two phase problems. Firstly, to correct Monotone Finite Volume Discretization of the non-physical behavior, we use a recently established the Convection-Diffusion Equation on Polyhedral saturation-dependent retardation term. Secondly, in the Meshes case of heterogeneous porous media, we apply a model with a capillary threshold pressure that controls the penetration We consider the cell-centered finite volume discretization process. Mathematically, we rewrite this model as inequal- of the steady convection-diffusion equation. The diffusion ity with possible discontinuities in the saturation and pres- tensor may be full and anisotropic and the operator may sure at the interfaces. Numerical examples in 2D and 3D have the dominated convection part. The computational show the influence of the modifications. mesh (conformal or non-conformal) is assumed to consist of convex polyhedral cells. The proposed finite volume Barbara Wohlmuth method is monotone, i.e. it preserves non-negativity of Universität Stuttgart the differential solution. Monotonicity of the method is IANS provided by nonlinear two-point diffusion and advection [email protected] fluxes derived on faces of mesh cells. The method is the 3D extension of the 2D finite volume discretization [1]. 1.Lip- Rainer Helmig nikov K., Svyatskiy D., Vassilevski Yu. Interpolation-free IWS monotone finite volume method for diffusion equations on [email protected] polygonal meshes.J.Comp.Phys., 2008 Kirill Nikitin Alexander Weiss Institute of Numerical Mathematics IANS RAS, Moscow, Russia [email protected] [email protected]

MS42 Alexander Danilov, Yuri Vassilevski Monotonicity for Multi Point Flux Approximation Institute of Numerical Mathematics Methods on Triangular Grids Russian Academy of Sciences [email protected], [email protected] We study the monotonicity behaviour of MPFA methods on triangular grid. For single phase flow, we find sufficient conditions for the MPFA O- and L-methods. The found MS42 monotonicity regions for the methods are also tested nu- Nonlinear Finite Volume Methods for Convection- merically. The tests are done for cases corresponding to Diffusion Problems on Unstructured Polygonal both homogeneous and heterogeneous media. We also in- Meshes vestigate the robustness of the methods with respect to monotonicity for two-phase flow. The results obtained in Predictive numerical simulations of subsurface processes this work may be utilised in grid generation. require not only more sophisticated physical models but also more accurate and reliable discretization methods. Eirik Keilegavlen The discretization methods used in existing simulations fail University of Bergen, Norway to preserve positivity of a continuum solution of the elliptic [email protected] equation when the media is anisotropic and heterogeneous and/or the mesh is strongly perturbed. We present the Ivar Aavatsmark nonlinear finite volume approach that guarantees positiv- Center for Integrated Petroleum Research ity of the discrete solution on unstructured meshes and University of Bergen for strongly anisotropic diffusion tensors. Recently several [email protected] variations of this approach have been proposed. We compare their numerical and computational properties.

MS42 Daniil Svyatskiy, Konstantin Lipnikov Los Alamos National Laboratory A Finite Volume Method for Solving the Steady [email protected], [email protected] Convection-Diﬀusion Equation

We discuss a cell-centered finite volume method to approx- Yuri Vassilevski imate the steady convection-diffusion equation on meshes Institute of Numerical Mathematics of triangles and tetrahedra. The method is second-order Russian Academy of Sciences accurate through a piecewise linear reconstruction within [email protected] each cell and at mesh vertices. A non-linear definition of the face gradients for the numerical diffusive fluxes allows us to demonstrate the existence of a Maximum Principle. MS43 We also consider a reformulation for meshes of convex poly- Atmospheric Simulation Using High Order Meth- gons of any shape, and the connection with the DDFV ods on Locally Adapted Unstructed Parallel Grids method and the MFD method. We address the issue of simulating atmospheric motion Gianmarco Manzini in 2d using a high order conservative scheme (DG) on Istituto di Matematica Applicata e Tecnologie unstructured, locally adaptive grids. Testcases include Informatiche classical mountain overflow problems and warm non- GS09 Abstracts 93

precipitating cloud model with 3 components of air. The MS43 latter being an intermediate step towards an implementa- A 2d Discontinuous Galerkin Model for the (Non)- tion of a simplified COSMO model using high order, con- hydrostatic Atmosphere servative scheme. The advantage of such an approach is in effective resolving of the impact of orography and dealing The vertical structure of the averaged free atmosphere is with boundary problems in more natural manner. dominated by the hydrostatic balance. Large scale waves, with horizontal spatial scales larger than 10km, are present Slavko Brdar in a non-hydrostatic model and develop similar for hydro- Abteilung für Angewandte Mathematik, Universität static equations. In the hydrostatic case, phenomena of Freiburg smaller scales either destroy the balance or do not give Hermann-Herder-Str.10, D-79104 Freiburg i. Br.,0761 203 correct wave speeds and dispersion properties. Wave prop- 5641 agation will be studied within a hydrostatic and a non- [email protected] hydrostatic 2-dimensional model. Both models are discretized with a high order discontinuous Galerkin method Andreas Dedner and a semi-implicit time stepping. Division of Applied Mathematics University of Freiburg, Germany Matthias Laeuter [email protected] Alfred Wegener Institute for Polar and Marine Research [email protected] Michael Baldauf Deutscher Wetterdienst Francis X. Giraldo [email protected] Associate Professor of Applied Mathematics NPS [email protected]

MS43 Marco Restelli High-Order Semi-implicit Time-integrators for the Max-Planck-Institut für Meteorologie Euler and Navier-Stokes Equations Hamburg, Germany [email protected] In this work, we describe the construction of high-order accurate in time semi-implicit methods for the Euler and Dörthe Handorf, Klaus Dethloff Navier-Stokes equations used in mesoscale nonhydrostatic Alfred Wegener Institute atmospheric modeling. The goal of this research is to com- [email protected], klaus.dethloff@awi.de pare and contrast various forms of the governing equations (e.g., should one use Exner or density for the mass and should one choose potential temperature, density potential MS43 temperature, or total energy). The form of the continuous New Grids for Flow on the Sphere governing equations used in the models can restrict one to only certain classes of time-integration methods (e.g., The logically rectangular finite volume grids for two- if the equations are in flux form, then it is not possible dimensional PDEs on the sphere and for three-dimensional to use classical semi-Lagrangian methods). In addition, problems in a spherical shell introduced in [SIAM Review some forms of the governing equations can be more expen- 50(2008) pp. 723-752] have nearly uniform cell size, avoid- sive to solve computationally than other forms. Another ing severe Courant number restrictions. We present recent topic of discussion concerns the inclusion of adaptive time- results with adaptive mesh refinement using the GeoClaw stepping machinery into these models. While not impor- software and demonstrate well-balanced methods that ex- tant to the outline of the talk, for the moment we are as- actly maintain equilibrium solutions, such as shallow water suming that an element-based continuous Galerkin method equations for an ocean at rest over arbitrary bathymetry is used for approximating the spatial derivatives. In the fu- or a stratified atmosphere in three dimensions. ture, discontinuous Galerkin methods will be included into this generalized approach. We will describe the challenges Randall J. LeVeque facing us with discontinuous Galerkin methods and how Applied Mathematics to implement them in conjunction with semi-implicit time- University of Washington (Seattle) integrators. [email protected]

Frank Giraldo Christiane Helzel Naval Postgraduate School, Department of Applied Ruhr-Universitaet Bochum Mathematics Germany 833 Dyer Road, Bldg. 232, Spanagel 262, Monterey, CA [email protected] 93943-5 [email protected] Donna Calhoun Commisariat a l’Energie Atomique Marco Restelli Paris Max-Planck Institute [email protected] Hamburg Germany [email protected] Marsha Berger Courant Institute of Mathematical Sciences Matthias Laeuter New York University Alfred-Wegener Institute [email protected] [email protected] 94 GS09 Abstracts

MS44 els. We will present results of investigations into time cy- Approaches to Coupled Land-energy Flux Model- cling and operator splitting methods for a coupled model ing including the ParFlow variably saturated subsurface flow code, the CLM land surface flow code, and the WRF atmo- We will discuss benefits and associated difficulties of con- spheric simulation code. This work performed under the structing coupled models to simulate interactions of the auspices of the U.S. Department of Energy by Lawrence groundwater-landsurface-atmosphere system. These mod- Livermore National Laboratory under Contract DE-AC52- els potentially provide understanding of two-way feedbacks 07NA27344. This work was supported by the LLNL Cli- and are, thus, a promising tool for process understanding mate Change Initiative. LLNL-ABS-409527. and prognosis. However, related physical processes cannot be described fully using first-principles approaches leading Carol S. Woodward to parameterizations that are intrinsically tied to partic- Lawrence Livermore Nat’l Lab ular spatiotemporal scales. Therefore, understanding of [email protected] process scalability is an important component in coupled model construction requiring careful consideration. Reed M. Maxwell Department of Geology and Geologic Engineering Stefan Kollet Colorado School of Mines Meteorological Institute [email protected] University of Bonn [email protected] Steven Smith, Julie Lundquist, Jeff Mirocha Lawrence Livermore National Laboratory MS44 [email protected], [email protected], [email protected] Introduction to the Minisymposium: Coupled Ap- proaches to Groundwater-atmospheric Modeling MS45 The linkage between groundwater and the lower atmo- Initiating Large Slope Movements by Rain-induced sphere occurs via shallow soil moisture and energy trans- Shear Bands port processes. Complex, coupled nonlinear physiochemi- Against the background of the global climate change, the cal processes and a wide range of spatiotemporal scales ne- computer aided prediction of landslides induced by heavy cessitates numerical simulation of these interactions. These rain events is of increasing importance in order to protect computationally challenging solutions must utilize efficient life and property in alpine regions. This makes it necessary algorithms and preconditioners resulting in a balance of to accurately model the complex inelastic deformation be- stability, efficiency and accuracy. This talk will introduce haviour of partially or fully saturated soil on the basis of these issues and demonstrate some numerical approaches sophisticated multi-phase continuum theories. In this re- to bridging these two systems. gard, we present a triphasic porous media model capable Reed M. Maxwell of describing all prominent hydraulic and solid mechani- Department of Geology and Geologic Engineering cal effects triggering the evolution of shear zones towards Colorado School of Mines complete slope failure. [email protected] Wolfgang Ehlers Institute for Mechanics MS44 University of Stuttgart [email protected] Surface-groundwater Flow Coupling Based on Boundary Condition Switching Bernd Markert, Ocan Avci We develop a model of surface-groundwater flow based on University of Stuttgart boundary condition switching between surface-subsurface [email protected], domains. The model is shown to be able to reproduce [email protected] relevant processes at different spatial and temporal scales. Explicit finite differences for surface routing and implicit finite elements for Richards equation allow for different MS45 time-stepping strategies to capture different time scales. A Double Continuum Approach for Two-phase Model performance is analyzed numerically on sample and Flow Simulation in Natural Slopes real-world test cases and theoretically within the context of domain decomposition methods. The fast infiltration of heavy rainfalls in macro-porous soils is one of the key processes which triggers the movement Mario Putti of natural slopes as it leads to a ’fast’ pressure increase Dept. Mathematical Methods and Models for Applied as well as to a fast saturation of a hillslope. The macro- Scieneces porous medium is characterized by a complex channel-like University of Padua network which cannot be discretely taken into account. To [email protected] simulate flow processes in such media, a double-continuum model concept for two-phase flow has been developed and should be presented showing results of plausibility tests MS44 as well as of a field experiment. Special emphasis is put Strategies for Coupling Subsurface Flow, Land Sur- on the exchange parameters which are determined from face, and Atmospheric Models laboratory experiments.

Fully coupled bedrock to atmosphere models require a Reinhard Hinkelmann strategy for time stepping and passing information be- TU Berlin tween the subsurface, land surface, and atmospheric mod- [email protected] GS09 Abstracts 95

Leopold Stadler part of the GE has access to a number of supercomput- TU Berlin, Germany ers located in the Nordic countries Denmark, Finland and [email protected] Norway. Storage and data-evaluation is provided by the Norway and partners in UK and Ireland. The infrastruc- Rainer Helmig ture is based on the middlewares ARC (Nordugrid) and IWS, University of Stuttgart, Germany DiGS (EPCC). It supports the simultaneous execution of Institut fur Wasserbau various instances of massively parallel simulations and the [email protected] subsequent evaluation of the generated data. The currently supported software is MUFTE-UG, a simulation platform Erwin Zehe for Multi-Phase-Multi-Component flow simulations. Simu- TU München lated time-series are stored in XML-annotated sets of files [email protected] and statistical investigations can be carried out on the base of the complex meta-data. The capability of the environment will be illustrated by selected models. MS45 Klaus Johannsen Theoretical and Experimental Aspects on Trigger- Bergen Center for Computational Science ing Rapid Mass Movements of the Flow-Type [email protected] Many of the world’s most devastating landslide disasters can be attributed to landslides of flow type involving non MS46 cohesive soils. The flow-type characteristics of the post- failure stage are linked to the initial acceleration of the Numerical Schemes with Low Dissipation for Mod- failed mass, determined by the soils’ mechanical instabil- elling Contaminant Transport in Porous Media on ity. In the presentation, experimental evidences of partially Simplicial Meshes saturated non cohesive soils leading to flow-type behaviour We present two numerical schemes with low dissipation for are illustrated and interpreted within a geomechanical con- modeling contaminant transport in porous media. Both ceptual framework. schemes use operator splitting and cell-centered finite vol- Giuseppe Sorbino ume paradigm. However, the schemes differ in the con- Professor, University of Salerno, italy struction of the diffusive flux and the advection substeps. [email protected] Also, the schemes are derived for different classes of 3D dynamic meshes, i.e. conformal tetrahedral and non- conformal hexahedral (octrees). We present the basic prop- Cristina Jommi erties of the schemes such as order of convergence, mono- Politecnico di Milano, Italy tonicity, computational efficiency, and compare them on [email protected] the solution of several test problems.

Ivan Kapyrin, Yuri Vassilevski, Kirill Nikitin MS45 Russian Academy of Sciences Internal Erosion in Soils: A Multi-phase Model on [email protected], [email protected], kir- Multiple Scales [email protected] Internal erosion, i.e. the debonding and movement of fines through the porous soil by hydraulic forces, could affect MS46 the mechanical and hydraulical stability of geostructures High Performance Simulation of CO2 Geological dramatically. Internal erosion is causative for many natu- Storage ral and technical disasters in connection with flood events and collapse-like slope failures where small triggers lead The objective of the French ANR project SHPCO2 is to de- to a liquefaction of the soil. To simulate internal erosion velop and study advanced numerical methods for the simu- processes, we propose a mixture theory-based multi-phase lation of CO2 reactive transport on massively parallel com- model which we compare with laboratory experiments. puters. We have identified four challenging subjects that we will discuss during the session. 1. Coupling multiphase Holger Steeb flow and reactive transport models. 2. Reactive transport Assistant Professor, U Twente, The Netherlands nonlinear solvers. 3. Time space domain decomposition Professor, U Bochum, Germany and local time stepping. 4. Dynamic load balancing for a [email protected] multi-physics and multi-domain application.

Stefan Diebels Anthony Michel Saarland University IFP [email protected] [email protected]

Michel Kern MS46 INRIA Computing Geological Storage of CO2: A Grid En- [email protected] vironment for Massively Parallel Simulation, Stor- age and Statistics Laurence halpern In this presentation we describe a grid environment Universit´e Paris 13 (GE) for massively parallel simulations related CO2- [email protected] sequestration in deep aquifers. In addition to the compute functionality, the environment provides data-storage facili- Jean Marc Gratien ties and tools for statistical data-exploration. The compute IFP 96 GS09 Abstracts

[email protected] and parallel (Additive Schwarz with coarse space correction) linear solvers for large-scale heterogeneous problems. Pascal Audigane Moreover, they possess the same advantages of other mul- BRGM tiscale techniques, but without the need of constructing a [email protected] coarse mesh, and they are well-suited for adaptive algebraic coarsening. Jacques Moutte Olivier Dubois ENSMSE IMA [email protected] [email protected]

MS46 Ilya D. Mishev Modelling the Transport of Particulate Suspen- ExxonMobil Upstream Research Company sions and Formation Damage During the Deep In- Department Technical Software Development jection of Supercritical Carbon Dioxide in Sand- [email protected] stone Formations Ludmil Zikatanov Prediction of CO2 injection performance in deep subsurface Department of Mathematics, aquifers and reservoirs rely on the well ability to maintain PennState University high flow rates of carbon dioxide during several decades [email protected] without significantly impairing the host formation. Dy- namics of solid particulate suspensions in permeable media are recognized as one major factor leading to injection well MS47 plugging in sandstones. The invading supercritical liquid- A Multiscale Finite Volume Method for Unsteady like fluid can contain variable concentrations of exogenous Stokes-Darcy Equations fine suspensions or endogenous particles generated in situ by colloidal or hydrodynamic release mechanisms. Sus- The talk focuses on the application of the iterative- pended solids can plug the pores leading to possible forma- multiscale-finite-volume (IMSFV) procedure to the Stokes- tion damage and permeability reduction in the vicinity of Darcy system, describing flow in porous media. The stan- the injector. As such, models which can predict well injec- dard IMSFV method is extended for solving the momen- tivity decline, are useful in the operations of planning, de- tum and pressure correction equations in a fractional time sign, and maintenance, related to carbon dioxide injection. stepping algorithm framework. The multiscale method al- In this study we developed a finite element based simula- lows to simulate flow and transport in porous media with tor to predict the injectivity decline nearby CO2 injection geometries that can be too complicated to be resolved by wells and also for production wells in the context of EOR. a feasible computational grid. The coarse scale ensures The numerical model solves implicitly a system of two cou- global coupling and the fine scale ensures appropriate res- pled sets of finite element equations corresponding to the olution. The method is illustrated with examples and is pressure-saturation two-phase flow, then a system of so- compared with fine scale solutions. lute and particles convection-diffusion equations. Particle equations are subject to mechanistic rate laws of colloidal, Oleg Iliev, Z. Lakdawala hydrodynamic release from pores bodies, blocking in pores Fraunhofer Institute for Industrial Mathematics bodies and pores throats, and interphase particles trans- Germany fer. The model was validated against available laboratory [email protected], [email protected] experiments at the core scale. At the field scale, challenges still exist for an accurate assessment of the permeability G Bonfigili change due to limited current knowledge of Supercritical Institute of Fluid Dynamics CO2 and water phases micro-interactions at pore surfaces, Switzerland but also to the multiscale nature of the numerical problem. bonfi[email protected] Numerical demonstration examples in a saline sandstone aquifer reveal that formation damage during CO2 injection Patrick Jenny will primarily depend on the injected particles wettability, Institute of Fluid Dynamics the injection flow rate, and the medium tortuosity. Other ETH Zurich simulation examples are provided for a CO2 injection in [email protected] a five spots pattern EOR oil field for performance assessment of the production with occurence of in-situ sanding in a poorly consolidated sandstone reservoir. MS47 A Multilevel Multiscale Mimetic (M 3) Method for Adil Sbai, Mohamed Azaroual Two-Phase Flows in Porous Media BRGM [email protected], [email protected] The M3 method builds recursively a problem-dependent multilevel hierarchy of models for flow in porous media. Each model is locally mass conservative. The method MS47 supports full diffusion tensors on unstructured polyhedral Using Energy Minimizing Basis Functions as a meshes and accommodates general coarsening strategies. Multiscale Method, With Applications to Multi- We describe well modeling and adaptive strategies for up- grid and Domain Decomposition Solvers dating the multilevel hierarchy. Numerical simulations for permeability fields with long correlation lengths show that We demonstrate the applicability of energy minimizing ba- even with large coarsening factors, 50 and more in each co- sis functions for two-phase flow simulations, and we high- ordinate direction, the multiscale solution remains within light their numerous benefits. We show how they can be implemented to obtain efficient serial (algebraic multigrid) GS09 Abstracts 97

5% of the fine-scale solution. Sci. Univ Colorado Denver [email protected] Konstantin Lipnikov Los Alamos National Laboratory Tiziana Giorgi [email protected] Department of Mathematics New Mexico State University David Moulton [email protected] Los Alamos National Laboratory Applied Mathematics and Plasma Physics [email protected] MS48 Multiscale Adaptive Modeling of Inertia and Non- Daniil Svyatskiy equilibrium Processes Los Alamos National Laboratory [email protected] New experimental and modeling techniques make possible to identify and quantify inertia, dynamic effects, and non-equilibrium processes that until recently by necessity MS47 were deemed next-order or lower-scale only. The new terms Multilevel Solvers and Upscaling Via Explicit En- and couplings that arise bring challenges for analysis and ergy Minimisation numerical modeling. We are concerned with how to determine their significance adaptively the way one handles grid In this talk we highlight the strong link between robust adaptivity. The talk will be partly based on joint research multilevel iterative solvers and upscaling/multiscale tech- with Showalter and Klein. niques for subsurface flow. Motivated by recent theoretical results for two-level overlapping Schwarz domain decom- Malgorzata Peszynska position methods, we investigate the construction of up- Department of Mathematics scaling techniques based on energy minimisation. These Oregon State University include the Multiscale Finite Element Method as a special [email protected] case, but in contrast to MsFEs do not require any artificial boundary conditions on coarse elements. We present and analyse a preconditioner for the arising constrained MS48 minimisation problem, that is robust to mesh refinement Two-scale Pore Network Modeling for Multiphase and arbitrary coefficient variation (requiring no scale sep- Flow in Heterogeneous Geometries aration). The resulting method is O(h−d) where h is the Most of the transport phenomena of interest in subsurface subgrid size. flow modeling occur on multiple scales, and the complex Robert Scheichl subsurface pore spaces geometry on micro scale is notorious Department of Mathematical Sciences for dictating macroscopic flow of interest. We present an al- University of Bath gorithm to geometrically match pore throat networks from [email protected] two separate scales (that can either originate from available measurements or be constructed according to generally ac- cepted knowledge) and show preliminary results for flow in Ivan G. Graham networks based on realistic carbonate geometry. University of Bath [email protected] Masa Prodanovic University of Texas at Austin Jan Van Lent Center for Petroleum and Geosystems Engineering Department of Mathematical Sciences [email protected] University of Bath [email protected] Adrian Sheppard Australian National University Ludmil Zikatanov Department of Applied Mathematics Pennsylvania State University [email protected] [email protected]

MS48 MS48 Experimental Analysis of Non-equilibrium Pro- Generalized Forchheimer Equation for Two-phase cesses for Multiphase Flow in Porous Media Flow Based on Hybrid Mixture Theory The effect of flow rate on interfacial configurations We discuss the derivation of a Forchheimer-type equation in porous media was investigated using computed x- for two-phase flow through an isotropic porous medium us- ray microtomography and image analysis. One full ing hybrid mixture theory. Hybrid mixture theory consists drainage/imbibition cycle was measured and subse- of upscaling field (conservation) equations by averaging, quently residual configurations were assessed following and then exploiting the entropy inequality to obtain consti- drainage/imbibition at flow rates varying over an order of tutive equations. Isotropic function theory is then used to magnitude. Results indicate that both flow rate and sys- simplify the equation for application to an isotropic porous tem history are important, especially for the imbibition medium. As time permits, we will discuss the extension of process. this theory to multiphase swelling materials. Dorthe Wildenschild Lynn Bennethum Oregon State University Dept Mathematical and Stat [email protected] 98 GS09 Abstracts

MS49 reactive solute transport in porous media. The transport Analysis of Numerical Methods for Coupling is modelled by a convection-diffusion-reaction equation, in- Transport Andgeochemistry Equations cluding equilibrium sorption. We especially considered the case of a Freundlich type isotherm, when the equation be- Reactive transport equations involve PDE for advection- comes degenerate. The algorithmic aspects of our scheme diffusion, algebraic equations for chemistry at equilibrium are presented in [F. A. Radu, M. Bause, A. Prechtel and S. and ODE for kinetic chemistry. Classical methods are Attinger, Analysis of an Euler implicit - mixed finite ele- based on a method of lines where spatial discretization is ment scheme for reactive solute transport in porous media, followed by temporal discretization. We analyze here the Numerical Mathematics and Advanced Applications, K. numerical properties and convergence of four such meth- Kunisch, G. Of and O. Steinbach (editors), Springer Ver- ods, namely SNIA, SIA, DSA and DAE. We illustrate the lag, 2008, pp. 513-520.] and the analysis of the discretiza- comparison by some numerical examples. tion error in [F. A. Radu, I. S. Pop and S. Attinger, Anal- ysis of an Euler implicit - mixed finite element scheme for Jocelyne Erhel reactive solute transport in porous media, Numerical meth- INRIA-Rennes, France ods for partial differential equations, 2008, to appear.]. We [email protected] focus here on the applicability of the Newton method on solving the nonlinear problems arising at each time step. Caroline de Dieuleveult For the degenerate case a regularization step is necessary. ANDRA An explicit condition for the quadratic convergence of the INRIA Rennes Newton method in terms of the discretization parameters caroline.de [email protected] and the regularization number is derived. Florin A. Radu MS49 UFZ-Helmholtz Center for Environmental Research, Efficient Solution of Large Reactive-Transport Leipzig Problems Including Mineral Reactions Germany fl[email protected] The global-implicit approach applied to large multicomponent reactive transport problems in general leads to large Iuliu Sorin Pop nonlinear systems. A method is proposed to reduce the size Dept of Mathematics and Computer Science of the system using equivalence reformulations, leading to TU Eindhoven an elimination or a decoupling of many of the unknowns. [email protected] If precipitations/dissolution reactions are involved, a formulation is given which can be solved by the semismooth Newton method. Numerical results of the proposed algo- MS50 rithms are presented. Balance-Preserving Finite Element Methods on Unstructured Meshes Serge Kraeutle Institute for Applied Mathematics The dynamical equations of motion for the atmosphere University of Erlangen-Nuremberg and ocean support oscillations a vast range of spatial and [email protected] temporal scales. However, large-scale flows in the atmosphere and ocean remain in a state of slow evolution called geostrophic balance in which fast oscillations are MS49 very weak; these slowly-evolving dynamical states repre- Adaptive, Selective Coupling of Multicomponent sent our weather and the global circulation patterns. To Transport and Kinetic Reactions make predictions on these timescales, special care must be taken to design numerical methods which reflect the prop- The efficiency of the process-preserving, globally implicit erties of this underlying balance. Recently there has been approach to solve reactive multicomponent transport prob- much interest in modelling the atmosphere and ocean on lems with Newton’s method can be enhanced by modifiy- adaptive unstructured meshes; this calls for new discretisa- ing the Jacobian. Therefore the reaction network, which tion methods which reflect geostrophic balance. We intro- defines the connectivity pattern of the system matrix, is duce a new family of mixed finite element methods which analysed to neglect terms whith the aim to decouple species provide the best possible representation of geostrophic bal- equations on the level of the linear solver without deteri- ance on unstructured meshes. The proofs of these proper- orating the quadratic performance of the global, process- ties are very simple since they are based on underlying ge- preserving iteration. The fully adaptive algorithm can be ometric structure: the discretisations have exact sequences used potentially in every time step, and works with direct which mimic the div-curl and curl-grad relations of vector as well as iterative linear solvers for reactions of kinetic analysis. type in arbitrary dimensions. Colin Cotter, David Ham Alexander Prechtel Imperial College Mathematics Department [email protected]., [email protected] University of Erlangen-Nuremberg, Germany [email protected] Sebastian Reich Universität Potsdam MS49 [email protected] Mixed Finite Elements and Newton Method for Reactive Solute Transport in Porous Media Christopher Pain Imperial College We present a mass conservative finite element scheme for [email protected] GS09 Abstracts 99

MS50 tended to the case of distorted hexagons and pentagons Discretised Poisson and Nambu Brackets in the (indeed, any polygonal voronoi grid), ensuring both satis- Context of an Atmospheric General Circulation factory Rossby wave propagation and energy conservation. Model Some sample numerical results will be shown.

We want to establish a coupled atmosphere and ocean John Thuburn model for climate simulations and numerical weather pre- School of Engineering, Computing and Mathematics diction. As model properties are foreseen (i) conservation Harrison Building, University of Exeter, North Park of mass, (ii) conservation of tracer mass and its consis- Road, EX tency with the continuity equation, (iii) conservation of [email protected] energy and a vortex quantity; all to be achieved on triangular/hexagonal meshes. Exploring the algebraic structure of Todd Ringler ﬂuid equations in Poisson/Nambu bracket form facilitates Los Alamos National Laboratory to obey these properties in the numerical realization. [email protected]

Almut Gassmann Bill Skamarock, Joe Klemp Max Planck Institute for Meteorology UCAR [email protected] [email protected], [email protected]

MS50 MS51 Hamiltonian Particle-mesh Simulations for a Non- Coupling of Ground and Surface Water hydrostatic Vertical Slice Model We solve the coupling of Richards equation in hetero- We develop a non-hydrostatic vertical slice model in the geneous soil with non-moving surface water or depth- context of the Hamiltonian Particle-Mesh Method (HPM) averaged shallow water equations. The Richards equation for the dry adiabatic atmosphere. The slice model is tested is treated without linearization by Kirchhoff transforma- with the bubble-experiments described in Robért (1992) tion, convex minimization and monotone multigrid meth- and the gravity wave experiment in Skamarock and Klemp ods in homogeneous soil and non-overlapping domain de- (1994). The solutions are maintained smooth largely due composition methods to address heterogeneity. Gravity is to a ”regularization” in the absence of the artificial diffu- included by upwinding. The coupling is provided by hy- sion. The regularization is implemented in harmony with a drostatic pressure and mass conservation leading to fixed conservative force field and does not interfere with the hy- point problems by different time scales for ground and sur- drostatically balanced reference state. The accuracy of the face water. HPM simulation is comparable to those in these references and the model performances show that the HPM method is Heiko Berninger, Ralf Kornhuber, Oliver Sander, potentially applicable to non-hydrostatic atmospheric flow Christian Grümme regimes. FU Berlin Fachbereich Mathematik und Informatik Seoleun Shin [email protected] Institute for Mathematics, University of Potsdam berlin.de, [email protected], [email protected] Am Neuen Palais 10, 14469 Potsdam, Germany berlin.de, [email protected] [email protected]

Sebastian Reich MS51 Universit¨at Potsdam Discontinuous Galerkin Methods for Coupling [email protected] Depth-integrated Shallow Water Models with Richards Equation

MS50 We describe a discontinuous Galerkin method for coupling Conservation and Wave Propagation on Hexagonal shallow water flow and unsaturated ground water flow. and Geodesic C-grids The local discontinuous Galerkin method is used to approximate both the shallow water equations and Richards’ A ‘geodesic’ grid, comprising hexagonal and pentagonal equation describing flow in the vadose zone. Coupling be- cells, is attractive for global atmospheric modelling between the two models is done weakly. Error estimates and cause it gives a nearly uniform and isotropic coverage of the numerical results are presented. sphere, avoiding the pole problems of a latitude-longitude grid. A C-grid staggering, in which the mass variable is Clint Dawson stored in cells and normal velocity components are stored Institute for Computational Engineering and Sciences at cell edges, is also considered attractive because it gives University of Texas at Austin a relatively good representation of fast waves and hence [email protected] the geostrophic adjustment process. However, early studies of wave propagation for the shallow water equations on a regular hexagonal C-grid showed spurious large frequen- MS51 cies for near-grid-scale Rossby waves - a serious obstacle to Hierarchic Modelling of Free Surface Shallow Wa- the use of such a scheme for global atmospheric modelling. ter Flow We show here that these spurious large frequencies can be avoided by a suitable discretization of the Coriolis terms. A Abstract not available at time of publication. geodesic grid comprises somewhat distorted hexagons and also pentagons. By careful consideration of the discrete Andreas Dedner vorticity budget, the regular hexagonal grid scheme is ex- Division of Applied Mathematics 100 GS09 Abstracts

University of Freiburg, Germany media are discussed. [email protected] Ivan Lunati Ecole Polytechnique Fédérale de Lausanne MS51 ivan.lunati@epfl.ch Mass Conservative DG/FV Schemes for Coupling the Richards Equation with Surface Flows MS52 We propose and analyze numerical schemes to couple sub- Detailed Pore Scale Fluid Displacement Modeling surface and overland flows. The governing equations are Via the Level Set Method Richards’s equation in the subsurface, the kinematic wave equation on the surface, and the matching of pressure and An accurate description of pore level immiscible fluid dis- normal velocity at the interface. Space-time discretiza- placement could significantly improve macroscopic param- tion uses Discontinuous Galerkin/Finite Volume schemes eter predictions in real porous media. We present a simple combined with a multi-step implicit scheme in the subsur- but robust quasi-static displacement model for drainage face. Multi-step coupling algorithms are proposed to en- and imbibition based on the level set method that results sure overall mass conservation. Numerical results illustrate in geometrically and topologically correct interfaces, and the performances of the proposed algorithms. is independent of the pore space complexity. Many applications include investigating fracture matrix transfer, and Alexandre Ern, Serge Piperno, Pierre Sochala coupling with sediment mechanics. The code, LSMPQS, is Universite Paris-Est publicly available. CERMICS, Ecole des Ponts [email protected], [email protected], Masa Prodanovic [email protected] University of Texas at Austin Center for Petroleum and Geosystems Engineering [email protected] MS52 Tomographic Analysis of Reactive Fluid Induced Steven L. Bryant Pore Structure Changes Petroleum and Geosystems Engineering Department University of Texas at Austin We have employed synchrotron microtomography with steven [email protected] flow-column experiments to capture and quantify snapshots in time of dissolution and secondary precipitation changes in the microstructure of sediments exposed to sim- MS52 ulated caustic waste. Dissolution induced changes included Pore Scale Modeling of Moving Crystal-fluid Inter- an increase in the number of larger pores. Precipitation in- faces Using Level Sets and Phase Field Models duced changes included reduction in the number of small pores and closure of small throats, with accompanying re- We present level-set and phase-field formulations of crys- duction in pore coordination numbers and reduction in the tal dissolution/precipitation processes on the pore scale. number of pore pathways. These formulations are then compared to each other and used to simulate the evolution of crystalline solid-fluid in- W. Brent Lindquist terfaces inside a pore. Furthermore we will briefly dis- State University of New York, Stony Brook cuss how these formulations can be used to upscale disso- [email protected] lution/precipitation processes to the Darcy scale.

Rong Cai Tycho L. van Noorden Stony Brook University Department of Mathematics & Computer Science [email protected] TU Eindhoven [email protected] Wooyong Um Paciﬁc Northwest National Lab. MS53 [email protected] Simulation of Core-Scale Multiphase Flow Experi- ments with CO2 and Brine Keith Jones Brookhaven National Lab Abstract not available at time of publication. [email protected] Sally Benson Energy Resources Engineering MS52 Stanford University Interfacial Energy, Surface Tension and Contact [email protected] Angle

Capillary phenomena can be equivalently described in MS53 terms of surface energies necessary to create the interfaces, Numerical Simulation of Key Mechanisms of CO2 or in terms of surface tensions that tend to contract the Sequestration in Stanford General Purpose Re- interfaces. We discuss the issues arising in presence of a search Simulator solid phase and the tension balance at the triple contact line, including the component perpendicular to the solid We present the capabilities of Stanford’s General Purpose when Youngs law applies. Also implications for porous Research Simulator (GPRS) to simulate CO2 sequestration problems. The key known mechanisms, including hystere- sis, diﬀusion and dispersion, and chemical equilibria have GS09 Abstracts 101

been incorporated in GPRS. Comparison between GPRS piecewise linear constraints. Our approach addresses reser- and other simulators show close agreement and competitive voir modeling challenges associated with accurate model- eﬃciency for non-mineralization cases. A CO2 mineraliza- ing of complex reservoir geometry and heterogeneous reser- tion case in the Johansen formation is presented, where we voir properties. Together with an accurate scale-up of ﬁne- demonstrate that the amount of mineralized CO2 depends scale geologic properties, our gridding approach improves strongly on the in-situ mineral composition. the consistency between geologic descriptions and reservoir simulation models, leading to more accurate simulation re- Yaqing Fan sults. Energy Resources Engineering Stanford University L Branets [email protected] ExxonMobil Houston Louis J. Durlofsky [email protected] Department of Energy Resources Engineering Stanford University Sartaj Ghai [email protected] ExxonMobil Upstream Research Company [email protected] Hamdi Tchelepi Petroleum Engineering Department Stephen L. Lyons Stanford University ExxonMobil Upstream Research Company [email protected] P.O. Box 2189 [email protected]

MS53 Xiao-Hui Wu Two-phase Flow in Deformable Porous Media: Ap- ExxonMobil Upstream Research Company plication to CO2 Storage [email protected] Recently, CO2 sequestration as concluding long-term stage of closed Carbon Dioxide Capture and Storage (CCS) pro- MS54 cesses considered for reducing carbon dioxide emissions A New Multiscale Approach for the Simulation of into the atmosphere is subject of worldwide intensive in- Multiphase Flow Processes in Porous Media vestigations. To take into account all the relevant phenomena during spreading and storage of the injected CO2 The contamination of the unsaturated zone with a light in the subsurface (flow and transport of multiple phases, non-aqueous phase liquid is studied, corresponding to a rock deformation, non-isothermal conditions, geochemical domain with randomly distributed heterogeneities where reactions) physically founded complex mathematical mod- complex three-phasethree-component processes are rele- els are required. The multiple coupled problems cannot be vant only in a small(local) subdomain. This subdomain solved analytically. Rather, sophisticated numerical meth- needs fine resolution as the complex processes are governed ods have to be applied. by small-scale effects. For a comprehensive fine-scale model taking into account three-phasethree-component processes Olaf Kolditz as well as heterogeneities in the whole (global) model do- Helmholtz Centre for Environmental Research main, data collection is expensive and computational time [email protected] is long. Therefore, we developed a general multi-scale concept where on the one hand, the global flow field influ- MS53 ences the local three-phasethree-component processes on the fine-scale. On the other hand, a coarse-scale satura- Modelling Physical Processes in CO2 Sequestration tion equation is solved where the effects of the fine-scale In this presentation, a series of models will be developed multi-phasemulti-component processes in the subdomain are captured by source/sink terms and the effects of fine- to describe the dispersal of CO2 plumes through a subsurface aquifer, including the effects of capillary retention, scale heterogeneities by a macrodispersion term. drainage through fault zones or leakage into a lower per- Rainer Helmig meability overlying seal rock. The models will be analysed IWS, University of Stuttgart, Germany to develop approximate similarity solutions to describe the Institut fur Wasserbau dispersal of the plume with time, and the ensuing shape [email protected] of the residual trapped CO2 as the continuing current mi- grates through the stata. Jennifer Niessner Andrew Woods Institut fuer Wasserbau (IWS) BP-Institute for Multiphase Flow Universitaet Stuttgart, Germany University of Cambridge [email protected] [email protected] Bernd Flemisch University of Stuttgart, Germany MS54 bernd.fl[email protected] Constrained Adaptive Voronoi Gridding for Reser- voir Modeling Markus Wolff, Jochen Fritz University of Stuttgart We present our recently developed techniques for adaptive Germany constrained 2.5D Voronoi grid generation based on a rigor- markus.wolff@iws.uni-stuttgart.de, [email protected] ous procedure of constructing Voronoi grid conforming to stuttgart.de 102 GS09 Abstracts

MS54 Majid Hassanizadeh Upscaling for Multiphase Flow on 3-D Adapted Utrecht University Grids [email protected]

In this talk we present a methodology for coarse-scale mod- H.K. Dahle eling of multiphase flow in 3-D channelized domains such University of Bergen, Norway as those encountered when simulating gas injection pro- [email protected] cesses. It integrates techniques for transmissibility upscaling, adaptive mesh refinement, and MPFA finite-volume discretization in order to balance accuracy, efficiency, and MS55 robustness. We focus on aspects that are specific to multi- Long Time Behavior for Dynamic Capillarity Mod- phase flow, including saturation-based adaptivity criteria, els and Relation to Hyperbolic Conservation Laws dynamic adaptation during transport, and streamline tracing. We discuss an extended BuckleyLeverett (BL) equation describing two-phase flow in porous media, including a third James V. Lambers order mixed derivatives term modeling dynamic effects in Stanford University the capillary pressure. We derive existence conditions for Department of Energy Resources Engineering traveling wave solutions, leading to admissible shocks for [email protected] the original BL equation violating the Oleinik entropy condition. This provides nonmonotone weak solutions of the Margot Gerritsen initial-boundary value problem for the BL equation con- Dept of Petroleum Engineering sisting of constant states separated by shocks, confirming Stanford University results obtained experimentally. [email protected] Cornelis J. van Duijn TU Eindhoven MS54 [email protected] Downscaling: the Inverse to Upscaling Lambertus A. Peletier Determination of conductivities from measured head-flow University of Leiden rate pairs is generally called inverse modelling. We present [email protected] two inversion methods: the Double Constraint method and Constrained Back Projection. We do so for two dis- Carlota Cuesta cretization methods: node-based finite elements and block- University of Nottingham centered finite differences. Downscaling is inverse mod- Nottingham, UK elling to determine fine-scale conductivities in coarse-scale [email protected] grid blocks. The examples show that downscaling is a practical complement to homogenization if the porous medium is not periodic. Yabin Fan, Iuliu Sorin Pop TU Eindhoven Anna Trykozko [email protected], [email protected] ICM, University of Warsaw [email protected] MS55 Getachew Mohammed Lattice Boltzmann Modeling of Macro-Porous Vrije Universiteit Brussel, Belgium Flow: Effects of Image Segmentation Algorithms [email protected] and Comparisons with Observed Data In this presentation we simulate saturated flow through Wouter Zijl macroporous soil columns (7.62x18 cm) with a lattice Vrije Universiteit Brussel, Brussels, Belgium Boltzmann model and compare results with measured sat- [email protected] urated hydraulic conductivities. Porous geometry was obtained with an industrial CT scanner yielding a resolution of 119 microns (656x656x1482 voxels) and processed with MS55 several segmentation algorithms to generate pore solid clas- Pore-network Modelling of Non-equilibrium Capil- sifications from gray-scale data. In this presentation we lary Pressure Effect will define the optimal resolution and discuss the merits of selected segmentation algorithms. Traditional two-phase flow models assume that macroscopic phase pressures difference is a function of macro- Marcel G. Schaap scopic saturation. However, under dynamic conditions, the University of Arizona difference of macroscopic phase pressures is known to be [email protected] a function of time rate of saturation change. We have developed a three-dimensional regular lattice dynamic pore- Markus Tuller network model in which we solve for the two fluid pressure 1Dept of Soil, Water and Environmental Science, fields separately. We have simulated both drainage and University of Arizona imbibitions processes for different viscosity ratios. [email protected] V. Joekar-Niasar Earth Sciences Department, Utrecht University Andrey Guber [email protected] 2U.S. Department of Agriculture [email protected] GS09 Abstracts 103

Yakov Pachepsky the transport equation. The ﬂow is numerically solved by U.S. Department of Agriculture the ﬁnite element method in the surface region whereas [email protected] it is approximated by the primal discontinuous Galerkin method of any order in the subsurface. The transport equation is solved with an improved discontinuous Galerkin MS55 method that minimizes the amount of overshoot and under- Upscaling Density-dependent Flow and the Role of shoot in the convection dominated regions. Convergence of Gravity Forces in Case of Transversal Dispersion the scheme and numerical simulations are shown.

In the talk we will discuss upscaling density-dependent Beatrice Riviere ﬂow, in particular the role gravity forces in case of transver- Rice University sal dispersion. We did some lab experiments, mathematical Houston, Texas, USA analysis and numerical computations. This is a highly in- [email protected] teresting topic, with many details not yet fully understood. Ruud Schotting MS56 Geosciences Guaranteed and Robust Discontinuous Galerkin Universtiy of Utrecht, The Netherlands a Posteriori Error Estimates for Convection- [email protected] diﬀusion-reaction Problems

We derive robust a posteriori error estimates for discon- MS56 tinuous Galerkin discretizations of stationary convection- Solute Transport in Heterogeneous Porous Media diffusion-reaction problems. The estimates do not involve any undetermined constants and can be used for actual er- Although being linear advection-dominated transport is ror control. They are based on H(div)-conforming diffusive a notoriously difficult problem. In strongly variable flow and convective flux reconstructions. They are also locally fields even high resolution finite volume methods may ex- efficient and hence suitable for adaptive mesh refinement. hibit a high degree of numerical diffusion. We present Numerical experiments illustrate their performance. an Eulerian-Langrangian Localized Adjoint method on unstructured grids in two space dimensions that is locally Martin Vohralik conservative and monotone. The scheme is compared to a Université Pierre et Marie Curie high-resolution discontinuous Galerkin scheme. Paris, France [email protected] Peter Bastian IWR Alexandre Ern University of Heidelberg Universite Paris-Est [email protected] CERMICS, Ecole des Ponts [email protected] MS56 Convergent Numerical Schemes for Reactive Flow Annette Stephansen in Unsaturated Porous Media Unifob Petroleum Centre for Integrated Petroleum Research Reactive porous media flow models are coupled systems [email protected] of nonlinear degenerate parabolic equations. Due to the degeneracy, solutions of such models are lacking regularity, and an efficient numerical simulation needs requires appro- MS57 priate discretization schemes. In this talk we consider In Linear Fluctuation-dissipation for Low Frequency this talk we analyze the convergence of a mixed finite ele- Climate Response ment scheme for reactive porous media flows. We focus on the coupling between the unsaturated flow component and Recently, we developed and tested novel computational the reactive component of the model. algorithms for predicting the mean linear response of a chaotic dynamical system to small changes in external forc- Florin A. Radu ing via the fluctuation-dissipation theorem (FDT). The UFZ-Helmholtz Center for Environmental Research, new linear response algorithms are tested on the T21 trun- Leipzig cation of the barotropic climate with realistic Earth-like to- Germany pography and two types of forcing which mimic behaviour fl[email protected] of the atmosphere at 300 and 500 hPa geopotential height. The new methods yield greater accuracy than classical Iuliu Sorin Pop FDT methods for the linear response of both mean state Dept of Mathematics and Computer Science and variance for both dynamical regimes. TU Eindhoven Rafail Abramov [email protected] Department of Mathematics, Statistics and Computer Science MS56 University of Illinois at Chicago [email protected] Numerical Solution of the Transport of Contami- nants in Surface and Subsurface Flows MS57 This work models groundwater contamination through rivers and lakes. The resulting multiphysics problem cou- Statistical Model for an Incompressible Particle- ples the Navier-Stokes equations, the Darcy equations and 104 GS09 Abstracts

mesh Method University of Houston [email protected] In long time simulations with numerical methods, statistical averages converge - under ergodicity assumptions - to Arjun Beri ensemble averages in an equilibrium measure. Which equi- University of Houston librium measure depends on the numerical method used. [email protected] In this talk we describe a model of the dynamics of the Hamiltonian particle-mesh method as adapted for quasigeostrophic potential vorticity flow. The HPM method MS58 preserves potential vorticity pointwise, and the motion of Numerical Analysis of the Navier-Stokes/Darcy discrete particles can be embedded in an area-preserving Coupling continuum flow. Using this knowledge, we propose a model based on random permutations of the initial PV distribu- We present mathematical and numerical models for sim- tion on a uniform particle arrangement. This model is val- ulating incompressible fluid flows through porous media. idated using Monte-Carlo simulations. Next we construct The main applications of our interest are the hydro- a statistical mechanics theory for the model. Finally, the logical environmental ones and mass transfer in biome- mean field predictions of the statistical mechanics theory chanics. We outline the analysis of a coupled Navier- are compared with long time simulations with HPM. A Stokes/Darcy problem. After proving its well-posedness nonlinear stream function-PV profile is observed for both using the Beavers and Joseph interface conditions, we in- skewed and flattened distributions. troduce a stable Galerkin finite element approximation and we study effective iterative schemes based on domain de- Jason Frank composition theory to compute its solution. Centrum Wiskunde & Informatica [email protected] Marco Discacciati Ecole Polytechnique Federale de Lausanne Svetlana Dubinkina Institute of Analysis and Scientific Computing CWI, Amsterdam marco.discacciati@epfl.ch [email protected] Lori Badea Institute of Mathematics of the Romanian Academy MS57 Bucharest, Romania On Stochastic Model Reduction Techniques [email protected] We will explore the connection between several stochastic model reduction techniques in dynamical systems with Alfio Quarteroni time scale separation. In particular, we will explore how Ecole Pol. Fed. de Lausanne the approach of stochastic centre manifold reduction is Alfio.Quarteroni@epfl.ch linked to the homogenization approach valid on long time scales. In an application we will then use both reduction MS58 techniques for data assimilation taking into account their validity on different temporal scales. A Fully Mixed Finite Element Method for the Cou- pling of Stokes and Darcy Flows Georg A. Gottwald School of Mathematics and Statistics In this paper we analyze a fully mixed finite element University of Sydney method for the coupling of fluid flow with porous me- [email protected] dia flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of MS57 normal forces, and the Beavers-Joseph-Saffman law. We Parametric Estimation of Effective Stochastic consider dual-mixed formulations in both the Stokes do- Models from Discrete Data main and the Darcy region, which yields the introduction of the traces of the porous media pressure and the It is often desirable to derive an effective stochastic model fluid velocity as suitable Lagrange multipliers. The finite for the physical process from observational and/or numer- element subspaces defining the discrete formulation em- ical data. Various techniques exist for performing estima- ploy Raviart-Thomas elements for the velocities, piecewise tion of drift and diffusion in stochastic differential equa- constants for the pressures, and continuous piecewise lin- tions from discrete datasets. In this talk we discuss the ear elements for the Lagrange multipliers. We apply the question of sub-sampling of the data when it is desirable Babuska-Brezzi theory together with a classical result on to approximate statistical features of a smooth chaotic tra- projection methods for Fredholm operators of index zero, jectory by a stochastic differential equation. In this case to show stability, convergence, and a priori error estimates estimation of stochastic differential equations would yield for the associated Galerkin scheme. In addition, we pro- incorrect results if the dataset is too dense in time. There- vide a residual-based a posteriori error estimator for this fore, the dataset has to sub-sampled (i.e. rarefied). coupled problem. Finally, some numerical results are reported. Ilya Timofeyev Dept. of Mathematics Gabriel Gatica Univ. of Houston Universidad de Concepcion [email protected] Departamento de Ingeniera Matematica [email protected] Robert Azencott Department of Mathematics Ricardo Oyarzua GS09 Abstracts 105

Universidad de Concepcion Darcy flow. [email protected] Benjamin Ganis Francisco J. Sayas University of Pittsburgh University of Minnesota Department of Mathematics [email protected] [email protected] Vivette Girault MS58 University of Paris VI Optimal Neumann-Neumann Solvers for Mortar [email protected] Coupling of Stokes-Darcy Danail Vassilev We consider the coupling across an interface of a fluid flow University of Pittsburgh and a porous media flow. The differential equations in- [email protected] volve Stokes equations in the fluid region and Darcy equations in the porous region, and coupled through an inter- Ivan Yotov face with Beaver-Joseph transmission conditions. The dis- Univeristy of Pittsburgh cretization consists of Stokes finite elements in the fluid re- Department of Mathematics gion, Raviart-Thomas finite elements in the porous region, [email protected] and the mortar Lagrange multipliers on the interface. We allow nonmatching meshes across the interface. Due to the small values of the permeability parameter of the porous MS59 medium and the nonmatching nature of the problem and Experimental Measurement and Modeling of the the discretization, the resulting symmetric indefinte dis- Oscillation of Oil-water Interface Lined with Para- crete system is ill conditioned and has a nontrivial saddle magnetic Nanoparticles point problem structure. In this talk we discuss these issues and show that preconditioners based on the Finite El- We present multidisciplinary effort in developing tech- ement by Tearing and Interconnecting (FETI) method are niques for determination of oil saturation in reservoir rocks more suitable than preconditioners based on the Balancing using paramagnetic nanoparticles. The efforts include Domain Decomposition (BDD) method. We discuss con- pore-scale experiments with nanoparticles designed to pref- dition number estimates for the preconditioners and their erentially absorb to the oil/water interface and that can dependence on the permeability and mesh size ratio across be detected remotely as well as numerical modeling. The the interface. Numerical experiments will be presented to modeling assumes capillarity to be a dominant restoring confirm the sharpness of the theoretical estimates. force when the oil-water interface is exposed to an oscillating external magnetic field, resulting in a pressure wave Marcus Sarkis from the interface movement. Worcester Polytechnic Institute Instituto de Matematica Pura e Aplicada (Brazil) Steven Bryant [email protected] Department of Petroleum and Geosystems Engineering Institute for Computational and Engineering Sciences Juan Galvis steven [email protected] Texas A&M University [email protected] Chun Huh University of Texas at Austin Department for Petroleum and Geosystems Engineering MS58 [email protected] Multiscale Mortar Methods for Coupling of Stokes and Darcy Flows Masa Prodanovic We discuss numerical modeling of coupled ground water University of Texas at Austin and surface water flows, based on Beavers-Joseph-Saffman Center for Petroleum and Geosystems Engineering interface conditions. The domain is decomposed into a [email protected] series of small subdomains (coarse grid) of either Stokes or Darcy type. The solution is resolved locally (on each MS59 coarse element) on a fine grid, allowing for non-matching grids across subdomain interfaces. Coarse scale mortar fi- Macroscale Modeling of Porous Media Systems: nite elements are introduced on the interfaces to impose The Devil is in the Deviations weakly certain continuity conditions. By eliminating the When applying averaging theory to obtain equations for subdomain unknowns the global fine scale problem is re- porous media flows, it is well known that deviation terms duced to a coarse scale interface problem, which is solved related to the difference between products of averages and using an iterative method. We precompute a multiscale averages of products require careful attention. When us- flux basis, solving a fixed number of fine scale subdomain ing the thermodynamically constrained averaging theory problems for each coarse scale mortar degree of freedom, (TCAT), one is also able to show that differences between on each subdomain independently. Taking linear combi- averages of quantities calculated over different domains nations of the multiscale flux basis functions replaces the can be important. Here, we illustrate this effect and pro- need to solve any subdomain problems during the inter- vide some examples where this issue impacts the equation face iteration. We present theoretical and numerical results forms. for local discretizations based on conforming or discontinuous elements for Stokes flow and mixed finite elements for William G. Gray University of North Carolina - Chapel Hill 106 GS09 Abstracts

[email protected] and solver.

Cass Miller Mojdeh Delshad UNC-Chapel Hill Department of Petroleum and Geosystems Engineering casey [email protected] The University of Texas at Austin [email protected]

MS59 Sunil G. Thomas Interfacial Area, Capillary Pressure and Saturation Center for subsurface modeling at the Pore-scale: Observations and Lattice Boltz- The University of Texas at Austin mann Simulations [email protected]

We present a comparison between interfacial areas ob- Mary Wheeler tained from microtomographic images of glass bead porous The University of Texas at Austin media and lattice-Boltzmann simulations for drainage and [email protected] imbibition processes. There is good agreement between the measured and simulated capillary pressure curves and interfacial areas and we find a unique capillary pressure- MS60 saturation-interfacial area relationship that is useful in de- Balance of Forces During CO2 Injection in Geolog- scribing hysteretic phenomena. Interfacial area per volume ical Formations is appears to be dependent upon the dominant flow mechanism and pore connectedness. The CO2 storage capacity of geological formations is of great interest for the selection of potential storage sites in Marcel G. Schaap, Mark Porter carbon capture and storage (CCS) projects. A detailed University of Arizona analysis essentially requires a thorough understanding of [email protected], [email protected] the interaction of forces acting within the system. By defining characteristic quantities for length, time, pressure and Dorthe Wildenschild velocity, the governing multiphase flow equations can be Oregon State University non-dimensionalised. This allows for the definition of phys- [email protected] ically sound dimensionless numbers in conformity with the multiphase flow equations. The dimensionless numbers resemble the ratios of acting forces like viscous, capillary and MS59 gravitational forces. An analysis of the relation of forces in Effect of Pore Space Morphology on Interfacial reservoirs with different parameter setups allows their in- Configurations in Porous Media tercomparison with respect to their CO2 storage capacity potential. To back up the analysis, a comprehensive reser- Fluid configurations in porous media can vary significantly voir parameter database with more than 1200 reservoirs is between drainage and imbibiton. Using computed x-ray analysed and statistical characteristics are derived. Effects microtomography, we measure significant differences in of reservoir parameters like depth, temperature, absolute wetting-nonwetting interfacial area for different pore space and relative permeability, as well as capillary pressure are morphology, and for drainage and imbibition. The data is investigated by analytical and numerical 1D and 3D ex- analyzed using pore network characterization and expres- periments. It is shown that dimensionless numbers can be sions based on energy dissipation. used to qualitatively order reservoirs by their CO2 storage capacity with respect to the forces acting in the reservoir. Dorthe Wildenschild Moreover, it is shown that the relative permeability rela- Department of Civil, Constr. and Environmental tions together with the residual saturations have a great Engineering influence on the balance of forces. Oregon State University [email protected] Rainer Helmig IWS, University of Stuttgart, Germany Masa Prodanovic Institut fur Wasserbau University of Texas at Austin [email protected] Center for Petroleum and Geosystems Engineering [email protected] Andreas Kopp University of Stuttgart, Germany [email protected] MS60 High Resolution Parallel Simulations of CO2 Stor- Holger Class age in Saline Aquifers Universitaet Stuttgart Modeling long-term movement and risk of escape of vast Scientist amounts of CO2 will require coupled models that capture [email protected] the physical and chemical evolution of the system at the appropriate scale. The geological models are often up- MS60 scaled for numerical models to reduce the computational times. However, upscaling causes loss of fine grid informa- Analytical Models of CO2 Storage at the Basin tion and introduces numerical dispersion. Long term, high- Scale Including Residual Trapping and Dissolution resolution, and large-scale modeling of flow and transport Carbon capture and storage will be a viable climate change of CO2 will be presented using an in-house simulator with mitigation technology only if several gigatonnes of carbon distributed computing and efficient numerical algorithms dioxide are injected every year. In this talk, we will present GS09 Abstracts 107

mathematical models of CO2 migration at the scale of a [email protected] geologic basin that, despite their simplicity, account for the essential flow physics during the injection and post- injection periods. In particular, we present new analytical MS61 results that include the combined effect of residual trapping Efficient Coarsening of Fluid Transport Problems and dissolution into the brine. We propose a new method for flow-based coarsening that Christopher MacMinn adapts to varying requirements with respect to accuracy MIT and simulation time. By adapting the coarse grid to high- Mechanical Engineering flow regions and retaining fine-grid fluxes along each coarse [email protected] edge, we achieve good accuracy of production curves and saturation profiles. Incorporating causality of the discrete Ruben Juanes fluxes as an additional measure enables the use of highly MIT efficient nonlinear block solvers. Civil and Environmental Engineering [email protected] Vera Louise Hauge SINTEF ICT [email protected] MS60 Probability Density Function Approach for Model- Knut-Andreas Lie ing Complex Multi-phase Flow in Porous Media SINTEF ICT, Dept. Applied Mathematics [email protected] We present a new methodology, which provides a link between Lagrangian statistics of phase particle evolution and Jostein R. Natvig Darcy scale dynamics. Each particle has a state vector con- SINTEF IKT sisting of its position, velocity, fluid phase information and [email protected] possibly other properties like phase composition. The approach is applied for modeling CO2 dissolution into brine and resulting non-equilibrium multiphase dynamics. It is MS61 shown that opposed to the stochastic formulation, the cor- Multi-scale Algorithm of Support Operator responding Darcy based deterministic formulation is un- Method closed. The multiscale method is based on using the coarse grid Manav Tyagi for pressure equation and fine grid for saturation equa- ETH Zurich tions. The essential feature of the method is construction Institute for Fluid Dynamics of the basis functions by solving the one-phase stationary [email protected] equations. These basis functions take account of fine grid structure. It is possible to construct total permeability Patrick Jenny tensor and to up-scale the relative permeability using the Institute of Fluid Dynamics dissipative energy integral approximation. The coarse grid ETH Zurich equation is solved using support operator method. Some [email protected] results of modeling are represented.

Hamdi Tchelepi Anna Pergament Petroleum Engineering Department Keldysh Institute for Applied Mathematics Stanford University [email protected] [email protected] MS61 MS61 MPFA Mortar Multiscale Method for Multiphase Darcy-Forchheimer Upscaling for Near-well Flow Flow in Porous Media Modeling An iterative coupling method employing a mortar MPFA The objective of this work is to provide a methodology method and a discontinuous Galerkin method for the pres- to upscale the Darcy-Fochheimer flow equation which ac- sure and saturation equations respectively is formulated counts for non-Darcy effects. These effects are important for multiphase flow. This approach can be viewed as a in high velocity regions (near-well). Unlike Darcy trans- multiscale scheme for the coupled multiphysics problem. missibility, the upscaled Darcy-Forchheimer transmissibil- Guangri Xue ity depends on flow rate. To overcome this difficulty an University of Texas at Austin iterative local-global upscaling technique is proposed. The [email protected] main idea is to use the rate information from global coarse model as target rate when performing the local upscaling. Mary Wheeler The University of Texas at Austin Mohammad Karimi-Fard [email protected] Stanford [email protected] Tim M. Wildey The University of Texas at Austin Louis J. Durlofsky Austin, USA Department of Energy Resources Engineering [email protected] Stanford University 108 GS09 Abstracts

MS62 the equations and multiscale heterogeneity of the medium, Stochastic Galerkin Method for Transport Equa- and the convergence of schemes. tion Son-Young Yi In this work we consider a transport equation with stochas- Oregon State University tic coefficients which model pollution concentration [email protected] −div((x, ω)) = f(x, ω)inG×⊗, G⊂R, ∇ − −→ Malgorzata Peszynska, Ralph Showalter (x, ω)=a(x, ω) c(x, ω) q (x, ω)c(x, ω), Department of Mathematics G c =0 on∂ , Oregon State University where ω is a random variable, a(x, ω) a diffusion coefficient, [email protected], modelled by a random field, c(x, ω) is the concentration of [email protected] one substance in another substance and the source term is −→ modelled by f(x, ω). The flow q (x, ω) can be computed MS63 from the equation predicting the groundwater flow through the aquifer G. The governing equations are Multi Point Flux and Mixed Finite Element Ap- −→ proximation in Porous Media: Error Analysis and −div( q (x, ω)) = p(x, ω)inG×⊗, G⊂R , Numerical Studies u = g(x)on∂G, −→ ∇ Here, in particular multi point flux and mixed finite el- where q (x, ω):=κ(x, ω) u(x, ω), the conductivity co- ement approximations of flow and transport processes in efficient κ(x, ω), the right-hand side p(x, ω) and the so- porous media are considered. A new proof of convergence lution u(x, ω) are random fields. The term ∇u models G for a multi point flux approximation scheme on triangu- the pressure gradient. The initial domain is occupied lar meshes is presented. Multi point flux approximation by the aquifer. After dicretisation of the deterministic control volume methods are discretization techniques de- and stochastic operators we apply the stochastic Galerkin velopped for an accurate and reliable reservoir simulation. method to solve this equation. In the conclusion we give a They offer explicit discrete fluxes, which allows a wide class numerical example. of applications. Various aspects of a reliable simulation Alexander Litvinenko, Martin Krosche, H. G. Matthies of simultaneous reactive transport processes are also ad- TU Braunschweig, Germany dressed. [email protected], [email protected], Markus Bause [email protected] Department Mathematics University of Erlangen-Nuremberg MS62 [email protected] Computational Modeling of Inertia Effects at Porescale MS63 We propose algorithms for computational upscaling of A Stability Criterion for Heterogenoues Density flow from porescale (microscale) to lab scale (mesoscale). Driven Flows We use traditional continuum Navier-Stokes solvers at Variable density flows can occur due to temperature dif- porescale. Properties of flow in complex pore geometries ferences in deep aquifers and due to salinity differences are averaged to derive permeability and inertia coefficients. in coastal aquifers and refuse dumps. Therefore, their Convergence of solutions and averaging techniques are ma- relevance cuts across many practical applications like ex- jor concerns but these can be relaxed if only mesoscopic ploitation of geothermal energy resources, oil recovery from parameters are needed. For media which are heterogeneous aquifers and remediation of contaminated sites. A typical and anisotropic at mesoscale we discuss appropriate non- feature of density dependent flow problems is that they Darcy models extending Forchheimer model. can become unstable (physically or numerically). Variable Anna Trykozko density flow problems are difficult to solve due to the non- Warsaw University linearities and coupling between fluid flow and solute trans- [email protected] port processes. A big challenge to-date is to derive a general criterion that states whether flow is physically stable or unstable; and the optimum computational grid resolution Malgorzata Peszynska required to solve the problem without creating numerical Department of Mathematics (artificial) instabilities. We present a new stability crite- Oregon State University rion for heterogeneous flow based on the homogenization [email protected] theory. Relevant numerical simulations are presented to sustain our theoretical results. MS62 Jude Musuuza Numerical Methods for Unsaturated Flow with Dy- University of Jena namic Capillary Pressure [email protected] Traditional unsaturated flow models use a capillary pressure-saturation relationship determined under static Sabine Attinger conditions. Recently it was proposed to extend this re- Institute of Computational Computational lationship to include dynamic effects and in particular flow EnvironmentaScience rates, which results in model equations of nonlinear, de- UFZ Leipzig generate pseudo-parabolic type. We study numerical dis- [email protected] cretizations of such models; we discuss the difficulties associated with the degenerate pseudo-parabolic character of Florin A. Radu GS09 Abstracts 109

UFZ-Helmholtz Center for Environmental Research, spreading effects. This propagation is cheaper than the 3D Leipzig wave propagation. Germany fl[email protected] Rafael Aleixo University of Campinas [email protected] MS63 Error Estimates for the Finite Volume Method for Francisco Silva Neto, Daniela Amazonas, Jesse Costa a Copper Heap Leaching Model Federal University of Para [email protected], [email protected], This work is motivated by a combined mixed finite element [email protected] (MFE) - finite volume (FV) scheme of a two phase flow model for the heap leaching of copper ores modeled by a Joerg Schleicher degenerate parabolic equation University of Campinas Dept. Applied Mathematics ∂tu −∇·(∇β(u)+F (u)) = r(u), in QT ≡ (0,T) × Ω. [email protected] (1) Initially we have u(0) = u0 in Ω, whereas u =0on∂Ω. In the above 0

Mary Wheeler In vertical transversally isotropic (VTI) media the acoustic The University of Texas at Austin wave equation is [email protected] 4 4 4 4 ∂ u 2 ∂ u 2 ∂ u 2 2 ∂ u −(1+2η)v = vv −2ηv vv (2) Tim M. Wildey ∂t4 ∂x2∂t2 ∂z2∂t2 ∂x2∂z2 The University of Texas at Austin Austin, USA where, u(x, z, t) is the pressure ﬁeld, η is a anisotropy pa- [email protected] rameter, and vv and v are, respectively, the vertical qP- wave velocity and NMO velocity. Paraxial wave-equation Ivan Yotov approximations are used to describe wave propagation with Univeristy of Pittsburgh a preferred direction. In this work, we derive paraxial ap- Department of Mathematics proximations for equation (1), using higher order Pad´e ap- [email protected] proximations, in order to reduce computation cost in migration algorithms with a good accuracy.

PP0 Rafael Aleixo University of Campinas 2.5D Finite-Diﬀerence Solution of the VTI Acous- [email protected] tic Wave Equation

2.5D processing is a mathematical formalism of a 3D wave Daniela Amazonas, Francisco Silva Neto propagation in a 2D model. Assuming that there is no Federal University of Para variation in the earth model in the transverse direction of [email protected], [email protected] the aquisition line. Using this symmetry, the 3D problem can be reduced to a repeated 2D problem. In this Joerg Schleicher work, we apply the 2.5D formalism to describe a VTI wave University of Campinas propagation in a 2D model that preserves 3D geometrical Dept. Applied Mathematics 110 GS09 Abstracts

[email protected] in which after each termination in a (local) minimum the error functional is changed. Applications to the identifica- Jesse Costa tion of Monod and van Genuchten parameters show signif- Federal University of Para icant improvements in possible accuracy. Furthermore, a [email protected] favourable form free approach with hierarchical treatment for the global parametrization of one- or multidimensional nonlinearities are used. Thereby, because of the so called PP0 curse of dimensionality sparse grids are applied in case of Anisotropic Complex-Padé Finite-Difference higher dimensional problems to decrease the degree of free- Depth Migration dom significantly. In addition the presented methods can also be combined with a hierarchical concept to filter out Standard real-valued finite-difference (FD) migration can- the most sensitive parameters and identify them first. In not handle evanescent waves correctly, which can lead to a further step these approaches can be used also within numerical instabilities in the presence of strong velocity experimental design to find more appropriate sequences of variations. A possible solution to these problems is the experiments which can be taken into account into an mul- complex Padé approximation, which avoids problems with tiexperiment identification approach. evanescent waves by a rotation of the branch cut of the complex square root. In this work, we apply this approx- Michael Blume imation to the acoustic wave equation for vertical trans- University of Erlangen-Nuremberg versely anisotropic media to derive more stable FD migra- Department of Mathematics tion for such media. [email protected]

Daniela Amazonas Peter Knabner Federal University of Para Universitat Erlangen-Nurenberg [email protected] Department of Mathematics [email protected] Rafael Aleixo University of Campinas [email protected] PP0 Detection and Approximation of Fault Lines from Joerg Schleicher Scattered Data University of Campinas Dept. Applied Mathematics We propose a method for the detection and accurate ap- [email protected] proximation of surface fault lines. First, to locate all the data points close to fault lines, we consider a procedure based on a local interpolation scheme involving a IDW for- Jesse Costa mula. Then, we find further sets of points generally closer Federal University of Para to the faults than the fault points. Finally, after applying [email protected] a nearest-neighbour searching procedure and a refinement technique, we outline some approximation methods for the PP0 fault lines. Fluid Flow, Transport and Reaction Processes, Roberto Cavoretto, Giampietro Allasia, Renata Besenghi, Monod and Van Genuchten Parametrization, Pa- Alessandra De Rossi rameter Identification, Output Least Squares Department of Mathematics Method, Formfree Identification, Adaptive Sqp University of Torino Method [email protected], [email protected], re- [email protected], [email protected] Recent challenges like bioremediation, longterm underground storage of reactive waste or underground carbon- dioxide sequestration require more and more complex mul- PP0 ticomponent reactive transport and fluid flow models. Al- A Method for Conditioning Stochastic Groundwa- though being demanding concerning their efficient numer- ter Flow Fracture Network Models. ical approximation, the decisive bottleneck in using such models seems to lie in the availability of the increasing Calculations of groundwater flow through fracture net- range of reaction and hydraulic flow parameters entering works are of great importance for performance assessments such a model (Monod parameters in multiplicative Monod of potential radioactive waste repositories located in hard models in conjunction with bioremediation and rate pa- rocks. We present a method for conditioning the transmis- rameters in kinetic mass action law models as well as van sivities in a fracture network model on observed measure- Genuchten parameters for the modelling of hydraulic prop- ments of groundwater heads and flows to boreholes. The erties ...). We address the reliable and accurate identifica- method is illustrated by application to a number of simple tion of such parameters from one of most controlled ex- test cases and to a model of a site for which field data are perimental set ups, namely from soil column breakthrough available. curves (letting the upscaling issue aside), but the following methology can also applied to field experiments. It is well- Andrew G. Milne known that the (missing) sensitivity and the correlation University of Nottingham of parameters prevent a reliable reconstruction from naive [email protected] history matching (output least squares minimization). For a fixed experimental setup we propose a systematic use of Andrew Cliffe the singular values of the sensitivity matrix in the defini- School of Mathematical Sciences tion of the error functional to design an adaptive approach University of Nottingham GS09 Abstracts 111

andrew.cliff[email protected] lower crustal material originating from the pro-wedge in the retro-wedge. In this study a Distinct Element Method Paul Houston is used to investigate the tectonic evolution of the Uralide School of Mathematical Sciences wedge and to determine the influence of the neighbourhood University of Nottingham, UK of strong island arc rocks and a serpentinitic melange, iso- [email protected] static compensation and basal viscous flow on the structure of the orogen. David Holton, Peter Jackson, Steven Joyce Ines Goerz Serco Technical and Assurance Services TU Bergakademie Freiberg [email protected], [email protected] [email protected], [email protected] PP0 PP0 Parameter Estimation for Water Transport in Het- erogeneous Porous Media A Modified Idw Algorithm for Scattered and Track Data Interpolation The solution of Richards’ equation requires the estimation of the parameters of a parametrisation of the hy- We propose an accurate and efficient interpolation method, draulic properties (capillary pressure-saturation curve, rel- and the relative algorithm, for modelling unknown surfaces. ative permeability). A typical method is multi-step out- It is based on a modified IDW formula (with least square flow, where a sample is placed on a ceramic plate and de- or radial basis function approximants as nodal functions) saturated be reducing the pressure stepwise at the lower and exploits the particular strip structure to optimize the boundary. Parameter estimation from multi-step outflow searching procedure of the nearby data points. The method experiments requires usually the assumption of macro- works well from both scattered data and track data, and scopic homogeneity for the sample. If the structure of guarantees a high parallelism. the sample (the arrangement of materials) can be deter- Alessandra De Rossi, Giampietro Allasia, Renata mined independently (e.g. by geophysical measurements) Besenghi, Roberto Cavoretto it is possible to take it into account in the inversion pro- Department of Mathematics cess and estimate the hydraulic properties of the subscale University of Torino materials. A very robust forward model massive parallel [email protected], [email protected], computing is necessary to get a fast solution of the large [email protected], [email protected] 3D forward problems which need to be solved. Olaf Ippisch PP0 Interdisziplinary Center for Scientific Computing University of Heidelberg Soil Reaction Estimates for Laterally Loaded Piles [email protected] Using Euler-Bernoulli Beam Theory and a Sim- ple Polynomial Curve Fitting Algorithm on Lateral Deflection Measurements Hans-Joerg Vogel Helmholtzzentrum fuer Umweltforschung - UFZ A simple numerical procedure is proposed to estimate soil [email protected] reactions along laterally loaded piles. The technique involves using lateral deflection measurements of the pile obtained from slope inclinometer measurements. The de- PP0 flected shape of the laterally loaded pile is estimated using Information Mining Models for Interdisciplinary a simple polynomial curve fitting algorithm that is applied Research sequentially to the slope inclinometer data with depth. The procedure is used to derive curvature versus depth and mo- The conference contribution describes the concept, implement versus depth. The procedure is calibrated with a mentation and application of an innovative information full-scale experimental program involving lateral load test mining approach in an interdisciplinary research project. to three well-characterized piles where slope inclinometer Target of the research project is to simulate the long-term data was available as well as curvature and moment data deformation of large mountain sides. One key challenge along the pile depth. The proposed procedure provides in the interdisciplinary research project is to identify the very good estimates of the measured bending moments and interaction of the different physical processes such as me- the soil reactions back-calculated using more conventional teorology, hydrology, surface flow, infiltration, sub-surface methods such as the use of a finite difference discretization flow, soil mechanics, shear band deformations and hill slope of the pile with the soil reaction modeled with p-y curves. movements with given geological and topographical heterogeneity. Key idea of this ongoing research work is to combine the different well known data mining methods to Sixto Fernandez, Miguel Pando identify relationship between the different physical state University of Puerto Rico at Mayaguez variables as interdisciplinary application. [email protected], [email protected] Frank Molkenthin, ChiYu Li, Vikramjeet Notay BTU Cottbus PP0 [email protected], ea05 [email protected], Evolution of the Uralide Orogenic Wedge-aNu- [email protected] merical Simulation

The Uralide orogen exhibits a bivergent orogenic wedge PP0 with a foreland thrust belt at the pro-wedge side and Model Integration and Coupeling in a Hydroinfor- 112 GS09 Abstracts

matics System PP0 Nonstandard FDTD Scheme for Computation of The conference contribution describes the concept, imple- Elastic Waves mentation and application of an innovative information system to couple different simulation models. Application Finite-difference method in time-domain (FDTD) is one of target is an interdisciplinary research project to simulate the most popular techniques used for modeling of wave the long-term deformation of large mountain sides. The propagation in many fields. Recently, FDTD schemes system supports the coupling of models from hydrology, called nonstandard FDTD have been developed in com- multi-phase groundwater flow and soil mechanics as well putational electromagnetics and acoustics to efficiently re- as laboratory experiments and field measurements by gen- duce the numerical dispersion and grid anisotropy. In this eralized sets of objects to manage physical state variables study we propose a nonstandard FDTD scheme for elastic including scaling, mapping and transformation. This ap- wave computation, which gives highly accurate solutions proach allows a more flexible coupling of simulation models both for P and S waves. from different disciplines on flexible scales and approximation levels. Hiroshi Takenaka Kyushu University Frank Molkenthin, Vikramjeet Notay, ChiYu Li [email protected] BTU Cottbus [email protected], Arash JafarGandomi [email protected], ea05 [email protected] Kyushu university [email protected] PP0 Colloidal Influence on Fluid Dynamics in Porous PP0 Media Efficient Time-Stepping for Advection Dominated A microscopic model at the pore scale for fluid flow in Reactive transport in Heterogeneous Porous Media porous media influenced by colloid dynamics is presented. Reactive transport in heterogeneous porous media is com- Special attention is paid to ad-/desorption processes of col- mon to many applications, including groundwater contam- loidal particles at the solid matrix caused by the total in- ination and CO2 storage. Such processes are inherently teraction energy between particles and matrix as well as multiscale in nature and highly non-linear,rendering accu- to thereby influenced evolving microstructure. In order rate and fast numerical solutions challenging. We demon- to achieve some macroscopic description of the concerned strate that a finite volume discretization can be integrated phenomena, the derived model is homogenized with the in time with exponential integrators where a linear system method of asymptotic two-scale expansions. is solved exactly. Using a Krylov subspace or Leja points Nadja Ray to approximate the exponential makes these methods com- University of Erlangen-Nuremberg petitive compared to standard integrators. [email protected] Antoine Tambue Heriot Watt University ,Edinburgh, UK PP0 [email protected] A New Method for Assigning ,the Eigenvalues Sign in Equation (Ax = λX) and (Ax = λBx) Sebastian Geiger Heriot-Watt University The inertia of an n × n complex matrix A, is defined to Edinburgh be an integer triple, In(A)=(π(A),ν(A),δ(A)), where [email protected] π(A) is the number of eigenvalues of A with positive real parts,ν(A) is the number of eigenvalues with negative real Lord Gabriel parts and δ(A) is the number of eigenvalues with zero real School of Mathematical and Computer sciences, Heriot parts. We are interested in computing the Inertia for large Watt unsymmetric generalized eigenproblem (A,B) for equation University , Edinburgh EH14 4AS ,UK Aϕ = λBϕ Where A and B are n × n large matrices. For [email protected] standard eigenvalues problem let B = Identity matrix. An obvious approach for determine Inertia of pair(A,B), is to transform this to a standard eigenproblem by inverting either A or B. In this paper we show that the eigenvalues sign can be computed by assigning the interval that including all the eigenvalues and this method is compared by results in Matlab.

Maryam Shamssolary Guilan university Rasht,Iran [email protected]

Hashem Saberi Najaﬁ Guilan university hnajaﬁ@guilan.ac.ir