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Workshop on
Simulation of Flow in Porous Media andApplications in Waste Management
and CO2 Sequestration
October 3-7, 2011
as part of the
Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment
This workshop will focus on mathematical and computational issues in subsurface flow. Subsurface flowproblems are inherently multiscale in space due to the large variability of material properties and in timedue to the coupling of many different physical processes, such as advection, diffusion, reaction and phaseexchange. Subsurface flow models still need considerable development. For example, nonequilibriumeffects, entrapped air, anomalous dispersion and hysteresis effects can still not be adequately described.Moreover, parameters of the models are difficult to access and often uncertain, linking this workshopto the Workshops 2 and 4. Computational issues in subsurface flows include the treatment of strongheterogeneities and anisotropies in the models, the efficient solution of transport-reaction problems withmany species, treatment of multiphase-multicomponent flows and the coupling of subsurface flow modelsto surface flow models given by shallow water or Stokes equations. With respect to energy and the envi-ronment, in particular the modelling and simulation of radioactive waste management and sequestrationof CO2 underground have gained high interest in the community in recent years. Both applications pro-vide unique challenges ranging from modelling of clay materials to treating very large scale models withhigh-performance computing.
The workshop will bring together key numerical mathematicians whose interest is in the analysis andcomputation of multiscale subsurface flow and practitioners from engineering and industry whose interestis in the applications of these core problems. Particular problems to be considered will be (i) The designof accurate methods for problems with unresolved (or unresolvable) scales and/or uncertainty in data;(ii) The efficient and robust coupling of different models describing porous media and free flow (such asDarcy, Brinkman, Stokes, Richards and shallow water); (iii) Fast linear algebra solvers for subsurfaceflow problems in heterogeneous media; (iv) Applications of the above methods and ideas in energy andthe environment, such as deep geological disposal of radioactive waste or carbon capture and storageunderground.
The workshop will also include a special session on “Fuel Cell Modeling” which leads to similarmathematical problems as subsurface flow simulation.
Workshop Organizers
Peter Bastian, Heidelberg University, GermanyJohannes Kraus, Johann Radon Institute, AustriaRobert Scheichl, University of Bath, UKMary F. Wheeler, University of Texas at Austin, USA
Welcome
to Linz and thank you very much for participating in the sixth RICAM Special Semester on Multi-scale Simulation & Analysis in Energy and the Environment, hosted by the Johann Radon Insitute forComputational and Applied Mathematics (RICAM) from October 3 to December 16, 2011.
Technological advances have greatly improved our quality of life. However, they bring with them ahuge surge in energy requirements which in turn puts at risk our entire bio-sphere. It is of paramountimportance to predict these risks and to develop better solutions for the future. One of the central tasksis the accurate simulation of multiphase flow above and under ground. The risk analysis and uncertaintyquantification, as well as the assimilation of data require statistical tools and efficient solvers for stochasticand deterministic PDEs as well as for the associated inverse problems. The key features that make itextremely hard to predict these physical phenomena accurately are the multiple time and length scalesthat arise, as well as the lack of and uncertainty in data. Because of the highly varying scales involved, theresolution of all scales is currently impossible even on the largest supercomputers. While there is a fairlylong history of empirically successful robust computational techniques for certain multiscale problems,the rigorous (numerical) analysis of such methods is of extremely high current interest.
The goal of the special semester is to provide a stimulating environment for civil engineers, hydrologists,meteorologists and other environmental scientists to address together with mathematicians working atthe cutting edge of rigorous numerical analysis for multiscale (direct and inverse) problems the emergingchallenges in the quantitative assessment of the risks and uncertainties of atmospheric and subsurfaceflow, focusing in particular on
• Simulation of Flow in Porous Media and Applications in Waste Management and CO2 Sequestration
• Large-Scale Inverse Problems and Applications in the Earth Sciences
• Data Assimilation and Multiscale Simulation in Atmospheric Flow
• Wave Propagation and Scattering, Direct and Inverse Problems and Applications in Energy andthe Environment
• Multiscale Numerical Methods and their Analysis and Applications in Energy and the Environment
• Stochastic Modelling of Uncertainty and Numerical Methods for Stochastic PDEs
Specific activities planned for the Special Semester are
• 4 thematic workshops addressing some of the key topics of the Special Semester;
• Special Lecture Series on ”Multilevel Methods for Multiscale Problems”;
• Graduate Seminar on ”Multiscale Discretization Techniques”;
• Wednesday Research Kitchen;
• Public Lecture by Prof. Jorn Behrens (KlimaCampus, Universitat Hamburg) on“Tsunami Fruh-Warnung: Mathematik und Wissenschaftliches Rechnen im Dienste der Sicherheit”.
We sincerely hope that you enjoy your stay in Linz!
Local Organizing Committee Program Committee
Robert Scheichl, Bath & RICAM (Chair) Peter Bastian, University of Heidelberg, GermanyJorg Willems, RICAM (Coordinator) Mike Cullen, MET Office, Exeter, UKJohannes Kraus, RICAM (Co-Coordinator) Heinz Engl, RICAM & University of Vienna, AustriaErwin Karer, RICAM (Co-Coordinator) Melina Freitag, University of Bath, UK
Ivan G. Graham, University of Bath, UKUlrich Langer, RICAM & University of Linz, AustriaMarkus Melenk, TU Vienna, AustriaRobert Scheichl, University of Bath, UK (Chair)Mary F. Wheeler, University of Texas at Austin, USA
Contents
Information 2Workshop Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Social Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Restaurants and Cafes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Program 5
Posters 7
Abstracts 8
Abstracts for Posters 18
List of Participants 22
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Information
Workshop Information
Registration. The workshop registration will be on October 3rd, 2011 from 8:30 - 9:10 next to theseminar room SP2 416 on the 4th floor of the Science Park Building 2 (see floor plan). Participantsthat arrive later in the week can register at the special semester office SP2 456.
Registration Fee. Non-invited participants are kindly asked to pay the registration fee in cash uponregistration.
Campus plan and overview map as well as a floor plan of the 4th floor of the workshop venue (Sci-ence Park Building 2) are located on the next pages.
Seminar room. The workshop will take place in seminar room SP2 416 on the 4th floor of the SciencePark Building 2 (see floor plan).
Program. A time schedule for the workshop is located on the backside of this booklet.
Coffee breaks. The coffee breaks will be in the corridor of the 4th floor of the Science Park Building 2.
Internet access. There will be an extra information sheet regarding internet access available at regis-tration.
Social Events
Welcome Reception & Poster Session. Monday, October 3th, 2011, 5:00 pm, at the 4th floor of theScience Park Building 2.
Conference Dinner. Thursday, October 6th, 2011, 7:00 pm, at the restaurant “Kepler’s“, situated inthe Mensa building.
Restaurants and Cafes
• Mensa Markt (lunch time only) - Main canteen of the University (see campus plan)
• KHG Mensa (lunch time only) - Smaller canteen - good traditional food (see overview map: “KHGLinz”)
• Pizzeria “Bella Casa” - Italian and Greek restaurant (located next to the tram stop)
• Chinese restaurant “Jadegarten” - (located close by the tram stop, adjacent to “Bella Casa”)
• Asia restaurant “A2” - (located behind the Science Park on Altenbergerstrasse)
• “Chat” cafe - coffee, drinks and sandwiches (located in the “Horsaaltrakt” - see overview map)
• Cafe “Sassi” - coffee, drinks and small snacks (located in the building “Johannes Kepler Universitat”- see overview map)
• Bakery “Kandur” - bakery and small cafe (located opposite the tram stop)
General Information
Accommodation. The arranged accomodation for invited participants is the “Sommerhaus” hotel. Youcan find its location in the overview map on page 4.
Special Semester Office: Room SP2 456. The special semester administrator is Susanne Dujardin.
Audiovisual & Computer Support. Room SP2 458, Wolfgang Forsthuber or Florian Tischler.
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Orientation/ Local Transport. From the railway station you have to take tram number 1 or 2 indirection “Universitat”. It takes about 25 minutes to reach the desired end stop “Universitat”.
In order to get to the city center of Linz (“Hauptplatz”) and back you have to take again tramnumber 1 or 2 (about 20 minutes). For more information see www.ricam.oeaw.ac.at/location/.
Taxi Numbers.+43 732 6969 Oberosterreichische Taxigenossenschaft+43 732 2244 2244 Linzer Taxi+43 732 781463 Enzendorfer Taxi & Transport+43 732 2214 Linzer Taxi+43 732 660217 LINTAX TaxibetriebsgesmbH
Further important phone numbers.+43 (0)732 2468 5222 RICAM & Special Semester Office (Susanne Dujardin)+43 (0)732 2468 5250/5255 RICAM IT Support (Florian Tischler/ Wolfgang Forsthuber)+43 (0)732 2457-0 Reception of Hotel Sommerhaus133 General emergency number for the police144 General emergency number for the ambulance
More information about RICAM can be found at www.ricam.oeaw.ac.at. See also the SpecialSemester webpage www.ricam.oeaw.ac.at/specsem/specsem2011/ for additional information.
Figure 1: 4th floor of Science Park Building 2.
Figure 2: Campus plan
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Figure 3: Overview map
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Program
Monday, October 3rd
08:30 - 09:10 Registration
09:10 - 09:20 Opening
09:20 - 10:10 Mary F. Wheeler (The University of Texas at Austin)
“Evaluating Long Term CO2 Storage in Saline Aquifers”
10:10 - 10:40 Coffee Break
10:40 - 11:30 Jan Martin Nordbotten (University of Bergen)
“Multiscale Modeling for CO2 Storage”
11:30 - 14:00 Lunch Break
14:00 - 14:50 Martin Vohralık (Universite Pierre et Marie Curie (Paris 6))
“Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics,and Mortar Coupling”
14:50 - 15:20 Coffee Break
15:20 - 16:10 Barbara Wohlmuth (Fakultat Mathematik, TU Munchen)
“A New Coupling Concept for Two-Phase Compositional Porous Media and Single-Phase Compositional Free Flow”
17:00 Poster Session & Welcome Reception
Tuesday, October 4th
08:30 - 09:20 Helge K. Dahle (University of Bergen)
“CO2-Migration: Effects and Upscaling of Caprock Topography.”
09:20 - 10:10 Laurence Halpern (LAGA. Universite Paris 13)
“Optimized Schwarz Waveform Relaxation for Reactive Transport Problems”
10:10 - 10:40 Coffee Break
10:40 - 11:30 Anthony Michel (IFP Energies nouvelles)
“Time-Space Domain Decomposition for Reactive Transport in Porous Media ”
11:30 - 14:00 Lunch Break
14:00 - 14:50 Andrew Cliffe (University of Nottingham)
“What should we do with Radioactive Waste?”
14:50 - 15:20 Coffee Break
15:20 - 16:10 Robert Marschallinger (OAW GIScience)
“Multi-scale 3D and 4D Modelling and Simulation in Geosciences”
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Wednesday, October 5th
08:30 - 09:20 Jurgen Becker (Fraunhofer ITWM)
“Pore-Scale Modelling of Porous Layers Used in Fuel Cells”
09:20 - 10:10 Andro Mikelic (Universite Lyon 1)
“Effective Pressure Interface Law for Transport Phenomena between an UnconfinedFluid and a Porous Medium using Homogenization”
10:10 - 10:40 Coffee Break
10:40 - 11:30 Jurgen Fuhrmann (Weierstrass Institute Berlin)
“Electrochemical Processes and Porous Media: Mathematical and Numerical Mod-eling”
11:30 - 14:00 Lunch Break
14:00 - 14:50 Marco Discacciati (Universitat Politecnica de Catalunya, Barcelona)
“Coupling Free and Porous-Media Flows: Modeling, Analysis, and Numerical Ap-proximation”
14:50 - 15:20 Coffee Break
15:20 - 16:10 Ivan Yotov (University of Pittsburgh)
“Mortar Multiscale Framework for Stokes-Darcy Flows”
Thursday, October 6th
08:30 - 09:20 Jocelyne Erhel (INRIA; Campus Universitaire de Beaulieu, Rennes, France)
“Numerical and Stochastic Models of Flow in 3D Discrete Fracture Networks”
09:20 - 10:10 Alain Bourgeat (Universite Lyon 1 - UCB, France)
“Modeling Compressible Multiphase Flow and Transport in Saturated-UnsaturatedPorous Media: Phase Appearance-Disappearance. Application to Gas Migrationin Underground Nuclear Waste Repository”
10:10 - 10:40 Coffee Break
10:40 - 11:30 Alexandre Ern (Universite Paris-Est, CERMICS)
“Discontinuous Galerkin Method for Two-Component Miscible Liquid-Gas PorousMedia Flows”
11:30 - 14:00 Lunch Break
14:00 - 14:50 Peter Bastian (Universitat Heidelberg)
“Numerical Solution of Compositional Two-Phase Flow in Porous Media”
14:50 Coffee Break
19:00 Conference Dinner
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Friday, October 7th
08:30 - 09:20 Yalchin Efendiev (Texas A&M University)
“Local-Global Multiscale Model Reduction Techniques for Flows in HeterogeneousPorous Media”
09:20 - 10:10 Clemens Pechstein (Johannes Kepler Universitat Linz)
“An Abstract Two-Level Additive Schwarz Method for Systems with High ContrastCoefficients”
10:10 - 10:40 Coffee Break
10:40 - 11:30 Ralf Kornhuber (Freie Universitat Berlin)
“Coupled Surface and Saturated/Unsaturated Ground Water Flow in Heteroge-neous Media”
11:30 Closing
Posters
The poster session will take place on the 4th floor of the 2nd Science Park Building. It will startat 5:00 pm on Monday, October 3rd.
Sergey Alyaev (Universitetet i Bergen)“Multiscale Simulations of Non-Darcy’s Flows”
Radim Blaheta (Institute of Geonics AS CR, Ostrava, CZ)“Micromechanics of Geomaterials and Geocomposites.”
Thomas Carraro (University of Heidelberg)“Modelling, Simulation and Optimization of the Microstructure of SOFC Porous Cathodes”
Christian Engwer (Institut fur Numerische und Angewandte Mathematik, Universitat Munster)“Numerical Upscaling in Porous Media”
Ivan Georgiev (Radon Institute for Computational and Applied Mathematics (RICAM), Linz)“Preconditioning of Non-Conforming FEM Systems”
Christian Goll (University of Heidelberg)“Design of Numerical Methods to Simulate Models of a Solid Oxide Fuel Cell”
Sridhara Nayak (Indian Institute of Technology, Kharagpur)“Impact on the Surface Temperature due to the Modifications of Underlying Land Surface Conditions:A Study over Western India”
Rebecca Neumann (University of Heidelberg)“Modeling Two-phase Flow with Disappearing Gas Phase”
Joerg Willems (Radon Institute for Computational and Applied Mathematics (RICAM), Linz)“Robust Preconditioners for General SPD Operators”
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Abstracts
“Numerical Solution of Compositional Two-Phase Flow in Porous Media”Peter BastianUniversitat HeidelbergInterdisziplinares Zentrum fur Wissenschaftliches RechnenIm Neuenheimer Feld 368, D-69120 Heidelberg
In this talk I present two different methods for solving two-phase flow problems in porous media.The first method is a fully-coupled discontinuous Galerkin scheme for incompressible two-phase flowin heterogeneous media. It is based on a wetting-phase pressure/capillary pressure formulation andassumes the diffusion-dominated regime. These primary variables are continuous when both phasesare present and simplify the formulation of the consistency and penalty terms at media discontinuities.The scheme can handle unstructured, nonconforming grids and tensor permeabilities in multiple spacedimensions. For the time discretization diagonally implicit Runge-Kutta schemes are employed toobtain a formally higher-order method in space and time. Numerical comparison with a cell-centeredfinite volume method using full upwinding and implicit Euler shows that the new scheme achievesvery accurate solutions on rather coarse grids.The second scheme treats compositional two-phase flow with phase disappearance. Based on anonwetting-phase pressure/capillary pressure formulation the scheme can handle the disappearanceof the nonwetting phase without switching of variables or adding complementarity constraints. Ap-plications of the method to the MoMas phase disappearance benchmark and a CO2 sequestrationbenchmark are presented.The last part of the talk will illustrate in some detail the software implementation of these and othernumerical schemes within the DUNE software framework (http://www.dune-project.org). Thisframework offfers great flexibility for implementing state-of-the-art discretization schemes and solverswhile retaining high performance and easy parallelization.This presentation is joint work with Olaf Ippisch and Rebecca Neumann.
“Pore-Scale Modelling of Porous Layers Used in Fuel Cells”Jurgen BeckerFraunhofer ITWM,Fraunhofer-Platz 1,67663 Kaiserslautern
In a proton exchange membrane (PEM) fuel cell a proton-conducting polymer membrane separatesanode and cathode. The membrane, together with catalyst and diffusion layers on both sides, formsthe membrane electrode assembly (MEA). This MEA consists of several porous layers on both thecathode and the anode side:
• the gas diffusion layer (GDL), usually a non-woven or woven carbon paper,• the micro-porous layer (MPL), usually made of carbon agglomerates, and• the catalyst layer (CL), which consists of carbon agglomerates, platinum particles and polymer
electrolyte.
The physical properties of such a porous layer are described by its macro-homogeneous properties, e.g.porosity, diffusivity, permeability and conductivity. Improving the performance of the cell is possibleby improving the cell as a whole, but also by optimizing each of the layers to its requirements.Optimization includes improving the micro-structure of each layer as material connectivity and poremorphology have a major impact on the properties.Therefore, in this talk I will present
1. how to create 3D virtual structure models of each layer,2. how to determine the effective properties of the layer numerically, and3. how to validate this approach.
The 3D structure models are created using stochastic processes; For example, GDL models are createdby placing fibres randomly using an anisotropic direction distribution. These fibres may be straightor bent, where the bending is determined by its own random process. For MPL and CL, agglomeratestructures of carbon particles are created randomly.
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Using these 3D models, the effective properties of the layers can be predicted by solving the appropriatepartial differential equations on the pore-scale model. To determine single-phase permeability, Stokes’equation is solved. Two-phase permeability values, which are of interest due to the production ofwater at the cathode, are determined by combining single-phase simulations with the pore morphologymethod. The effective diffusivity is determined solving Laplace’s equation. For MPL and CL, alsoKnudsen diffusion is considered, as pore sizes become comparable to the mean free path of the gas.To validate this approach I compare experimentally measured GDL properties with numerically de-termined properties. For this purpose, a tomography image of the GDL is used as model to ensuremicro-structural geometric similarity between experiment and simulation.
“Modeling Compressible Multiphase Flow and Transport in Saturated-Unsaturated Porous Media: PhaseAppearance-Disappearance. Application to Gas Migration in Underground Nuclear Waste Repository”Alain BourgeatUniversite Lyon 1 - UCB, France
Motivated by modelling the gas migration in an underground nuclear waste repository, we derive a newcompositional model of compressible multiphase flow and transport in porous media, with interphasemass transfer, The liquid phase is composed of water and dissolved hydrogen and the gas phase iscomposed of vaporized water and hydrogen. One of the main difficulty appearing in the usual modelsis their inadequacy to take in account both fully and partially water saturated situations ; leadingto numerical problems or unphysical numerical constraints. The new unified modeling of fully andpartially water saturated porous materials, presented in our talk, is based on fundamental principlesof fluid mechanic and thermodynamic; and its main interest is to make possible a unified numericaltreatment of fully and partially water saturated situations. Under adequate assumptions, the existenceof solutions for equations corresponding to this ”unified fully partially saturated” formulation couldbe proved. We present numerical simulations showing the efficiency of this modelling.
“What should we do with Radioactive Waste?”Andrew CliffeSchool of Mathematical Sciences,University of Nottingham
Most radioactive waste arises from civil nuclear power programmes. Opinions are sharply divided whenit comes to nuclear power: some countries intend to phase it out altogether, others are heavily relianton it for electricity generation and will be for the foreseeable future. However, everyone is agreedthat radioactive wastes must be disposed of in a safe manner. This talk will review the options thathave been considered for safe long-term disposal of radioactive waste and explain why deep geologicaldisposal is now the (almost) universally preferred solution. A deep geological disposal facility is acombination of an engineered and a natural system and any analysis of the safety performance of sucha facility must take into account the uncertainties inherent in natural systems. The techniques usedto deal with uncertainty will be outlined. The important case of the uncertainties arising from limitedinformation about rock properties and their impact on transport of radionuclides from a deep disposalfacility back to the human environment will be considered in some detail, illustrating the importanceof modern developments in uncertainty quantification and the solution of stochastic partial differentialequations.
“CO2-migration: Effects and Upscaling of Caprock Topography.”Helge K. DahleDept. of Mathematics,University of Bergen, Norway
In prospective sites for CO2 storage, such as a saline aquifer or abandoned petroleum reservoir, thesubsurface conditions are such that CO2 is a supercritical fluid and slightly soluble in water and thusforms a separate fluid phase that is less dense and much less viscous than the resident brine. Becauseof the viscosity and density differences the CO2 will be captured under the caprock and then migrateas a thin plume under the influence of gravity. It follows that the dynamics and distribution of the
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CO2 plume will depend on the topography of the caprock.
In this presentation we demonstrate how caprock topography may impact plume migration and dis-tribution. In particular we note how caprock roughness reduces migration speeds. Open issues to bediscussed are how subscale caprock roughness may be upscaled, and how roughness can be parame-terized.
The presentation is based on joint work with Halvor M. Nilsen, SINTEF ICT, Norway and SarahGasda, Uni Research, Norway
“Coupling Free and Porous-Media Flows: Modeling, Analysis, and Numerical Approximation”Marco DiscacciatiLaboratori de Calcul Numeric (LaCaN).Universitat Politecnica de Catalunya (UPC BarcelonaTech),Barcelona, [email protected]
In this talk we consider the modeling and numerical simulation of coupled free/porous-media flows.We present different modeling approaches involving the Navier-Stokes equations to represent theincompressible fluid and Darcy of Fochheimer equations in the porous region. We discuss and comparedifferent coupling strategies based on the so-called penalization method or on the application of thetransmission conditions of Beavers-Joseph-Saffman.After giving some results on the well-posedness of the resulting coupled models, we illustrate a domaindecomposition framework to set up possible iterative methods to compute their finite element solution.We discuss the effectiveness and robustness of such algorithms showing several numerical results.Finally, we present some possible applications of the models that we have studied.
“Local-Global Multiscale Model Reduction Techniques for Flows in Heterogeneous Porous Media”Yalchin EfendievTexas A&M University
The development of numerical algorithms for simulations of flow processes in large-scale highly het-erogeneous porous formations is challenging because properties of natural geologic porous formations(e.g., permeability) display high variability and complex spatial correlation structures which can spana hierarchy of length scales. It is usually necessary to resolve a wide range of length and time scales,which can be prohibitively expensive, in order to obtain accurate predictions of the flow, mechanicaldeformation, and transport processes under investigation. In practice, some types of coarsening (orupscaling) of the detailed model are usually performed before the model can be used to simulatecomplex processes. Many approaches have been developed and applied successfully when a scale sepa-ration adequately describes the spatial variability of the subsurface properties (e.g., permeability) thathave bounded variations. The quality of these approaches deteriorates for comp! lex heterogeneitieswithout scale separation and high contrast. In this talk, I will describe multiscale model reductiontechniques that can be used to systematically reduce the degrees of freedoms of fine-scale simulationsand discuss applications to preconditioners and coupling to global model reduction tools. Numer-ical results will be presented that show that one can improve the accuracy of multiscale methodsby systematically adding new coarse basis functions, obtain contrast-independent preconditioners forcomplex heterogeneities, and get reduced order models at low cost.
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“Numerical and Stochastic Models of Flow in 3D Discrete Fracture Networks”Jocelyne ErhelINRIA; Campus Universitaire de Beaulieu,Rennes, France;[email protected]
This is joint work with Jean-Raynald de Dreuzy (CNRS, UMR Geosciences, Rennes), Geraldine Pichot(INRIA, Rennes) and Baptiste Poirriez (INSA, UMR IRISA, Rennes).
Underground water is naturally channelled in fractured media, where interconnections can be veryintricate. Discrete Fracture Networks are based on a geometrical model, where fractures are 2Ddomains, for example ellipses, which form a 3D network. Stochastic models rely on probability lawsto define the geometry, in particular the length distribution of fractures. In our model, we define apower law, which induces a large range of scales. This multiscale model is quite challenging to handle,since a few large fractures can interact with many small fractures. Physical laws are quite simple, withPoseuille’s flow equations inside each fracture and continuity of pressure and flux at the intersectionsbetween the fractures. Boundary conditions are applied at the borders of the fractures and of thenetwork, which is limited by a finite cube. Our numerical model relies on a mixed hybrid finite elementmethod, which is well suited for such problems. With a conforming mesh, continuity conditions areeasy to apply, but with a non conforming mesh, mortar relations must be devised. A non conformingmesh allows meshing the fractures independently, in order to adapt the mesh step to the fracturescale. Because the network is generated randomly, mesh generation can fail when small angles appearat the interface of a fracture (the interface is the set of intersections with other fractures). We havedeveloped an original discretization procedure, with a two-step algorithm, acting first at the networklevel then at the fracture level. This method removes small angles so that mesh generation is feasibleand leads to a good aspect ratio. On the other hand, this approach creates geometrical configurationswhere more than two fractures can share an intersection edge. This brings up a new difficulty for themortar method, where new relations must be defined. This spatial discretization leads to a symmetricpositive definite linear system, with a large sparse matrix. We have investigated the efficiency of severallinear solvers on parallel and distributed computers. Since the network can be easily partitioned intosubdomains (the fractures), we have developed a hybrid solver based on domain decomposition. Thisapproach decouples in some sense the flow at the fracture scale from the interactions at the networkscale. The Schur complement, which gathers the unknowns at the intersections of the network, is solvedwith a preconditioned conjugate gradient. We combine Neumann Neumann, defined at the fracturescale, with a global preconditioner, defined at the network scale, based on a deflation formulation.The numerical model and the solver are implemented in the software MPFRAC, which is embeddedinto the scientific platform H2OLab. Our numerical experiments highlight the efficiency of this Schursolver.
“Discontinuous Galerkin Method for Two-Component Miscible Liquid-Gas Porous Media Flows”Alexandre ErnUniversite Paris-Est, CERMICS,Ecole des Ponts, 6& 8 Av. B. Pascal,77455 Marne-la-Vallee cedex 2, France
We consider two-component (typically, water and hydrogen) miscible liquid-gas porous media flowsincluding gas-phase (dis)appearance, as motivated by hydrogen production in underground reposito-ries for radioactive waste. Following Smaı’s Ph.D. thesis (Universite Claude Bernard Lyon, 2009),we formulate the governing equations in terms of liquid pressure and dissolved hydrogen density asmain unknowns, leading mathematically to a nonlinear elliptic-parabolic system of PDEs, in which theequations degenerate when the gas phase disappears. We develop a discontinuous Galerkin methodfor space discretization, combined with a backward Euler scheme for time discretization and an in-complete Newton method for linearization. Numerical examples deal with gas-phase (dis)appearance,ill-prepared initial conditions, and heterogeneous problem with different rock types. This is joint workwith I. Mozolevski (Universidade Federal de Santa Catarina, Brazil).
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“Electrochemical Processes and Porous Media: Mathematical and Numerical Modeling”Jurgen FuhrmannWeierstrass Institute for Applied Analysis and StochasticsMohrenstr. 3910117 Berlin, Germany
Electrochemical effects in porous media are ubiquitous in nature, industry and everyday life. Impor-tant examples are electrochemical energy conversion and storage devices like fuel cells and batteries,where porous electrodes allow to provide a large interface area between electrolytes and solid stateconductors.In electrochemical systems, flow, transport, reactions and electric field are tightly coupled. To in-troduce the general setting of modeling in electrochemical devices, we start with the Nernst-Planck-Poisson system describing the movement of ions due to advection, diffusion and the self-consistentelectric field established by the distribution of charged particles. This system is coupled to electro-chemical reactions on electrode surfaces. As outside of boundary layers, electro-neutrality prevails,this system can be converted to Ohm’s law with special boundary reaction terms. In a porous medium,a further upscaling step results in the porous electrode equations which are a base ingredient of modelsof electrochemical systems containing porous structures.As a result we present a multiphase-multicomponent ansatz in porous media augmented by equationsdescribing the electrostatic potential, which influences transport and reactions in various ways.The implicit Euler, Voronoi box based finite volume method allows to derive a framework for thenumerical implementation of mathematical models based on reaction-diffusion-convection systems.Particular advantages of the method are unconditional stability, positivity, discrete maximum prin-ciple, local and global mass conservation, and efficient ways to solve stationary and time dependentcases. It relies on the ability to create Delaunay meshes conforming to interior and exterior boundaries.We mention challenges connected with the resolution of boundary layers and handling of anisotropies.The talk concludes with results from applications which have been implemented using the approachpresented.
“Optimized Schwarz Waveform Relaxation for Reactive Transport Problems”Laurence HalpernLAGA. University Paris 13.93430 Villetaneuse, France
Schwarz waveform relaxation algorithms have been introduced in the last decade to solve linear prob-lems of various types in parallel by domain decomposition in space. Each subdomain evolves withits own time grid in time windows, and the iteration between the subdomains takes place at the endof the time window. Much attention has been paid earlier to the design of of fast algorithms forlinear problems, by choosing the type and the coefficients of the transmission conditions between thesubdomains [1].In the reactive transport process, a small time scale is needed in a reactive zone localized in theneighbourhood of mobile interfaces between water and gas, whereas larger time scales are involved inthe mildly reactive zone. This is the motivation of the SHP-CO2 project with the french ANR andthe IFPEN. Within this project, we have introduced various types of Schwarz waveform relaxationalgorithms for non-linear systems [2,3]. They are coupled with Krylov acceleration and Newtonalgorithms for the non-linear part. The aim of this talk is to present our latest progress from atheoretical point of view. Numerical aspects will be evaluated on toy problems. These results are ajoint activity with the PhD student Florian Haeberlein and Anthony Michel at IFP, Filipa Caetanoat University Paris 11, J’er’emie Szeftel at ENS, Martin Gander at Geneva University. Applicationsof the strategies to real problems will be presented by Anthony Michel.References[1] D. Bennequin, M. Gander and L. Halpern. A Homographic Best Approximation Problem withApplication to Optimized Schwarz Waveform Relaxation. Math. Comp. 78 (2009), no. 265, 185223.[2] F. Caetano, M. Gander, L. Halpern and J. Szeftel. Schwarz waveform relaxation algorithms forsemilinear reaction-diffusion. Networks and heterogeneous media Volume 5, Number 3, pp 487–505,September 2010.[3]F. Haeberlein, L. Halpern & A. Michel, Krylov subspace accelerators for non-overlapping Schwarzwaveform relaxation methods applied to coupled nonlinear reactive transport systems in the contextof CO2 geological storage simulation. Proceeding DD20, 2011, submitted.
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“Coupled Surface and Saturated/Unsaturated Ground Water Flow in Heterogeneous Media”Ralf KornhuberFreie Universitat Berlin,Institut fur Mathematik,Arnimallee 6, 14195 Berlin
Richards equations for saturated/unsaturated groundwater flow is based on state equations relatingsaturation to capillary pressure. The numerical solution of the resulting degenerate parabolic problemstypically suffers from strong nonlinearities and ill-conditioning in the presence of strongly varyingsaturation. As a remedy, we suggest a solver-friendly discretization based on Kirchhoff transformationwhich can be reinterpreted in physical variables in terms of suitable quadrature rules. In this wayill-conditioning is separated from the numerical solution process. We show convergence and provideerror estimattes This approach is extended to heterogeneous state equations by domain decompositionmethods based on nonlinear transmission conditions. We suggest suitable coupling conditions ofground water flow and shallow water equations for surface water flow. The coupled system is solvedby a Dirichlet-Neumann-type iteration accounting for the multiple time scales. The performance ofthe algorithms is illustrated by numerical computations.
“Multi-scale 3D and 4D Modelling and Simulation in Geosciences”Robert MarschallingerOAW GIScience,Schillerstr. 30,5020 Salzburg
Geoscience computing typically deals with three-dimensional (“3D”) spatially referenced data; inprocess modelling, time enters as an extra, fourth dimension. Mostly, volumes are involved; thus,geoscience modelling and simulation necessitates volume data structures that can handle large rangesof object scale, geometric precision and shape complexity. Solid modelling is state-of-the-art for por-traying volume objects because it backs up the unambiguous representation of arbitrarily shaped 3Dobjects and provides automated analysis and Boolean relationship of the involved solid objects. Muchas in the 2D realm, where areal data can be represented either in vector or raster form, in the 3Ddomain, boundary representation (“B-Rep”) and voxel modelling (“VM”) are used to portray volumedata. B-Rep aggregates the total solid model from self-contained, complexly shaped solid objectsand has its strengths in the quasi-natural presentation and in a straightforward, manual editing ofobjects. By contrast VM, with the roots in 2D raster data processing, is based on tesselating thewhole model universe. VM, as the standard output format of geoscience interpolation and simula-tion algorithms, excels in representing continuous spatial variation and in analytical flexibility. BothB-Rep and VM are generically scale-invariant; i.e., the full scale range covered by geosciences – frommicroscopic to megascopic objects – can be described with B-Rep and VM. Abstracting the geo-science analysis, modelling and simulation frameworks in a 3D modelling universe or in a space-time(hyper)prism, exhaustiveness/sparsity and precision/error of original (measured or acquired) data canbe explored in space and space/time. In the macro or mega scales, because of the high costs of 3Dsubsurface data acquisition (e.g., drilling or geophysical campaigns), the associated modelling uni-verses and space-time (hyper)prisms contain only sparse and clustered original data. This is why,for the macroscopic/megascopic scales, reliable and efficient 3D/4D modelling and interpolation andsimulation algorithms are mandatory to fill the spatial/spatiotemporal “gaps” in the respective mod-elling universes or space-time hyperprisms. Especially in the macro- and mega scales, geostatisticsplays a central role in providing stochastic-based estimation and simulation of spatial and space-timedata and associated incertainty. Toward the other end of the geoscience scale range, data acquisitionin the micro-scale has become straightforward and affordable. Recent advances in destruction-freematerials analysis like micro computed tomography (“µCT”) or Neutron Tomography (“NT”) makethe (micro)structures in geological materials accessible as VMs: paleontologic fossil associations, hardrock textures and sediment structures can be portrayed in detail. Today, the micro-scale geosciencemodelling universes are exhaustively filled with original data! Object based image analysis in its mul-tidimensional flavour (“xd-OBIA”), is essential for meaningful classification of geoscience µCT data:petrographical, sedimentological or paleontological expert knowledge can be successfully incorporatedin the classification process to build precise 3D microstructure VMs from originally noisy, single chan-nel µCT image stacks. Combining the above-mentioned aspects and methods, a novel testbed withstunning research opportunities is opened, cross-fertilizing different research fields: xd-OBIA in com-bination with µCT and NT can be applied to create precise VMs of geoscientific micro-objects. These
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exhaustive data sets can be utilized as “Gold” Standards, the spatial variability of which can bequantified by geostatistical variography and multipe-point geostatistical training images. Sequentiallythinning out the exhaustive data, geostatistical interpolation and simulation can be benchmarked, ina controlled environment of natural structures, to re-build the “Gold” Standard. In the end, with thewell-known paradigm of scale-invariance of geological structures in mind, relevant geostatistical mod-elling and simulation insights derived from geoscience microstructures will hopefully be propagatedback to the macro- and mega scales to create more precise 3D and 4D geoscience models from sparseinput data.
“Time-Space Domain Decomposition for Reactive Transport in Porous Media ”Anthony MichelIFP Energies nouvelles,1 et 4 avenue de Bois-Preau,92852 Rueil-Malmaison Cedex - France
In this talk I will present applications of time-space domain decomposition techniques to multi-speciesreactive transport problems. This is a joint work with F. Haeberlein and L. Halpern which contributesto the ANR-SHPCO2 project on High Performance Simulation for CO2 Geological Storage. Thetheoretical background will be presented in another talk by L. Halpern.
“Effective Pressure Interface Law for Transport Phenomena between an Unconfined Fluid and a PorousMedium using Homogenization”Andro MikelicUniversite Lyon 1,Departement de mathematiques and Institut Camille Jordan,Villeurbanne, France
We present modeling of the incompressible viscous flows in the domain containing unconfined fluidand a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interfacecondition was undertaken by Jager and Mikelic [SIAM J. Appl. Math. 60 (2000), p. 1111-1127] usingthe homogenization method. So far the interface law for the pressure was conceived and confirmedonly numerically. In this article we derive the Beavers and Joseph law for a general body force byestimating the pressure field approximation. Different than in the Poiseuille flow case, the velocityapproximation is not divergence-free and the precise pressure estimation is essential. Finally, this newestimate allows us to justify rigorously the pressure jump condition using the Navier boundary layer,already used to calculate the constant in the law by Beavers and Joseph.
This is a joint work with Anna Marciniak-Czochra (IWR and BIOQUANT, Universitat Heidelberg,Germany)
“Multiscale Modeling for CO2 Storage”Jan Martin NordbottenDepartment of MathematicsUniversity of Bergen
The large spatial and temporal scales over which the evolution of stored CO2 must be assessed, forcesus to consider coarse spatial and temporal discretizations. Such discretizations cannot reasonably beexpected to be convergent to the standard equations of porous media flow, which are valid on muchfiner scales, and have solution structures that cannot be resolved on coarse grids.Therefore, there is a need to develop coarse-scale models that are suitable to be discretized by thecomputational grids we can afford.In this talk, we discuss the framework for developing such coarse models, emphasizing the developmentof both coarse 3D and 2D models for CO2 storage in geological formations. We will pay particularattention to cases where the parameter functions change not only quantitatively, but also qualitatively,and highlight the novel computational considerations that arise as a consequence thereof.
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“An Abstract Two-Level Additive Schwarz Method for Systems with High Contrast Coefficients”Clemens PechsteinInstitute of Computational MathematicsJohannes Kepler UniversityAltenberger Str. 69, 4040 Linz (A)[email protected]
Robust domain decomposition solvers for the finite element discretization of scalar elliptic problemswith heterogeneous (high contrast, or multiscale) coefficients have been studied for some time. Thisincludes both iterative substructuring methods and overlapping Schwarz methods. Using weightedPoincare inequalities and/or spectral theory, robustness can theoretically be guaranteed in a largevariety of cases. However, there is only little theory available for systems of PDEs, such as linearizedelasticity or problems in H(curl).In this talk, we consider an abstract framework for overlapping Schwarz methods for variationallyposed systems of PDEs. Essentially, we only require positive semi-definite element stiffness matricesand their connectivity. As usual, the local subspaces are defined on overlapping subdomains. The keyingredient is an abstract coarse space constructed from a particular eigenproblem in the overlap of eachsubdomain as well as an algebraic partition of unity. We provide a rigorous and robust convergencetheory and show some numerical results for the cases of Darcy and linearized elasticity.
The talk is on joint work with V. Dolean (Universite de Nice), P. Hauret (Michelin), F. Nataf (UniversiePierre et Marie Curie), R. Scheichl (University of Bath), and N. Spillane (Universite Pierre et MarieCurie).
“Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling”Martin VohralıkLaboratoire Jacques-Louis Lions,Universite Pierre et Marie Curie (Paris 6),B.C. 187, 4 place Jussieu,75252 Paris, France
We consider discretizations of a model elliptic problem by means of different numerical methods ap-plied separately in different subdomains, termed multinumerics, coupled using the mortar technique.The grids need not match along the interfaces. We are also interested in the multiscale setting, wherethe subdomains are partitioned by a mesh of size h, whereas the interfaces are partitioned by a mesh ofmuch coarser size H, and where lower-order polynomials are used in the subdomains and higher-orderpolynomials are used on the mortar interface mesh. We derive several fully computable a posteriorierror estimates which deliver a guaranteed upper bound on the error measured in the energy norm.Our estimates are also locally efficient and one of them is robust with respect to the ratio H/h underan assumption of sufficient regularity of the weak solution. The present approach allows bounding sep-arately and comparing mutually the subdomain and interface errors. A subdomain/interface adaptiverefinement strategy is proposed and numerically tested. This is a joint work with Gergina V. Penchevaand Mary F. Wheeler (UT Austin) and Tim Wildey (Sandia National Labs).
“Evaluating Long Term CO2 Storage in Saline Aquifers”Mary Fanett WheelerDirector, Center for Subsurface Modeling,Institute for Computational Engineering and Sciences,The University of Texas at Austin,201 East 24th Street,ACE 5.324 — Campus Mail C0200,Austin, TX 78712
Currently the world obtains more than 80% of its energy (coal, oil, gas) for the global economy fromthe subsurface. The byproducts of consuming these fuels such as greenhouse gas accumulation in theatmosphere are serious and potentially devastating. Renewables such as solar energy and wind farmsmay take many decades to develop before becoming economically feasible alternatives capable of re-placing or reducing fossil energy usage. A major hope for the near future is geologic sequestration,
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a proven means of permanent CO2 greenhouse-gas storage. This method involves injecting CO2 ,generally in supercritical form, directly into underground geological formations. Oil and gas fields,saline formations, unmineable coal seams, and saline-filled basalt formations are considered as storagesites. Various physical processes such as highly impermeable caprock and geochemical trapping mech-anisms would prevent the CO2 from escaping to the surface. Unfortunately, it is difficult to designand manage such efforts. Predictive computational simulation may be the only means to account forthe lack of complete characterization of the subsurface environment, the multiple scales of the variousinteracting processes, the large areal extent of storage sites such as saline aquifers, and the need forlong time predictions.In this presentation we discuss multiscale, multiphysics algorithms for accurately predicting the fate ofinjected CO2 in conditions governed by multiphase flow, rock mechanics, multicomponent transport,thermodynamic phase behavior, chemical reactions within both the fluid and the rock, and the couplingof all these phenomena over multiple time and spatial scales. Both theoretical and computationalresults will be presented.
“A New Coupling Concept for Two-Phase Compositional Porous Media and Single-Phase CompositionalFree Flow”Barbara WohlmuthFakultat Mathematik, TU Munchen
Joint work with Rainer Helmig, Andreas Lauser, Klaus Mosthaf (IWS Uni Stuttgart).
Flow and transport processes in domains composed of a porous medium and an adjacent free-flowregion appear in a wide range of industrial, environmental and medical applications. Although of highrelevance, the mathematical modeling and the numerical simulation remains challenging. This talkaddresses two issues: firstly how to transfer information between the two sub-system and secondlyhow how to solve numerically phase changes within a sub-system.Two basic strategies for the description of mass and momentum transfer in coupled free and porous-medium flow on the Darcy scale can be identified. In the single-domain approach, one set of equationsis assumed to be valid in the whole domain and the coupling is realized via a transition zone, wherematerial parameters are varied. In the two-domain approach two sets of equations are used within thedifferent subdomains. To obtain a well-posed setting, additional transfer conditions at the interfacehave to be imposed. So far these concepts have been developed for single-phase single-component sys-tems describing the coupling for mass and momentum. However, in many applications compositionalmulti-phase flow occurs. Here, we generalize the two-domain approach for a non-isothermal two-phase two-component model and introduce suitable coupling conditions. The interface is assumed tobe simple in the sense that it has no thickness and cannot store mass, momentum or energy. Couplingconditions for mass, momentum and energy are defined based on flux continuity and thermodynamicequilibrium. Moreover, the coupling concept employs the Beavers-Joseph concept in the knowledgeof its limitations to parallel, single phase flow. The presented model may also be used in applicationssimilar to evaporation, e.g. the design of industrial drying processes.Many practically relevant multi-phase problems for flow and transport in porous media require knowl-edge of the composition of the involved fluid phases in order to adequately approximate the underlyingphysical processes. One major issue of many contemporary multi-phase multi-component models arephase transitions. A sound incorporation of these transitions into the flow model is essential sincethe appearance or disappearance of a fluid phase changes the underlying physics of the local problem.If not handled properly, this tends to cause numerical oscillations when solving the strongly nonlin-ear system of partial differential equations. Currently, there are two common classes of multi-phase,multi-component models when it comes to determining the local thermodynamic state. The first classuses a flash calculation which determines the local thermodynamic state from the overall mass of theindividual components. Flash calculations are stable in regard to phase transitions, but exhibit twomajor drawbacks: Firstly, to get well-defined fluid pressures, they require to assume that all fluidphases are compressible; secondly, they tend to be computationally expensive because, in general,they imply that a non-linear system of equations of the size of all thermodynamic quantities relevantfor the partial differential equations needs to be solved. The second class of models locally adapts theset of primary variables to the local phase state. This externally imposed phase state is then used forthe calculation until the results become physically inconsistent – which is indicated, for example, bynegative saturations. When such a condition is detected at a given spatial location, the set of presentphases is altered and the primary variables are switched to physically meaningful quantities. For thisreason, this approach is usually referred to as primary variable switching (PVS). Compared to flash
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calculations, this approach is locally more efficient, since the thermodynamic state can be calculatedindependently for each fluid phase. However, quite often numerical oscillations can be observed whichthen result in extremely small time-steps or even a break down of the algorithm. Hence, the secondgoal of the present contribution is to meet the demand for a robust and efficient implicit numericalscheme that is capable of handling phase transitions.To do so, we formulate the conditions for the local presence of fluid phases as a set of so-called comple-mentarity or Karush–Kuhn–Tucker (KKT) conditions. Mathematically, this leads to the structure ofvariational inequality. As similar conditions also occur in other important applications like contact orobstacle problems, there exist many approaches of treating these complimentarity constraints. Here wemake use of the fact that the KKT conditions can equivalently be reformulated as a non-differentiablebut semismooth equation, termed nonlinear complementarity function (NCP). Combined with thebalance equations, a system of nonlinear equations is obtained that can be solved by means of asemismooth Newton method with locally superlinear convergence. As the KKT conditions and thenon-linearities of the material are handled within the same Newton loop, a nested iteration for thedetermination of the local phase state is avoided.
“Mortar Multiscale Framework for Stokes-Darcy Flows”Ivan YotovDepartment of Mathematics, University of Pittsburgh
We discuss numerical modeling of Stokes-Darcy flows based on the Beavers-Joseph-Saffman interfaceconditions. The domain is decomposed into a series of small subdomains (coarse grid) of either Stokesor Darcy type. The subdomains are discretized by appropriate Stokes or Darcy finite elements. Thesolution is resolved locally (in each coarse element) on a fine grid, allowing for non-matching gridsacross subdomain interfaces. Coarse scale mortar finite elements are introduced on the interfaces toapproximate the normal stress and impose weakly continuity of the velocity. Stability and a priorierror analysis is presented for fairly general grid configurations. By eliminating the subdomain un-knowns the global fine scale problem is reduced to a coarse scale interface problem, which is solvedusing an iterative method. We precompute a multiscale flux basis, solving a fixed number of finescale subdomain problems for each coarse scale mortar degree of freedom, on each subdomain inde-pendently. Taking linear combinations of the multiscale flux basis functions replaces the need to solveany subdomain problems during the interface iteration. Numerical results for coupling Taylor-HoodStokes elements with Raviart-Thomas Darcy elements are presented.This is joint work with Ben Ganis, University of Texas at Austin, Vivette Girault, Paris VI, andDanail Vassilev, Rensselaer Polytechnic Institute
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Abstracts for Posters
“Multiscale Simulations of Non-Darcy’s Flows”Sergey AlyaevUniversitetet i Bergen, Matematisk institutt,Postboks 7803, 5020 BERGEN
The standard approximation for flow-pressure relationship in porous media is Darcy’s law. It isjustified and gives good results for slow flows, however in a number of applications with faster flowregimes it breaks down. These applications include flows that may occur near wells and in fracturedregions in subsurface. Moreover, those flows are common for industrial and near surface porous media.Darcy’s law can be derived by means of homogenization from the Stokes’ equation on the pore scale.Stokes’ equation does not take into account non-linear effects of the flows that are of importance forflows with larger Reynolds numbers. The standard continuum mechanics approach for those casesis using non-linear Navier-Stokes equations for the fine scale. To perform larger scale simulations ofnon-linear flow solving the Navier-Stokes equation is not feasible due to time and memory limitations.As an alternative we apply multiscale techniques.We present a heterogeneous multiscale method that on the coarse scale only assumes conservationof mass on control volumes, that is, no phenomenological Darcy-type relationship for velocity ispresumed. The fluid fluxes are instead provided by a fine scale Navier-Stokes mixed finite elementsolver. This methodology, that we will refer to as multiscale simulation is different from a commonmultiscale modelling procedure of upscaling. The difference is, that in the case of MS modellingone chooses the coarse scale model in advance based on physical reasoning and then gets effectiveparameters from solving some sort of fine scale equations. The advantage of MS simulation is thatthe results of it will coincide with Darcy’s law (with upscaled parameters) without increasing thecomputational time asymptotically for the slow flows. Yet it will deliver better results for faster flowregimes without the need of choosing another coarse scale model by a user.We consider application of the methodology in the context of
• Weakly compressible near-well flows with oscillating boundary conditions;• Porous media with large pores lacking scale separation;• Particle transport in porous media.
The work is being carried out in collaboration with Jan M. Nordbotten and Eirik Keilegavlen.
“Micromechanics of Geomaterials and Geocomposites.”Radim BlahetaInstitute of Geonics AS CR,Studentska 1768,708 00 Ostrava-Poruba, Czech Republic
The poster addresses three topics. The first one is the micro FEM analysis of processes in geomaterialsand geocomposites (which arose from grouting for improving the geomaterials). We consider processesof deformation and flow in porous media and the FEM modelling should give answer to the questionswhat are the effective properties, how the changes in microstructure influence the macroscale behaviourand also how to optimize the microstructure. The second topic is the iterative solution (joint work withO. Axelsson and V. Sokol). The micro FEM simulations lead to the solution of large-scale systems,which are frequently very ill-conditioned due to oscillations and high jumps (contrast) in materialcoefficients. Therefore, we are motivated in seeking parallelizable and robust iterative solution methodsand we shall present here some results concerning the variants of multi-level Schwarz methods withcoarse spaces constructed by aggregations. We also touch the construction of block preconditioners formixed FEM solution of Darcy flow problems. The third topic is inverse analysis (joint work with R.Hrtus and R. Kohut). We are interested in micro FEM analysis, which uses input based on assigningthe local material properties according to tomography scans (providing the material distribution) andproperties of individual material components. These properties are determined with the aid of testsof macroscale behaviour on the specimens with known material distribution and solution of inverseproblems for identification of properties of selected material components. We describe this approachand provide some results for the case of coal-PE resin geocomposites.
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“Modelling, Simulation and Optimization of the Microstructure of SOFC Porous Cathodes”Thomas CarraroInstitute for Applied Mathematics, University of Heidelberg
The performance of a solid oxide fuel cell (SOFC) is strongly affected by electrode polarization losses,which are related to the composition and the microstructure of the porous materials. A model that candecouple the effects associated to the geometrical arrangement, shape and size of the particles on oneside and the material properties on the other can give a relevant improvement in the understandingof the underlying processes.A porous mixed ionic and electronic conducting (MIEC) cathode was reconstructed by a tomographytechnique based on focused ion beam coupled with scanning electronic microscope (FIB/SEM). Thedetailed geometry of the microstructure is used for 3D calculations of the electrochemical processes inthe electrode. The area specific resistance (ASR) of the reconstructed porous cathode is calculated asa performance index. A model based on the finite element method (FEM), which complexity requiresthe use of high performance computing techniques (HPC), has been developed.In this work we show the comparison of the 3D microstructure model with a 1D homogenized one.A trusted reduced model by homogenization can be used to optimize the design of experiments andincrease the precision of a fitting procedure. First steps towards the optimal experimental design forimpedance measurements for SOFC are shown.
“Numerical Upscaling in Porous Media”Christian EngwerInstitut fur Numerische und Angewandte MathematikUniversitat Munster
For the simulation of transport processes in porous media effective parameters for the physical pro-cesses on the target scale are required. Numerical upscaling can help where experiments are notpossible, or hard to conduct.Bastian and Engwer proposed an Unfitted Discontinuous Galerkin (UDG) method for PDEs on do-mains with a complicated geometric shape. This method is well suited for simulations on the porescale. The method uses finite element meshes which are significantly coarser then those required bystandard conforming finite element approaches and is flexible enough to be used for elliptic, hyper-bolic and parabolic problems. Essential boundary conditions are incorporated using DiscontinuousGalerkin discretization on a cut-cell mesh.We apply this method to numerical upscaling using direct simulation on the pore scale and presentdifferent applications. The method is robust with respect to computations on coarse meshes.
“Preconditioning of Non-Conforming FEM Systems”Ivan GeorgievComputational Methods for Direct Field Problems,Radon Institute for Computational and Applied Mathematics (RICAM),Altenberger Strasse 69,A-4040 Linz, AUSTRIA,[email protected]
Joint work with J. Kraus, RICAM.
We present different approaches for preconditioning of linear algebraic systems obtained from non-conforming discretizations of scalar elliptic and linear elasticity problems. We consider interior penaltydiscontinuous Galerkin discterizations of linear elasticity equations and we propose a space splittingwhich gives rise to uniform preconditioners. For the problem with Dirichlet boundary conditionsimposed on the entire boundary the linear non-conforming finite elements provides a locking-freediscretization. We devise an optimal order multilevel method for the considered 3D pure displacementelasticity problem. Finaly we present a two-level method for the scalar elliptic problems with highlyvarying coefficients. The proposed generalized hierarchical basis yields a robust splitting with respectto mesh size and jump discontinuities of the coefficients.
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“Design of Numerical Methods to Simulate Models of a Solid Oxide Fuel Cell”Christian GollInstitute of Applied Mathematics, University of Heidelberg, Germany
The motivation of this work is to model the behaviour of a reactive gas mixture in the anode and theoverlying gas channel of a solid oxide fuel cell (SOFC). Via impedance measurements, polarizationlosses arising during the operation of the fuel cell can be identified. To achive this, a coupled systemof PDEs has to be solved numerically. This system contains (Navier-)Stokes and Darcy equationsto characterize the flow as well as the Stefan-Maxwell/Dusty-Gas model to describe diffusion andreaction of the species.Over the last years, a lot of work has been put into the coupling conditions for the Stokes/Darcy-systemalong the interface between fluid and porous region. In 2001, Jaeger, Mikelic and Neuss proposed aset of conditions for the laminar viscous flow over a porous bed, which actually allows to decouple theproblem and make it easier to compute. We compare these ’decoupling conditions’ numerically witha fully coupled approach.
“Impact on the Surface Temperature due to the Modifications of Underlying Land Surface Conditions: AStudy over Western India”Sridhara NayakCenter for Oceans, Rivers, Atmosphere and Land Sciences;Indian Institute of Technology, Kharagpur;Kharagpur 721 302, INDIA
Joint work with M. Mandal.
The important anthropogenic influences on global warming are greenhouse gases and changes in landuse & land cover. It is well accepted that the greenhouse gases are main causes of global warmingand recent climate change, but changes in land use & land cover are also contributing to a certainextent. The changes in land use & land cover modify the underlying land surface conditions. Themodifications in land surface conditions change the interaction between land surface and atmosphere,i.e., the exchange of energy and moisture between land surface and atmosphere. Presence of vege-tation modifies surface albedo, absorption of solar radiation, sensible and latent heat fluxes. Hence,brings in changes in the earth’s radiation balance. The changes in land surface conditions modify theevapotranspiration and hence moisture exchange. The exchange of energy and moisture contributessignificantly in determining local, regional and even global climate. The modifications in land surfaceconditions result in emission or removal of CO2 in the atmosphere and thus contributing regionalwarming or cooling. In this study we have two objectives. First attempt has been made to investigatesurface temperatures during 1973-2009 over Western India and the impact on the surface temperaturedue to the modifications in land surface conditions the over the region. This is based on temperaturedatasets from observation as obtained from India Meteorological Department and NCEP/NCAR re-analysis (NNRP1). The impact on the surface temperature due to the modifications in land surfaceconditions is estimated based on deviation in temperature in the observation and reanalysis datasets.The observed temperature datasets indicates warming over Western India is 0.13C per decade. Theresult shows the modifications in land surface conditions during 1973-2005 contributing to this warm-ing is 0.05C per decade. Second attempt has been made to investigate the changes in land use & landcover over the region during the period 1975-2005. This is investigated based on four land use & landcover datasets as obtained from Global Land Cover Facility (GLCF). The change in land surfaces isinvestigated by quantifying the land covered with various land use & land cover types. The compari-son of the change in surface temperature with the change in land surface indicates the warming dueto the modifications in underlying land surface conditions is because of the reduction of area underopen forest and subsequent increase of the area under agricultural land.
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“Modeling Two-phase Flow with Disappearing Gas Phase”Rebecca NeumannUniversity of HeidelbergInterdisciplinary Center for Scientific ComputingIm Neuenheimer Feld 36869120 Heidelberg
Carbon Capture and Storage (CCS) is a recently discussed new technology, aimed at allowing anongoing use of fossil fuels while preventing the produced CO2 to be released to the atmosphere. CSSinvolves two components (water and CO2) in two phases (liquid and gas). To model the process,a multiphase flow equation is used. One of the big problems arising in two-phase flow simulationsis the disappearance of the gas phase, which leads to a degeneration of the equations satisfied bythe saturation. A standard choice of primary variables, which is the pressure of one phase and thesaturation of the other phase, cannot be applied here.We developed a new approach using the pressure of the nonwetting phase and the capillary pressureas primary variables. We implemented this new choice of primary variables in the DUNE simulationframework and present the numerical results for some test cases.
“Robust Preconditioners for General SPD Operators”Joerg WillemsComputational Methods for Direct Field Problems,Radon Institute for Computational and Applied Mathematics (RICAM),Altenberger Strasse 69,A-4040 Linz, AUSTRIA,[email protected]
An abstract setting for robustly preconditioning symmetric positive definite (SPD) operators is pre-sented. The method belongs to the class of additive Schwarz preconditioners, and it requires onlyrather mild assumptions naturally satisfied by operators resulting from the discretization of severalimportant partial differential equations. The term ”robust” refers to the property of the conditionnumbers of the preconditioned systems being independent of mesh parameters and problem parame-ters. Important instances of such problem parameters are in particular (highly varying) coefficients.The core of this method is the construction of the coarse space based on the solution of local gen-eralized eigenvalue problems. The abstract framework is applied to the scalar elliptic equation andBrinkman’s equations with coefficients varying over several orders of magnitude. Since Brinkman’sequations modeling flows in highly porous media constitute a saddle point problem, the abstractframework is not immediately applicable. This difficulty is overcome by resorting to the stream func-tion formulation. The latter is, however, only used for the coarse space construction, while the actualsolution process is carried out in the primal variables, i.e., velocity and pressure. Several numericalexamples are presented to illustrate the properties of the method.
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List of Participants
Alyaev Sergey Universitetet i Bergen [email protected]
Andreev Roman SAM, ETH Zurich [email protected]
Arbenz Peter ETH Zurich, Chair ofComputational Science
Bastian Peter University of Heidelberg [email protected]
Becker Jurgen Fraunhofer ITWM,Kaiserslautern
Blaheta Radim Institute of Geonics AS CR,Ostrava, CZ
Bourgeat Alain UCB Lyon 1 [email protected]
Buck Marco Fraunhofer Institute forIndustrial Mathematics
Caiazzo Alfonso WIAS Berlin [email protected]
Carraro Thomas University of Heidelberg [email protected]
Challa Durga Prasad RICAM, Linz [email protected]
Cliffe Andrew University of Nottingham [email protected]
Collis Joe University of Nottingham [email protected]
Dahle Helge K. University of Bergen, Norway [email protected]
Dashti Masoumeh University of Warwick,Mathematics Institute
Discacciati Marco Universitat Politecnica deCatalunya, Barcelona
Efendiev Yalchin Texas A&M University [email protected]
Engl Heinz RICAM & University of Vienna [email protected]
Engwer Christian Universitat Munster [email protected]
Erhel Jocelyne Inria [email protected]
Ern Alexandre University Paris-Est, CERMICS [email protected]
Frank Elisabeth Johannes Kepler UniversityLinz
Freitag Melina University of Bath [email protected]
Fuhrmann Jurgen Weierstrass Institute Berlin [email protected]
Gahalaut Krishan P.S. RICAM, Linz [email protected]
Georgiev Ivan RICAM, Linz [email protected]
Goll Christian University of Heidelberg [email protected]
Halpern Laurence Universite Paris 13 [email protected]
Hrtus Rostislav Institute of Geonics of the ASCR, v.v.i., Ostrava, CZ
Kar Manas RICAM, Linz [email protected]
Karer Erwin RICAM, Linz [email protected]
Kollmann Markus Doctoral ProgramComputational Mathematics,Linz
Kolmbauer Michael Johannes Kepler UniversityLinz
Kornhuber Ralf FU Berlin [email protected]
Kraus Johannes RICAM, Linz [email protected]
Langer Ulrich Johannes Kepler UniversityLinz
Livshits Irene Ball State University [email protected]
Mahmoud Alaa Al-Azhar University, Faculty ofScience
Marschallinger Robert OAW GIScience [email protected]
Mataln Marianne Montanuniversitat Leoben [email protected]
Melenk Jens Markus TU Wien [email protected]
Michel Anthony IFP Energies nouvelles [email protected]
Mikelic Andro Universite Lyon 1, Deptmathematiques and ICJ
22
Nayak Sridhara Indian Institute of Technology,Kharagpur
Neumann Rebecca University of Heidelberg [email protected]
Nguyen Trung Thanh RICAM, Linz [email protected]
Nordbotten Jan Martin University of Bergen [email protected]
Oberaigner Eduard Montanuniversitat Leoben [email protected]
Park Minho University of Nottingham [email protected]
Pechstein Clemens Johannes Kepler UniversityLinz
Peterseim Daniel Humboldt-Universitat zuBerlin, Institut fur Mathematik
Scheichl Robert University of Bath [email protected]
Sini Mourad RICAM, Linz [email protected]
Teckentrup Aretha University of Bath, Departmentof Mathematical Sciences
Tomar Satyendra RICAM, Linz [email protected]
Ullmann Elisabeth University of Bath [email protected]
Vohralık Martin LJLL, University Paris 6 [email protected]
Wachsmuth Daniel RICAM, Linz [email protected]
Wheeler Mary F. The University of Texas atAustin
Willems Jorg RICAM, Linz [email protected]
Wohlmuth Barbara Technische UniversitatMunchen
Yang Huidong RICAM, Linz [email protected]
Yotov Ivan University of Pittsburgh [email protected]
Zikatanov Ludmil The Pennsylvania StateUniversity
23
Mon
day
Tue
sday
Wed
nesd
ayT
hurs
day
Frid
ay
8:30
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pen
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Din
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40m
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Aft
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each
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are
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