Simulation of Flow in Porous Media and Applications in Waste ...

Workshop on
Simulation of Flow in Porous Media and
Applications 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 flow
problems are inherently multiscale in space due to the large variability of material properties and in time
due to the coupling of many different physical processes, such as advection, diffusion, reaction and phase
exchange. Subsurface flow models still need considerable development. For example, nonequilibrium
effects, 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 workshop
to the Workshops 2 and 4. Computational issues in subsurface flows include the treatment of strong
heterogeneities and anisotropies in the models, the efficient solution of transport-reaction problems with
many species, treatment of multiphase-multicomponent flows and the coupling of subsurface flow models
to surface flow models given by shallow water or Stokes equations. With respect to energy and the environment,
in particular the modelling and simulation of radioactive waste management and sequestration
of CO2 underground have gained high interest in the community in recent years. Both applications provide
unique challenges ranging from modelling of clay materials to treating very large scale models with
high-performance computing.
The workshop will bring together key numerical mathematicians whose interest is in the analysis and
computation of multiscale subsurface flow and practitioners from engineering and industry whose interest
is in the applications of these core problems. Particular problems to be considered will be (i) The design
of 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 as
Darcy, Brinkman, Stokes, Richards and shallow water); (iii) Fast linear algebra solvers for subsurface
flow problems in heterogeneous media; (iv) Applications of the above methods and ideas in energy and
the environment, such as deep geological disposal of radioactive waste or carbon capture and storage
underground.
The workshop will also include a special session on “Fuel Cell Modeling” which leads to similar
mathematical problems as subsurface flow simulation.
Workshop Organizers
Peter Bastian, Heidelberg University, Germany
Johannes Kraus, Johann Radon Institute, Austria
Robert Scheichl, University of Bath, UK
Mary 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 Multiscale
Simulation & Analysis in Energy and the Environment, hosted by the Johann Radon Insitute for
Computational 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 a
huge surge in energy requirements which in turn puts at risk our entire bio-sphere. It is of paramount
importance to predict these risks and to develop better solutions for the future. One of the central tasks
is the accurate simulation of multiphase flow above and under ground. The risk analysis and uncertainty
quantification, as well as the assimilation of data require statistical tools and efficient solvers for stochastic
and deterministic PDEs as well as for the associated inverse problems. The key features that make it
extremely hard to predict these physical phenomena accurately are the multiple time and length scales
that arise, as well as the lack of and uncertainty in data. Because of the highly varying scales involved, the
resolution of all scales is currently impossible even on the largest supercomputers. While there is a fairly
long 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 at
the cutting edge of rigorous numerical analysis for multiscale (direct and inverse) problems the emerging
challenges in the quantitative assessment of the risks and uncertainties of atmospheric and subsurface
flow, 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 and
the 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. Jörn Behrens (KlimaCampus, Universität Hamburg) on
“Tsunami Früh-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, Germany
Jörg Willems, RICAM (Coordinator) Mike Cullen, MET Office, Exeter, UK
Johannes Kraus, RICAM (Co-Coordinator) Heinz Engl, RICAM & University of Vienna, Austria
Erwin Karer, RICAM (Co-Coordinator) Melina Freitag, University of Bath, UK
Ivan G. Graham, University of Bath, UK
Ulrich Langer, RICAM & University of Linz, Austria
Markus Melenk, TU Vienna, Austria
Robert Scheichl, University of Bath, UK (Chair)
Mary F. Wheeler, University of Texas at Austin, USA

Contents
Information 2
Workshop Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Social Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Restaurants and Cafes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Program 5
Posters 7
Abstracts 8
Abstracts for Posters 18
List of Participants 22
1

Information
Workshop Information
Registration. The workshop registration will be on October 3rd, 2011 from 8:30 - 9:10 next to the
seminar room SP2 416 on the 4th floor of the Science Park Building 2 (see floor plan). Participants
that 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 upon
registration.
Campus plan and overview map as well as a floor plan of the 4th floor of the workshop venue (Science
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 Science
Park 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 registration.
Social Events
Welcome Reception & Poster Session. Monday, October 3th, 2011, 5:00 pm, at the 4th floor of the
Science Park Building 2.
Conference Dinner. Thursday, October 6th, 2011, 7:00 pm, at the restaurant “Kepler’s“, situated in
the 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: “KHG
Linz”)
• 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 “Hörsaaltrakt” - see overview map)
• Cafe “Sassi” - coffee, drinks and small snacks (located in the building “Johannes Kepler Universität”
- 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. You
can 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.
2

Orientation/ Local Transport. From the railway station you have to take tram number 1 or 2 in
direction “Universität”. It takes about 25 minutes to reach the desired end stop “Universität”.
In order to get to the city center of Linz (“Hauptplatz”) and back you have to take again tram
number 1 or 2 (about 20 minutes). For more information see www.ricam.oeaw.ac.at/location/.
Taxi Numbers.
+43 732 6969 Oberösterreichische 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 Sommerhaus
133 General emergency number for the police
144 General emergency number for the ambulance
More information about RICAM can be found at www.ricam.oeaw.ac.at. See also the Special
Semester webpage www.ricam.oeaw.ac.at/specsem/specsem2011/ for additional information.
Figure 1: 4th floor of Science Park Building 2.
Figure 2: Campus plan
3

Figure 3: Overview map
4

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)
10:10 - 10:40 Coffee Break
“Evaluating Long Term CO2 Storage in Saline Aquifers”
10:40 - 11:30 Jan Martin Nordbotten (University of Bergen)
11:30 - 14:00 Lunch Break
“Multiscale Modeling for CO2 Storage”
14:00 - 14:50 Martin Vohralík (Université Pierre et Marie Curie (Paris 6))
14:50 - 15:20 Coffee Break
“Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics,
and Mortar Coupling”
15:20 - 16:10 Barbara Wohlmuth (Fakultät Mathematik, TU München)
“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. Université Paris 13)
10:10 - 10:40 Coffee Break
“Optimized Schwarz Waveform Relaxation for Reactive Transport Problems”
10:40 - 11:30 Anthony Michel (IFP Energies nouvelles)
11:30 - 14:00 Lunch Break
“Time-Space Domain Decomposition for Reactive Transport in Porous Media ”
14:00 - 14:50 Andrew Cliffe (University of Nottingham)
14:50 - 15:20 Coffee Break
“What should we do with Radioactive Waste?”
15:20 - 16:10 Robert Marschallinger ( ÖAW GIScience)
“Multi-scale 3D and 4D Modelling and Simulation in Geosciences”
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Wednesday, October 5th
08:30 - 09:20 Jürgen Becker (Fraunhofer ITWM)
“Pore-Scale Modelling of Porous Layers Used in Fuel Cells”
09:20 - 10:10 Andro Mikelić (Université Lyon 1)
10:10 - 10:40 Coffee Break
“Effective Pressure Interface Law for Transport Phenomena between an Unconfined
Fluid and a Porous Medium using Homogenization”
10:40 - 11:30 Jürgen Fuhrmann (Weierstrass Institute Berlin)
11:30 - 14:00 Lunch Break
“Electrochemical Processes and Porous Media: Mathematical and Numerical Modeling”
14:00 - 14:50 Marco Discacciati (Universitat Politècnica de Catalunya, Barcelona)
14:50 - 15:20 Coffee Break
“Coupling Free and Porous-Media Flows: Modeling, Analysis, and Numerical Approximation”
15:20 - 16:10 Ivan Yotov (University of Pittsburgh)
Thursday, October 6th
“Mortar Multiscale Framework for Stokes-Darcy Flows”
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 (Université Lyon 1 - UCB, France)
10:10 - 10:40 Coffee Break
“Modeling Compressible Multiphase Flow and Transport in Saturated-Unsaturated
Porous Media: Phase Appearance-Disappearance. Application to Gas Migration
in Underground Nuclear Waste Repository”
10:40 - 11:30 Alexandre Ern (Université Paris-Est, CERMICS)
11:30 - 14:00 Lunch Break
“Discontinuous Galerkin Method for Two-Component Miscible Liquid-Gas Porous
Media Flows”
14:00 - 14:50 Peter Bastian (Universität Heidelberg)
14:50 Coffee Break
“Numerical Solution of Compositional Two-Phase Flow in Porous Media”
19:00 Conference Dinner
6

Friday, October 7th
08:30 - 09:20 Yalchin Efendiev (Texas A&M University)
“Local-Global Multiscale Model Reduction Techniques for Flows in Heterogeneous
Porous Media”
09:20 - 10:10 Clemens Pechstein (Johannes Kepler Universität Linz)
10:10 - 10:40 Coffee Break
“An Abstract Two-Level Additive Schwarz Method for Systems with High Contrast
Coefficients”
10:40 - 11:30 Ralf Kornhuber (Freie Universität Berlin)
11:30 Closing
Posters
“Coupled Surface and Saturated/Unsaturated Ground Water Flow in Heterogeneous
Media”
The poster session will take place on the 4th floor of the 2nd Science Park Building. It will start
at 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 für Numerische und Angewandte Mathematik, Universität Münster)
“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”
7

Abstracts
“Numerical Solution of Compositional Two-Phase Flow in Porous Media”
Peter Bastian
Universität Heidelberg
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
Im 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 flow
in heterogeneous media. It is based on a wetting-phase pressure/capillary pressure formulation and
assumes the diffusion-dominated regime. These primary variables are continuous when both phases
are 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 space
dimensions. For the time discretization diagonally implicit Runge-Kutta schemes are employed to
obtain a formally higher-order method in space and time. Numerical comparison with a cell-centered
finite volume method using full upwinding and implicit Euler shows that the new scheme achieves
very accurate solutions on rather coarse grids.
The second scheme treats compositional two-phase flow with phase disappearance. Based on a
nonwetting-phase pressure/capillary pressure formulation the scheme can handle the disappearance
of the nonwetting phase without switching of variables or adding complementarity constraints. Applications
of the method to the MoMas phase disappearance benchmark and a CO2 sequestration
benchmark are presented.
The last part of the talk will illustrate in some detail the software implementation of these and other
numerical schemes within the DUNE software framework (http://www.dune-project.org). This
framework offfers great flexibility for implementing state-of-the-art discretization schemes and solvers
while 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”
Jürgen Becker
Fraunhofer ITWM,
Fraunhofer-Platz 1,
67663 Kaiserslautern
In a proton exchange membrane (PEM) fuel cell a proton-conducting polymer membrane separates
anode and cathode. The membrane, together with catalyst and diffusion layers on both sides, forms
the membrane electrode assembly (MEA). This MEA consists of several porous layers on both the
cathode 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 possible
by 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 pore
morphology 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, and
3. how to validate this approach.
The 3D structure models are created using stochastic processes; For example, GDL models are created
by placing fibres randomly using an anisotropic direction distribution. These fibres may be straight
or bent, where the bending is determined by its own random process. For MPL and CL, agglomerate
structures of carbon particles are created randomly.
8

Using these 3D models, the effective properties of the layers can be predicted by solving the appropriate
partial 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 of
water at the cathode, are determined by combining single-phase simulations with the pore morphology
method. The effective diffusivity is determined solving Laplace’s equation. For MPL and CL, also
Knudsen 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 determined
properties. For this purpose, a tomography image of the GDL is used as model to ensure
micro-structural geometric similarity between experiment and simulation.
“Modeling Compressible Multiphase Flow and Transport in Saturated-Unsaturated Porous Media: Phase
Appearance-Disappearance. Application to Gas Migration in Underground Nuclear Waste Repository”
Alain Bourgeat
Université Lyon 1 - UCB, France
Motivated by modelling the gas migration in an underground nuclear waste repository, we derive a new
compositional model of compressible multiphase flow and transport in porous media, with interphase
mass transfer, The liquid phase is composed of water and dissolved hydrogen and the gas phase is
composed of vaporized water and hydrogen. One of the main difficulty appearing in the usual models
is their inadequacy to take in account both fully and partially water saturated situations ; leading
to numerical problems or unphysical numerical constraints. The new unified modeling of fully and
partially water saturated porous materials, presented in our talk, is based on fundamental principles
of fluid mechanic and thermodynamic; and its main interest is to make possible a unified numerical
treatment of fully and partially water saturated situations. Under adequate assumptions, the existence
of solutions for equations corresponding to this ”unified fully partially saturated” formulation could
be proved. We present numerical simulations showing the efficiency of this modelling.
“What should we do with Radioactive Waste?”
Andrew Cliffe
School of Mathematical Sciences,
University of Nottingham
Most radioactive waste arises from civil nuclear power programmes. Opinions are sharply divided when
it comes to nuclear power: some countries intend to phase it out altogether, others are heavily reliant
on it for electricity generation and will be for the foreseeable future. However, everyone is agreed
that radioactive wastes must be disposed of in a safe manner. This talk will review the options that
have been considered for safe long-term disposal of radioactive waste and explain why deep geological
disposal is now the (almost) universally preferred solution. A deep geological disposal facility is a
combination of an engineered and a natural system and any analysis of the safety performance of such
a facility must take into account the uncertainties inherent in natural systems. The techniques used
to deal with uncertainty will be outlined. The important case of the uncertainties arising from limited
information about rock properties and their impact on transport of radionuclides from a deep disposal
facility back to the human environment will be considered in some detail, illustrating the importance
of modern developments in uncertainty quantification and the solution of stochastic partial differential
equations.
“CO2-migration: Effects and Upscaling of Caprock Topography.”
Helge K. Dahle
Dept. of Mathematics,
University of Bergen, Norway
In prospective sites for CO2 storage, such as a saline aquifer or abandoned petroleum reservoir, the
subsurface conditions are such that CO2 is a supercritical fluid and slightly soluble in water and thus
forms a separate fluid phase that is less dense and much less viscous than the resident brine. Because
of the viscosity and density differences the CO2 will be captured under the caprock and then migrate
as a thin plume under the influence of gravity. It follows that the dynamics and distribution of the
9

CO2 plume will depend on the topography of the caprock.
In this presentation we demonstrate how caprock topography may impact plume migration and distribution.
In particular we note how caprock roughness reduces migration speeds. Open issues to be
discussed are how subscale caprock roughness may be upscaled, and how roughness can be parameterized.
The presentation is based on joint work with Halvor M. Nilsen, SINTEF ICT, Norway and Sarah
Gasda, Uni Research, Norway
“Coupling Free and Porous-Media Flows: Modeling, Analysis, and Numerical Approximation”
Marco Discacciati
Laboratori de Càlcul Numèric (LaCàN).
Universitat Politècnica de Catalunya (UPC BarcelonaTech),
Barcelona, Spain.
marco.discacciati@upc.edu
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 the
incompressible fluid and Darcy of Fochheimer equations in the porous region. We discuss and compare
different coupling strategies based on the so-called penalization method or on the application of the
transmission conditions of Beavers-Joseph-Saffman.
After giving some results on the well-posedness of the resulting coupled models, we illustrate a domain
decomposition 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 Efendiev
Texas A&M University
The development of numerical algorithms for simulations of flow processes in large-scale highly heterogeneous
porous formations is challenging because properties of natural geologic porous formations
(e.g., permeability) display high variability and complex spatial correlation structures which can span
a 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, mechanical
deformation, and transport processes under investigation. In practice, some types of coarsening (or
upscaling) of the detailed model are usually performed before the model can be used to simulate
complex processes. Many approaches have been developed and applied successfully when a scale separation
adequately describes the spatial variability of the subsurface properties (e.g., permeability) that
have bounded variations. The quality of these approaches deteriorates for comp! lex heterogeneities
without scale separation and high contrast. In this talk, I will describe multiscale model reduction
techniques that can be used to systematically reduce the degrees of freedoms of fine-scale simulations
and discuss applications to preconditioners and coupling to global model reduction tools. Numerical
results will be presented that show that one can improve the accuracy of multiscale methods
by systematically adding new coarse basis functions, obtain contrast-independent preconditioners for
complex heterogeneities, and get reduced order models at low cost.
10

“Numerical and Stochastic Models of Flow in 3D Discrete Fracture Networks”
Jocelyne Erhel
INRIA; Campus Universitaire de Beaulieu,
Rennes, France;
Jocelyne.Erhel@inria.fr
This is joint work with Jean-Raynald de Dreuzy (CNRS, UMR Geosciences, Rennes), Géraldine Pichot
(INRIA, Rennes) and Baptiste Poirriez (INSA, UMR IRISA, Rennes).
Underground water is naturally channelled in fractured media, where interconnections can be very
intricate. Discrete Fracture Networks are based on a geometrical model, where fractures are 2D
domains, for example ellipses, which form a 3D network. Stochastic models rely on probability laws
to define the geometry, in particular the length distribution of fractures. In our model, we define a
power 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, with
Poseuille’s flow equations inside each fracture and continuity of pressure and flux at the intersections
between the fractures. Boundary conditions are applied at the borders of the fractures and of the
network, which is limited by a finite cube. Our numerical model relies on a mixed hybrid finite element
method, which is well suited for such problems. With a conforming mesh, continuity conditions are
easy to apply, but with a non conforming mesh, mortar relations must be devised. A non conforming
mesh allows meshing the fractures independently, in order to adapt the mesh step to the fracture
scale. Because the network is generated randomly, mesh generation can fail when small angles appear
at the interface of a fracture (the interface is the set of intersections with other fractures). We have
developed an original discretization procedure, with a two-step algorithm, acting first at the network
level then at the fracture level. This method removes small angles so that mesh generation is feasible
and leads to a good aspect ratio. On the other hand, this approach creates geometrical configurations
where more than two fractures can share an intersection edge. This brings up a new difficulty for the
mortar method, where new relations must be defined. This spatial discretization leads to a symmetric
positive definite linear system, with a large sparse matrix. We have investigated the efficiency of several
linear solvers on parallel and distributed computers. Since the network can be easily partitioned into
subdomains (the fractures), we have developed a hybrid solver based on domain decomposition. This
approach decouples in some sense the flow at the fracture scale from the interactions at the network
scale. The Schur complement, which gathers the unknowns at the intersections of the network, is solved
with a preconditioned conjugate gradient. We combine Neumann Neumann, defined at the fracture
scale, 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 embedded
into the scientific platform H2OLab. Our numerical experiments highlight the efficiency of this Schur
solver.
“Discontinuous Galerkin Method for Two-Component Miscible Liquid-Gas Porous Media Flows”
Alexandre Ern
Université Paris-Est, CERMICS,
Ecole des Ponts, 6& 8 Av. B. Pascal,
77455 Marne-la-Vallée cedex 2, France
We consider two-component (typically, water and hydrogen) miscible liquid-gas porous media flows
including gas-phase (dis)appearance, as motivated by hydrogen production in underground repositories
for radioactive waste. Following Smaï’s Ph.D. thesis (Université Claude Bernard Lyon, 2009),
we formulate the governing equations in terms of liquid pressure and dissolved hydrogen density as
main unknowns, leading mathematically to a nonlinear elliptic-parabolic system of PDEs, in which the
equations degenerate when the gas phase disappears. We develop a discontinuous Galerkin method
for space discretization, combined with a backward Euler scheme for time discretization and an incomplete
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 work
with I. Mozolevski (Universidade Federal de Santa Catarina, Brazil).
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“Electrochemical Processes and Porous Media: Mathematical and Numerical Modeling”
Jürgen Fuhrmann
Weierstrass Institute for Applied Analysis and Stochastics
Mohrenstr. 39
10117 Berlin, Germany
Electrochemical effects in porous media are ubiquitous in nature, industry and everyday life. Important
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 state
conductors.
In electrochemical systems, flow, transport, reactions and electric field are tightly coupled. To introduce
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-consistent
electric field established by the distribution of charged particles. This system is coupled to electrochemical
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 models
of electrochemical systems containing porous structures.
As a result we present a multiphase-multicomponent ansatz in porous media augmented by equations
describing 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 the
numerical implementation of mathematical models based on reaction-diffusion-convection systems.
Particular advantages of the method are unconditional stability, positivity, discrete maximum principle,
local and global mass conservation, and efficient ways to solve stationary and time dependent
cases. 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 approach
presented.
“Optimized Schwarz Waveform Relaxation for Reactive Transport Problems”
Laurence Halpern
LAGA. University Paris 13.
93430 Villetaneuse, France
Schwarz waveform relaxation algorithms have been introduced in the last decade to solve linear problems
of various types in parallel by domain decomposition in space. Each subdomain evolves with
its own time grid in time windows, and the iteration between the subdomains takes place at the end
of the time window. Much attention has been paid earlier to the design of of fast algorithms for
linear problems, by choosing the type and the coefficients of the transmission conditions between the
subdomains [1].
In the reactive transport process, a small time scale is needed in a reactive zone localized in the
neighbourhood of mobile interfaces between water and gas, whereas larger time scales are involved in
the mildly reactive zone. This is the motivation of the SHP-CO2 project with the french ANR and
the IFPEN. Within this project, we have introduced various types of Schwarz waveform relaxation
algorithms for non-linear systems [2,3]. They are coupled with Krylov acceleration and Newton
algorithms for the non-linear part. The aim of this talk is to present our latest progress from a
theoretical point of view. Numerical aspects will be evaluated on toy problems. These results are a
joint activity with the PhD student Florian Haeberlein and Anthony Michel at IFP, Filipa Caetano
at University Paris 11, J’er’emie Szeftel at ENS, Martin Gander at Geneva University. Applications
of 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 with
Application 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 for
semilinear 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 Schwarz
waveform relaxation methods applied to coupled nonlinear reactive transport systems in the context
of CO2 geological storage simulation. Proceeding DD20, 2011, submitted.
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“Coupled Surface and Saturated/Unsaturated Ground Water Flow in Heterogeneous Media”
Ralf Kornhuber
Freie Universität Berlin,
Institut für Mathematik,
Arnimallee 6, 14195 Berlin
Richards equations for saturated/unsaturated groundwater flow is based on state equations relating
saturation to capillary pressure. The numerical solution of the resulting degenerate parabolic problems
typically suffers from strong nonlinearities and ill-conditioning in the presence of strongly varying
saturation. As a remedy, we suggest a solver-friendly discretization based on Kirchhoff transformation
which can be reinterpreted in physical variables in terms of suitable quadrature rules. In this way
ill-conditioning is separated from the numerical solution process. We show convergence and provide
error estimattes This approach is extended to heterogeneous state equations by domain decomposition
methods based on nonlinear transmission conditions. We suggest suitable coupling conditions of
ground water flow and shallow water equations for surface water flow. The coupled system is solved
by a Dirichlet-Neumann-type iteration accounting for the multiple time scales. The performance of
the algorithms is illustrated by numerical computations.
“Multi-scale 3D and 4D Modelling and Simulation in Geosciences”
Robert Marschallinger
ÖAW GIScience,
Schillerstr. 30,
5020 Salzburg
Geoscience computing typically deals with three-dimensional (“3D”) spatially referenced data; in
process 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 ranges
of object scale, geometric precision and shape complexity. Solid modelling is state-of-the-art for portraying
volume objects because it backs up the unambiguous representation of arbitrarily shaped 3D
objects and provides automated analysis and Boolean relationship of the involved solid objects. Much
as in the 2D realm, where areal data can be represented either in vector or raster form, in the 3D
domain, boundary representation (“B-Rep”) and voxel modelling (“VM”) are used to portray volume
data. B-Rep aggregates the total solid model from self-contained, complexly shaped solid objects
and has its strengths in the quasi-natural presentation and in a straightforward, manual editing of
objects. By contrast VM, with the roots in 2D raster data processing, is based on tesselating the
whole model universe. VM, as the standard output format of geoscience interpolation and simulation
algorithms, excels in representing continuous spatial variation and in analytical flexibility. Both
B-Rep and VM are generically scale-invariant; i.e., the full scale range covered by geosciences – from
microscopic to megascopic objects – can be described with B-Rep and VM. Abstracting the geoscience
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 can
be explored in space and space/time. In the macro or mega scales, because of the high costs of 3D
subsurface data acquisition (e.g., drilling or geophysical campaigns), the associated modelling universes
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 and
simulation algorithms are mandatory to fill the spatial/spatiotemporal “gaps” in the respective modelling
universes or space-time hyperprisms. Especially in the macro- and mega scales, geostatistics
plays a central role in providing stochastic-based estimation and simulation of spatial and space-time
data and associated incertainty. Toward the other end of the geoscience scale range, data acquisition
in the micro-scale has become straightforward and affordable. Recent advances in destruction-free
materials analysis like micro computed tomography (“µCT”) or Neutron Tomography (“NT”) make
the (micro)structures in geological materials accessible as VMs: paleontologic fossil associations, hard
rock textures and sediment structures can be portrayed in detail. Today, the micro-scale geoscience
modelling universes are exhaustively filled with original data! Object based image analysis in its multidimensional
flavour (“xd-OBIA”), is essential for meaningful classification of geoscience µCT data:
petrographical, sedimentological or paleontological expert knowledge can be successfully incorporated
in the classification process to build precise 3D microstructure VMs from originally noisy, single channel
µCT image stacks. Combining the above-mentioned aspects and methods, a novel testbed with
stunning research opportunities is opened, cross-fertilizing different research fields: xd-OBIA in combination
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 be
quantified by geostatistical variography and multipe-point geostatistical training images. Sequentially
thinning out the exhaustive data, geostatistical interpolation and simulation can be benchmarked, in
a controlled environment of natural structures, to re-build the “Gold” Standard. In the end, with the
well-known paradigm of scale-invariance of geological structures in mind, relevant geostatistical modelling
and simulation insights derived from geoscience microstructures will hopefully be propagated
back to the macro- and mega scales to create more precise 3D and 4D geoscience models from sparse
input data.
“Time-Space Domain Decomposition for Reactive Transport in Porous Media ”
Anthony Michel
IFP 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-species
reactive transport problems. This is a joint work with F. Haeberlein and L. Halpern which contributes
to the ANR-SHPCO2 project on High Performance Simulation for CO2 Geological Storage. The
theoretical background will be presented in another talk by L. Halpern.
“Effective Pressure Interface Law for Transport Phenomena between an Unconfined Fluid and a Porous
Medium using Homogenization”
Andro Mikelić
Université Lyon 1,
Département de mathématiques and Institut Camille Jordan,
Villeurbanne, France
We present modeling of the incompressible viscous flows in the domain containing unconfined fluid
and a porous medium. For such setting a rigorous derivation of the Beavers-Joseph-Saffman interface
condition was undertaken by Jäger and Mikelić [SIAM J. Appl. Math. 60 (2000), p. 1111-1127] using
the homogenization method. So far the interface law for the pressure was conceived and confirmed
only numerically. In this article we derive the Beavers and Joseph law for a general body force by
estimating the pressure field approximation. Different than in the Poiseuille flow case, the velocity
approximation is not divergence-free and the precise pressure estimation is essential. Finally, this new
estimate 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, Universität Heidelberg,
Germany)
“Multiscale Modeling for CO2 Storage”
Jan Martin Nordbotten
Department of Mathematics
University of Bergen
The large spatial and temporal scales over which the evolution of stored CO2 must be assessed, forces
us to consider coarse spatial and temporal discretizations. Such discretizations cannot reasonably be
expected to be convergent to the standard equations of porous media flow, which are valid on much
finer 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 the
computational grids we can afford.
In this talk, we discuss the framework for developing such coarse models, emphasizing the development
of both coarse 3D and 2D models for CO2 storage in geological formations. We will pay particular
attention 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.
14

“An Abstract Two-Level Additive Schwarz Method for Systems with High Contrast Coefficients”
Clemens Pechstein
Institute of Computational Mathematics
Johannes Kepler University
Altenberger Str. 69, 4040 Linz (A)
clemens.pechstein@numa.uni-linz.ac.at
Robust domain decomposition solvers for the finite element discretization of scalar elliptic problems
with heterogeneous (high contrast, or multiscale) coefficients have been studied for some time. This
includes both iterative substructuring methods and overlapping Schwarz methods. Using weighted
Poincaré inequalities and/or spectral theory, robustness can theoretically be guaranteed in a large
variety of cases. However, there is only little theory available for systems of PDEs, such as linearized
elasticity or problems in H(curl).
In this talk, we consider an abstract framework for overlapping Schwarz methods for variationally
posed systems of PDEs. Essentially, we only require positive semi-definite element stiffness matrices
and their connectivity. As usual, the local subspaces are defined on overlapping subdomains. The key
ingredient is an abstract coarse space constructed from a particular eigenproblem in the overlap of each
subdomain as well as an algebraic partition of unity. We provide a rigorous and robust convergence
theory and show some numerical results for the cases of Darcy and linearized elasticity.
The talk is on joint work with V. Dolean (Université de Nice), P. Hauret (Michelin), F. Nataf (Universié
Pierre et Marie Curie), R. Scheichl (University of Bath), and N. Spillane (Université Pierre et Marie
Curie).
“Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling”
Martin Vohralík
Laboratoire Jacques-Louis Lions,
Université 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 applied
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, where
the subdomains are partitioned by a mesh of size h, whereas the interfaces are partitioned by a mesh of
much coarser size H, and where lower-order polynomials are used in the subdomains and higher-order
polynomials are used on the mortar interface mesh. We derive several fully computable a posteriori
error 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 under
an assumption of sufficient regularity of the weak solution. The present approach allows bounding separately
and comparing mutually the subdomain and interface errors. A subdomain/interface adaptive
refinement strategy is proposed and numerically tested. This is a joint work with Gergina V. Pencheva
and Mary F. Wheeler (UT Austin) and Tim Wildey (Sandia National Labs).
“Evaluating Long Term CO2 Storage in Saline Aquifers”
Mary Fanett Wheeler
Director, 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 from
the subsurface. The byproducts of consuming these fuels such as greenhouse gas accumulation in the
atmosphere are serious and potentially devastating. Renewables such as solar energy and wind farms
may take many decades to develop before becoming economically feasible alternatives capable of replacing
or reducing fossil energy usage. A major hope for the near future is geologic sequestration,
15

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 storage
sites. Various physical processes such as highly impermeable caprock and geochemical trapping mechanisms
would prevent the CO2 from escaping to the surface. Unfortunately, it is difficult to design
and manage such efforts. Predictive computational simulation may be the only means to account for
the lack of complete characterization of the subsurface environment, the multiple scales of the various
interacting processes, the large areal extent of storage sites such as saline aquifers, and the need for
long time predictions.
In this presentation we discuss multiscale, multiphysics algorithms for accurately predicting the fate of
injected 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 coupling
of all these phenomena over multiple time and spatial scales. Both theoretical and computational
results will be presented.
“A New Coupling Concept for Two-Phase Compositional Porous Media and Single-Phase Compositional
Free Flow”
Barbara Wohlmuth
Fakultät Mathematik, TU München
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-flow
region appear in a wide range of industrial, environmental and medical applications. Although of high
relevance, the mathematical modeling and the numerical simulation remains challenging. This talk
addresses two issues: firstly how to transfer information between the two sub-system and secondly
how 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 porousmedium
flow on the Darcy scale can be identified. In the single-domain approach, one set of equations
is assumed to be valid in the whole domain and the coupling is realized via a transition zone, where
material parameters are varied. In the two-domain approach two sets of equations are used within the
different subdomains. To obtain a well-posed setting, additional transfer conditions at the interface
have to be imposed. So far these concepts have been developed for single-phase single-component systems
describing the coupling for mass and momentum. However, in many applications compositional
multi-phase flow occurs. Here, we generalize the two-domain approach for a non-isothermal twophase
two-component model and introduce suitable coupling conditions. The interface is assumed to
be simple in the sense that it has no thickness and cannot store mass, momentum or energy. Coupling
conditions for mass, momentum and energy are defined based on flux continuity and thermodynamic
equilibrium. Moreover, the coupling concept employs the Beavers-Joseph concept in the knowledge
of its limitations to parallel, single phase flow. The presented model may also be used in applications
similar to evaporation, e.g. the design of industrial drying processes.
Many practically relevant multi-phase problems for flow and transport in porous media require knowledge
of the composition of the involved fluid phases in order to adequately approximate the underlying
physical processes. One major issue of many contemporary multi-phase multi-component models are
phase transitions. A sound incorporation of these transitions into the flow model is essential since
the 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 nonlinear
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 class
uses a flash calculation which determines the local thermodynamic state from the overall mass of the
individual components. Flash calculations are stable in regard to phase transitions, but exhibit two
major drawbacks: Firstly, to get well-defined fluid pressures, they require to assume that all fluid
phases 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 relevant
for the partial differential equations needs to be solved. The second class of models locally adapts the
set of primary variables to the local phase state. This externally imposed phase state is then used for
the calculation until the results become physically inconsistent – which is indicated, for example, by
negative saturations. When such a condition is detected at a given spatial location, the set of present
phases is altered and the primary variables are switched to physically meaningful quantities. For this
reason, this approach is usually referred to as primary variable switching (PVS). Compared to flash
16

calculations, this approach is locally more efficient, since the thermodynamic state can be calculated
independently for each fluid phase. However, quite often numerical oscillations can be observed which
then result in extremely small time-steps or even a break down of the algorithm. Hence, the second
goal of the present contribution is to meet the demand for a robust and efficient implicit numerical
scheme 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 complementarity
or Karush–Kuhn–Tucker (KKT) conditions. Mathematically, this leads to the structure of
variational inequality. As similar conditions also occur in other important applications like contact or
obstacle problems, there exist many approaches of treating these complimentarity constraints. Here we
make use of the fact that the KKT conditions can equivalently be reformulated as a non-differentiable
but semismooth equation, termed nonlinear complementarity function (NCP). Combined with the
balance equations, a system of nonlinear equations is obtained that can be solved by means of a
semismooth Newton method with locally superlinear convergence. As the KKT conditions and the
non-linearities of the material are handled within the same Newton loop, a nested iteration for the
determination of the local phase state is avoided.
“Mortar Multiscale Framework for Stokes-Darcy Flows”
Ivan Yotov
Department of Mathematics, University of Pittsburgh
We discuss numerical modeling of Stokes-Darcy flows based on the Beavers-Joseph-Saffman interface
conditions. The domain is decomposed into a series of small subdomains (coarse grid) of either Stokes
or Darcy type. The subdomains are discretized by appropriate Stokes or Darcy finite elements. The
solution is resolved locally (in each coarse element) on a fine grid, allowing for non-matching grids
across subdomain interfaces. Coarse scale mortar finite elements are introduced on the interfaces to
approximate the normal stress and impose weakly continuity of the velocity. Stability and a priori
error analysis is presented for fairly general grid configurations. By eliminating the subdomain unknowns
the global fine scale problem is reduced to a coarse scale interface problem, which is solved
using an iterative method. We precompute a multiscale flux basis, solving a fixed number of fine
scale subdomain problems for each coarse scale mortar degree of freedom, on each subdomain independently.
Taking linear combinations of the multiscale flux basis functions replaces the need to solve
any subdomain problems during the interface iteration. Numerical results for coupling Taylor-Hood
Stokes elements with Raviart-Thomas Darcy elements are presented.
This is joint work with Ben Ganis, University of Texas at Austin, Vivette Girault, Paris VI, and
Danail Vassilev, Rensselaer Polytechnic Institute
17

Abstracts for Posters
“Multiscale Simulations of Non-Darcy’s Flows”
Sergey Alyaev
Universitetet i Bergen, Matematisk institutt,
Postboks 7803, 5020 BERGEN
The standard approximation for flow-pressure relationship in porous media is Darcy’s law. It is
justified and gives good results for slow flows, however in a number of applications with faster flow
regimes it breaks down. These applications include flows that may occur near wells and in fractured
regions 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 for
flows with larger Reynolds numbers. The standard continuum mechanics approach for those cases
is using non-linear Navier-Stokes equations for the fine scale. To perform larger scale simulations of
non-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 conservation
of mass on control volumes, that is, no phenomenological Darcy-type relationship for velocity is
presumed. The fluid fluxes are instead provided by a fine scale Navier-Stokes mixed finite element
solver. This methodology, that we will refer to as multiscale simulation is different from a common
multiscale modelling procedure of upscaling. The difference is, that in the case of MS modelling
one chooses the coarse scale model in advance based on physical reasoning and then gets effective
parameters from solving some sort of fine scale equations. The advantage of MS simulation is that
the results of it will coincide with Darcy’s law (with upscaled parameters) without increasing the
computational time asymptotically for the slow flows. Yet it will deliver better results for faster flow
regimes 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 Blaheta
Institute 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 geomaterials
and geocomposites (which arose from grouting for improving the geomaterials). We consider processes
of deformation and flow in porous media and the FEM modelling should give answer to the questions
what are the effective properties, how the changes in microstructure influence the macroscale behaviour
and also how to optimize the microstructure. The second topic is the iterative solution (joint work with
O. 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 material
coefficients. Therefore, we are motivated in seeking parallelizable and robust iterative solution methods
and we shall present here some results concerning the variants of multi-level Schwarz methods with
coarse spaces constructed by aggregations. We also touch the construction of block preconditioners for
mixed 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 assigning
the local material properties according to tomography scans (providing the material distribution) and
properties of individual material components. These properties are determined with the aid of tests
of macroscale behaviour on the specimens with known material distribution and solution of inverse
problems for identification of properties of selected material components. We describe this approach
and 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 Carraro
Institute 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 can
decouple the effects associated to the geometrical arrangement, shape and size of the particles on one
side and the material properties on the other can give a relevant improvement in the understanding
of the underlying processes.
A porous mixed ionic and electronic conducting (MIEC) cathode was reconstructed by a tomography
technique based on focused ion beam coupled with scanning electronic microscope (FIB/SEM). The
detailed geometry of the microstructure is used for 3D calculations of the electrochemical processes in
the electrode. The area specific resistance (ASR) of the reconstructed porous cathode is calculated as
a performance index. A model based on the finite element method (FEM), which complexity requires
the 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 and
increase the precision of a fitting procedure. First steps towards the optimal experimental design for
impedance measurements for SOFC are shown.
“Numerical Upscaling in Porous Media”
Christian Engwer
Institut für Numerische und Angewandte Mathematik
Universität Münster
For the simulation of transport processes in porous media effective parameters for the physical processes
on the target scale are required. Numerical upscaling can help where experiments are not
possible, or hard to conduct.
Bastian and Engwer proposed an Unfitted Discontinuous Galerkin (UDG) method for PDEs on domains
with a complicated geometric shape. This method is well suited for simulations on the pore
scale. The method uses finite element meshes which are significantly coarser then those required by
standard conforming finite element approaches and is flexible enough to be used for elliptic, hyperbolic
and parabolic problems. Essential boundary conditions are incorporated using Discontinuous
Galerkin discretization on a cut-cell mesh.
We apply this method to numerical upscaling using direct simulation on the pore scale and present
different applications. The method is robust with respect to computations on coarse meshes.
“Preconditioning of Non-Conforming FEM Systems”
Ivan Georgiev
Computational Methods for Direct Field Problems,
Radon Institute for Computational and Applied Mathematics (RICAM),
Altenberger Strasse 69,
A-4040 Linz, AUSTRIA,
ivan.georgiev@oeaw.ac.at
Joint work with J. Kraus, RICAM.
We present different approaches for preconditioning of linear algebraic systems obtained from nonconforming
discretizations of scalar elliptic and linear elasticity problems. We consider interior penalty
discontinuous Galerkin discterizations of linear elasticity equations and we propose a space splitting
which gives rise to uniform preconditioners. For the problem with Dirichlet boundary conditions
imposed on the entire boundary the linear non-conforming finite elements provides a locking-free
discretization. We devise an optimal order multilevel method for the considered 3D pure displacement
elasticity problem. Finaly we present a two-level method for the scalar elliptic problems with highly
varying coefficients. The proposed generalized hierarchical basis yields a robust splitting with respect
to mesh size and jump discontinuities of the coefficients.
19

“Design of Numerical Methods to Simulate Models of a Solid Oxide Fuel Cell”
Christian Goll
Institute 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 the
overlying gas channel of a solid oxide fuel cell (SOFC). Via impedance measurements, polarization
losses arising during the operation of the fuel cell can be identified. To achive this, a coupled system
of PDEs has to be solved numerically. This system contains (Navier-)Stokes and Darcy equations
to characterize the flow as well as the Stefan-Maxwell/Dusty-Gas model to describe diffusion and
reaction of the species.
Over the last years, a lot of work has been put into the coupling conditions for the Stokes/Darcy-system
along the interface between fluid and porous region. In 2001, Jaeger, Mikelić and Neuss proposed a
set of conditions for the laminar viscous flow over a porous bed, which actually allows to decouple the
problem and make it easier to compute. We compare these ’decoupling conditions’ numerically with
a fully coupled approach.
“Impact on the Surface Temperature due to the Modifications of Underlying Land Surface Conditions: A
Study over Western India”
Sridhara Nayak
Center 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 land
use & land cover. It is well accepted that the greenhouse gases are main causes of global warming
and recent climate change, but changes in land use & land cover are also contributing to a certain
extent. The changes in land use & land cover modify the underlying land surface conditions. The
modifications 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 vegetation
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 the
evapotranspiration and hence moisture exchange. The exchange of energy and moisture contributes
significantly in determining local, regional and even global climate. The modifications in land surface
conditions result in emission or removal of CO2 in the atmosphere and thus contributing regional
warming or cooling. In this study we have two objectives. First attempt has been made to investigate
surface temperatures during 1973-2009 over Western India and the impact on the surface temperature
due to the modifications in land surface conditions the over the region. This is based on temperature
datasets from observation as obtained from India Meteorological Department and NCEP/NCAR reanalysis
(NNRP1). The impact on the surface temperature due to the modifications in land surface
conditions 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. The
result shows the modifications in land surface conditions during 1973-2005 contributing to this warming
is 0.05C per decade. Second attempt has been made to investigate the changes in land use & land
cover over the region during the period 1975-2005. This is investigated based on four land use & land
cover datasets as obtained from Global Land Cover Facility (GLCF). The change in land surfaces is
investigated by quantifying the land covered with various land use & land cover types. The comparison
of the change in surface temperature with the change in land surface indicates the warming due
to the modifications in underlying land surface conditions is because of the reduction of area under
open forest and subsequent increase of the area under agricultural land.
20

“Modeling Two-phase Flow with Disappearing Gas Phase”
Rebecca Neumann
University of Heidelberg
Interdisciplinary Center for Scientific Computing
Im Neuenheimer Feld 368
69120 Heidelberg
Carbon Capture and Storage (CCS) is a recently discussed new technology, aimed at allowing an
ongoing use of fossil fuels while preventing the produced CO2 to be released to the atmosphere. CSS
involves 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 simulations
is the disappearance of the gas phase, which leads to a degeneration of the equations satisfied by
the saturation. A standard choice of primary variables, which is the pressure of one phase and the
saturation of the other phase, cannot be applied here.
We developed a new approach using the pressure of the nonwetting phase and the capillary pressure
as primary variables. We implemented this new choice of primary variables in the DUNE simulation
framework and present the numerical results for some test cases.
“Robust Preconditioners for General SPD Operators”
Joerg Willems
Computational Methods for Direct Field Problems,
Radon Institute for Computational and Applied Mathematics (RICAM),
Altenberger Strasse 69,
A-4040 Linz, AUSTRIA,
joerg.willems@ricam.oeaw.ac.at
An abstract setting for robustly preconditioning symmetric positive definite (SPD) operators is presented.
The method belongs to the class of additive Schwarz preconditioners, and it requires only
rather mild assumptions naturally satisfied by operators resulting from the discretization of several
important partial differential equations. The term ”robust” refers to the property of the condition
numbers of the preconditioned systems being independent of mesh parameters and problem parameters.
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 generalized
eigenvalue problems. The abstract framework is applied to the scalar elliptic equation and
Brinkman’s equations with coefficients varying over several orders of magnitude. Since Brinkman’s
equations modeling flows in highly porous media constitute a saddle point problem, the abstract
framework is not immediately applicable. This difficulty is overcome by resorting to the stream function
formulation. The latter is, however, only used for the coarse space construction, while the actual
solution process is carried out in the primal variables, i.e., velocity and pressure. Several numerical
examples are presented to illustrate the properties of the method.
21

List of Participants
Alyaev Sergey Universitetet i Bergen cobxo3bot@gmail.com
Andreev Roman SAM, ETH Zürich andreevr@math.ethz.ch
Arbenz Peter ETH Zürich, Chair of
Computational Science
arbenz@inf.ethz.ch
Bastian Peter University of Heidelberg peter.bastian@iwr.uni-heidelberg.de
Becker Jürgen Fraunhofer ITWM,
Kaiserslautern
juergen.becker@itwm.fhg.de
Blaheta Radim Institute of Geonics AS CR,
Ostrava, CZ
blaheta@ugn.cas.cz
Bourgeat Alain UCB Lyon 1 alain.bourgeat@univ-lyon1.fr
Buck Marco Fraunhofer Institute for
Industrial Mathematics
marco.buck@itwm.fraunhofer.de
Caiazzo Alfonso WIAS Berlin caiazzo@wias-berlin.de
Carraro Thomas University of Heidelberg thomas.carraro@iwr.uni-heidelberg.de
Challa Durga Prasad RICAM, Linz durga.challa@oeaw.ac.at
Cliffe Andrew University of Nottingham Andrew.Cliffe@nottingham.ac.uk
Collis Joe University of Nottingham pmxjc2@nottingham.ac.uk
Dahle Helge K. University of Bergen, Norway helge.dahle@math.uib.no
Dashti Masoumeh University of Warwick,
Mathematics Institute
M.Dashti@warwick.ac.uk
Discacciati Marco Universitat Politècnica de
Catalunya, Barcelona
marco.discacciati@gmail.com
Efendiev Yalchin Texas A&M University efendiev@math.tamu.edu
Engl Heinz RICAM & University of Vienna heinz.engl@oeaw.ac.at
Engwer Christian Universität Münster christian.engwer@wwu.de
Erhel Jocelyne Inria jocelyne.erhel@irisa.fr
Ern Alexandre University Paris-Est, CERMICS ern@cermics.enpc.fr
Frank Elisabeth Johannes Kepler University
Linz
elisabeth.frank@jku.at
Freitag Melina University of Bath m.freitag@maths.bath.ac.uk
Fuhrmann Jürgen Weierstrass Institute Berlin juergen.fuhrmann@wias-berlin.de
Gahalaut Krishan P.S. RICAM, Linz krishan.gahalaut@oeaw.ac.at
Georgiev Ivan RICAM, Linz ivan.georgiev@oeaw.ac.at
Goll Christian University of Heidelberg christian.goll@iwr.uni-heidelberg.de
Halpern Laurence Université Paris 13 halpern@math.univ-paris13.fr
Hrtus Rostislav Institute of Geonics of the AS
CR, v.v.i., Ostrava, CZ
hrtus@ugn.cas.cz
Kar Manas RICAM, Linz manas.kar@oeaw.ac.at
Karer Erwin RICAM, Linz erwin.karer@oeaw.ac.at
Kollmann Markus Doctoral Program
Computational Mathematics,
Linz
markus.kollmann@dk-compmath.jku.at
Kolmbauer Michael Johannes Kepler University
Linz
kolmbauer@numa.uni-linz.ac.at
Kornhuber Ralf FU Berlin kornhuber@math.fu-berlin.de
Kraus Johannes RICAM, Linz johannes.kraus@oeaw.ac.at
Langer Ulrich Johannes Kepler University
Linz
ulanger@numa.uni-linz.ac.at
Livshits Irene Ball State University ilivshits@bsu.edu
Mahmoud Alaa Al-Azhar University, Faculty of
Science
allaaly2@yahoo.com
Marschallinger Robert ÖAW GIScience robert.marschallinger@oeaw.ac.at
Mataln Marianne Montanuniversität Leoben marianne.mataln@unileoben.ac.at
Melenk Jens Markus TU Wien melenk@tuwien.ac.at
Michel Anthony IFP Energies nouvelles anthony.michel@ifpen.fr
Mikelić Andro Université Lyon 1, Dépt
mathématiques and ICJ
mikelic@univ-lyon1.fr
22

Nayak Sridhara Indian Institute of Technology,
Kharagpur
sridharanayakiitkgp@gmail.com
Neumann Rebecca University of Heidelberg rebecca.neumann@iwr.uni-heidelberg.de
Nguyen Trung Thanh RICAM, Linz trung-thanh.nguyen@oeaw.ac.at
Nordbotten Jan Martin University of Bergen Jan.Nordbotten@mi.uib.no
Oberaigner Eduard Montanuniversität Leoben ero@unileoben.ac.at
Park Minho University of Nottingham min.park@nottingham.ac.uk
Pechstein Clemens Johannes Kepler University
Linz
clemens.pechstein@numa.uni-linz.ac.at
Peterseim Daniel Humboldt-Universität zu
Berlin, Institut für Mathematik
peterseim@math.hu-berlin.de
Scheichl Robert University of Bath R.Scheichl@bath.ac.uk
Sini Mourad RICAM, Linz mourad.sini@oeaw.ac.at
Teckentrup Aretha University of Bath, Department
of Mathematical Sciences
A.L.Teckentrup@bath.ac.uk
Tomar Satyendra RICAM, Linz satyendra.tomar@oeaw.ac.at
Ullmann Elisabeth University of Bath E.Ullmann@bath.ac.uk
Vohralík Martin LJLL, University Paris 6 vohralik@ann.jussieu.fr
Wachsmuth Daniel RICAM, Linz daniel.wachsmuth@oeaw.ac.at
Wheeler Mary F. The University of Texas at
Austin
mfw@ices.utexas.edu
Willems Jörg RICAM, Linz joerg.willems@oeaw.ac.at
Wohlmuth Barbara Technische Universität
München
barbara.wohlmuth@ma.tum.de
Yang Huidong RICAM, Linz huidong.yang@oeaw.ac.at
Yotov Ivan University of Pittsburgh yotov@math.pitt.edu
Zikatanov Ludmil The Pennsylvania State
University
ltz@math.psu.edu
23

Monday Tuesday Wednesday Thursday Friday
Opening (9:10) Helge K. Dahle Jürgen Becker Jocelyne Erhel Yalchin Efendiev
8:30-9:20
Local-Global Multiscale Model
Reduction Techniques for Flows
Numerical and Stochastic
Models of Flow in 3D Discrete
Pore-Scale Modelling of Porous
Layers Used in Fuel Cells
CO2-Migration: Effects and
Upscaling of Caprock
in Heterogeneous Porous Media
Fracture Networks
Topography
Mary F. Wheeler Laurence Halpern Andro Mikelić Alain Bourgeat Clemens Pechstein
9:20-10:10
Modeling Compressible
Effective Pressure Interface Law
for Transport Phenomena
An Abstract Two-Level Additive
Schwarz Method for Systems
Multiphase Flow and Transport
in Saturated-Unsaturated Porous
Optimized Schwarz Waveform
Relaxation for Reactive
Media: Phase
between an Unconfined Fluid
and a Porous Medium using
Evaluating Long Term CO2
Storage in Saline Aquifers
with High Contrast Coefficients
Transport Problems
Appearance-Disappearance.
Homogenization
Application to Gas Migration ...
Coffee Coffee Coffee Coffee Coffee
Jan Martin Nordbotten Anthony Michel Jürgen Fuhrmann Alexandre Ern Ralf Kornhuber
10:40-11:30
Coupled Surface and
Time-Space Domain
Saturated/Unsaturated Ground
Water Flow in Heterogeneous
Discontinuous Galerkin Method
for Two-Component Miscible
Electrochemical Processes and
Porous Media: Mathematical
Decomposition for Reactive
Transport in Porous Media
Multiscale Modeling for CO2
Storage
Liquid-Gas Porous Media Flows
and Numerical Modeling
Media
Lunch Lunch Lunch Lunch Lunch
Martin Vohralík Andrew Cliffe Marco Discacciati Peter Bastian
14:00-14:50
Numerical Solution of
Coupling Free and Porous-Media
Flows: Modeling, Analysis, and
Robust a Posteriori Error
Control and Adaptivity for
Compositional Two-Phase Flow
in Porous Media
What should we do with
Radioactive Waste?
Numerical Approximation
Multiscale, Multinumerics, and
Mortar Coupling
Coffee Coffee Coffee Coffee
Barbara Wohlmuth Robert Marschallinger Ivan Yotov
15:20-16:10
Multi-scale 3D and 4D
A New Coupling Concept for
Two-Phase Compositional
Mortar Multiscale Framework
for Stokes-Darcy Flows
Modelling and Simulation in
Geosciences
Porous Media and Single-Phase
Compositional Free Flow
17:00 Poster
19:00 Dinner
Each talk is 40 minutes long. After the end of each talk, there are 10 minutes for discussion.