Journées Scientifiques du GNR MoMaS
CIRM Marseille
du 23 au 25 novembre 2009

Session 1 (chaire A. Ern)

10h00 - 10h15   Ouverture des journées
                      J. Vairon (Président du Conseil de Groupement du GNR)
                      H. Flocard (Directeur du programme PACEN du CNRS)
10h15 - 11h00 M. Juntunen, A. Hannukainen, J. Könnö and  R. Stenberg (University of Helsinki) présentation
                      Finite element metods for the Brinkman and Biot models
11h00 - 11h15   T. Russell (NSF) présentation
                      NSF-supported projects related to MoMaS science
11h15 - 11h30   L. Loth (ANDRA) présentation
                      De la recherche à des outils opérationnels: éléments de stratégie de valorisation des acquis du GNR
11h30 - 11h55   F. Dumortier, M. Eddi et S. Granet (EdF) présentation
                      Les modélisations du stockage pratiquées à la R&D d'EdF : pratiques et besoins
11h55 - 12h20   Ph. Montarnal, Th. Abballe, F. Caro et E. Laucoin (CEA Saclay DM2S/LSET) présentation
                      Développements pour les écoulements et le transport en milieux poreux dans le code MPCube : modèles multiphasiques, EF/VF multi-échelles, adaptation de maillage, utilisation du parallélisme

Session 2 (chaire G. Allaire)

13h45 - 14h30   R. Shaw (BGS) présentation
                      The FORGE (Fate of repository gases) pan European Project
14h30 - 14h55   O. Angélini, K. Brenner, C. Chavant, E. Chénier, R. Eymard, S. Granet, et D. Hilhorst présentation
                      Méthodes mathématiques et numériques pour les écoulements diphasiques avec dissolution en milieu poreux
14h55 - 15h20   A. Pazdniakou et P.M. Adler
                      Ecoulements à deux phases en milieux poreux

Session 3 (chaire A. Mikelic)

15h45 - 16h10   E. Lemarchand présentation
                      Micromechanics analysis of chemo-physical damage phenomena in cement-based materials
16h10 - 16h35  J. Beaurain et R. Fernandes présentation
                      Problèmes aux limites avec matériaux adoucissants: suivi des solutions bifurquées et comparaison de deux formulations discrètes (lagrangien augmenté ou par formulation à deux champs)
16h35 - 17h00   M.C. Néel, A. Zoia, M. Joelson, A. Cartalade and C. Danquigny présentation
                      Fractional operators and non-linearities for memory effects in porous media
17h00 - 17h30   Benchmarks (bilan/en cours/a venir)

(17h30 - 19h30  Réunion du bureau du GNR)

Session 8 : Posters (de 20h30 à 22h00)

Auteur, titre

Session 4 (chaire S. Huberson)

09h00 - 09h45   H. Matthies and E. Zander (University of Braunschweig) présentation
                      Sparse representations in uncertainty quantification
09h45 - 10h10  G. Pépin, J.-M. Martinez et F. Gaudier (ANDRA et CEA) présentation
                      Polynômes de chaos et réseau de neurones: développement et application à des cas tests de type performance assessment
10h10 - 10h35   O. Le Maitre, A. Nouy and L. Mathelin présentation
                      Generalized spectral decomposition and separated representations for the solution of uncertain advection-diffusion-reaction equations

Session 5 (chaire O. Le Maître)

11h00 - 11h25   L. El Alaoui, A. Ern and M. Vohralik présentation
                      A posteriori stopping criterion for Newton methods for nonlinear problems
11h25 - 11h50  J. Blum and D. Auroux présentation
                      Transport parameter estimation and uncertainty analysis in hydro-geological media
11h50 - 12h15   S. Huberson présentation
                      Méthodes particulaires pour les milieux poreux

Session 6 (chaire F. Hubert)

13h45 - 14h30   R. Scheichl (University of Bath) présentation
                      Multilevel iterative solvers: Robustness and links to upscaling
14h30 - 14h55   J. Jaffré
                      Solveurs pour l'écoulement et le transport dans le champ lointain
14h55 - 15h20   J. Erhel, J. Carrayrou, M. Kern and A. Younes présentation
                      Méthodes numériques pour le transport réactif
15h20 - 15h45   B. Cochepin présentation
                      Bilan et nouveaux défis du transport réactif

Session 7 (chaire R. Herbin)

16h15 - 17h00   B. Flemisch, R. Helmig, K. Mosthaf, I. Rybak and B. Wohlmuth (University of Stuttgart) présentation
                      A new coupling concept for multi-phase multi-component porous media and free flow
17h00 - 17h25   J. Droniou présentation
                      Remarks on discretizations of convection-diffusion equations using hybrid mimetic mixed methods
17h25 - 17h50   F. Hubert présentation
                      Recent developments on finite volume schemes for anisotropic heterogeneous diffusion problems in three space dimensions
17h50 - 18h15   R. Eymard présentation
                      A nine point cell centered scheme for anisotropic heterogeneous diffusion problems

Session 9 (chaire A. Ern)

09h00 - 09h45   B. Schweizer (University of Dortmund) présentation
                      Porous media and plasticity: Homogenization for equations with hysteresis
09h45 - 10h10   A. Mikelic présentation
                      Rigorous derivation of a hyperbolic model for Taylor's expansion
10h10 - 10h35   G. Allaire, R. Brizzi, A. Mikelic and A. Piatnitski présentation
                      Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media

Session 10 (chaire G. Allaire)

11h15 - 11h40  D. Stemmelen, W. Salameh, S. Leclerc et C. Moyne présentation
                      Imagerie par résonance magnétique appliquée aux problèmes de transport en milieu poreux
11h40 - 12h05  C. Choquet et A. Mikelic présentation
                      Rigorous upscaling of the reactive flow with finite kinetics and under dominant Péclet number
12h05 - 12h30  O. Gipouloux, A. Bourgeat, A. Genty and G. Mathieu présentation
                      Far field numerical simulation of a global model of an underground waste repository: comparaison with the local model simulations

Session 11 (chaire A. Bourgeat)

14h00 - 14h25   B. Amaziane, A. Bourgeat and M. Panfilov présentation et présentation
                      Modeling and Numerical Simulation of the Migration of Gas in the System of a Storage of Radioactive Waste
14h25 - 14h50   A. Bourgeat, O. Gipouloux et F. Smaï présentation
                      Validation par tests numériques du modèle X-p, pour la migration de gaz dans un stockage souterrain de déchets nucléaires HAVL
14h50 - 15h15   Z. Khalil et M. Saad présentation
                      Analyse mathématique et numérique de modèles d'écoulements diphasiques compressibles
15h15 - 15h40 A. Ern, I. Mozolevski and L. Schuh présentation
                       Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures

Abstracts of talks by invited speakers

H. Matthies
Computational approaches to systems involving random fields or stochastic processes have to discretise these fields or processes. This produces -when compared to the deterministic case- many variables in the computation, resulting in a very high-dimensional problem. Based on the conviction that the essential stochastic properties of the system are close to some -albeit unknown- lower dimensional manifold, one may try to approximate the response of the system by a data-sparse representation.
The basis for this sparse representation has to be found in the course of the computation. One first approach is to exploit the natural tensor product structure between basis vectors describing the physical / deterministic behaviour and a basis describing the stochastic response. There are two steps involved here: one is to find a good basis for the physical description, and the other to find / compute a good basis for the stochastic part. One well-known example is the Karhunen-Loève expansion, resulting from the eigenvalue analysis of the covariance. One problem is of course that the covariance of the response is not known beforehand. We will discuss on how to approximate the basis along with the solution. The singular value decomposition, which is very closely related to the Karhunen-Loève expansion, is optimal in that it uses the minimal number of dyadic products. Furthermore, the stochastic part of this product is itself again naturally an element of a tensor product with potentially many factors, containing functions of just one random variable. This fact can be exploited additionally, and also used to obtain an adaptive approximation of the stochastic part.

R. Scheichl
In this talk we compare multilevel iterative solvers and certain upscaling/multiscale techniques for elliptic PDEs with highly variable coefficients. These arise in practice, for example, in the computation of flow in heterogeneous porous media, in both the deterministic and (Monte-Carlo simulated) stochastic cases. When there is no a priori scale separation, standard multiscale techniques require the solution of local "cell" problems in each cell, leading to a computational complexity that can be no better than linear in N, where N is the number of unknowns on the subgrid (globally). Moreover, except for the periodic case, no theory is yet available that analyses the dependency of the accuracy of the upscaled solutions on the coefficient variation. Multilevel iterative methods, such as multigrid or domain decomposition, on the other hand, lead to a similar computational cost with respect to subgrid size (i.e. O(N)), but here the computational cost will in general depend on the coefficient variation. In a series of recent papers we have analysed, both numerically and theoretically, various simple variants of multigrid and domain decomposition methods that are robust to strong coefficient variation. The similarity of some of these to certain multiscale techniques provides also guidelines for the design of robust multiscale techniques and theoretical tools for their analysis.

B. Schweizer
We present two applications in which hysteresis phenomena are crucial features of the problem. One is porous media flow where hysteresis appears through the bottle-neck effect. Another is plasticity where the stress-strain relation remembers the history of the process. In both applications, homogenization questions appear naturally, namely in the following form: Given a volume that is occupied by different materials with different hysteresis properties, what is the averaged hysteresis property? We present an approach that adopts the method of oscillating test-functions and that gives strong theorems and simple proofs even in the context of stochastic homogenization.

R. Shaw
The multiple barrier concept is the cornerstone of all proposed schemes for underground disposal of radioactive wastes. The concept invokes a series of barriers, both engineered and natural, between the waste and the surface. Achieving this concept is the primary objective of all disposal programmes, from site appraisal and characterisation to repository design and construction. However, the performance of the repository as a whole (waste, buffer, engineering disturbed zone, host rock), and in particular its gas transport properties, are still poorly understood. Issues still to be adequately examined that relate to understanding basic processes include: dilational versus visco-capillary flow mechanisms; long-term integrity of seals, in particular gas flow along contacts; role of the EDZ as a conduit for preferential flow; laboratory to field up-scaling. Understanding gas generation and migration is thus vital in the quantitative assessment of repositories and is the focus of the research in this proposal for an integrated, multi-disciplinary project. The FORGE project is a pan-European project with links to international radioactive waste management organisations, regulators and academia, specifically designed to tackle the key research issues associated with the generation and movement of repository gasses with partners from 24 organisations in 12 European countries. Of particular importance are the long-term performance of bentonite buffers, plastic clays, indurated mudrocks and crystalline formations. Further experimental data are required to reduce uncertainty relating to the quantitative treatment of gas in performance assessment. FORGE will address these issues through a series of laboratory and field-scale experiments, including the development of new methods for up-scaling allowing the optimisation of concepts through detailed scenario analysis. The FORGE partners are committed to training and CPD through a broad portfolio of training opportunities and initiatives which form a significant part of the project.
Further details on the FORGE project and its outcomes can be accessed at www.FORGEproject.org.

R. Stenberg
The parameter dependent Brinkman problem, covering a field of problems from the Darcy equations to the Stokes problem, is studied. A mathematical framework is introduced for analyzing the problem. Using this we prove uniform a priori and a posteriori estimates for three families of finite element methods. We also present numerical results. For the Biot model we present a framework by which it is rather strightforward to perform a mathematical analysis.

B. Wohlmuth
Numerical simulations of transport phenomena in structures composed by a porous layer and an adjacent free flowing fluid are usually based on models utilizing Darcy's law in the porous media, whereas in free flow regions a (Navier-)Stokes model is used. Up to now, the coupling of free flow with porous medium flow has been considered only for single-phase systems. We extend this classical concept to two-component non-isothermal flow with two phases inside the porous medium and a single phase inside the free flow region. Our model also takes into account evaporation and condensation processes. We discuss the coupled model and its iterative solution by means of several numerical examples.

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