Journées Scientifiques du GNR MoMaS
CIRM Marseille
du 2 au 4 novembre 2011

Session 1 (chaire A. Ern)

10h30 - 11h15   Conférence invitée: M. Ohlberger, Universitaet Muenster.
                           Error control and adaptivity for numerical multiscale methods.

11h15 - 11h40   M. Vohralik
                           A framework for robust a posteriori error control and adaptivity for unsteady nonlinear convection-diffusion problems.

11h40 - 12h05   D. Moreau
                           Hexahedral adaptive remeshing.

12h05 - 12h30   Présentation 3, thème C: C. Chainais
                           Simulation numérique de la corrosion d'acier dans les conditions de stockage souterrain.

Session 2 (chaire A. Bourgeat)

14h00 - 14h45   Conférence invitée: R. Helmig, University of Stuttgart.
                           Efficient Modeling of Flow and Transport in Porous Media Using Multiphysics and Multiscale Approaches.

14h45 - 15h10   J. Erhel et M. Kern
                           MoMaS: 10 years of reactive transport.

15h10 - 15h35   R. Herbin et F. Hubert
                           3D benchmark on anisotropic and heterogeneous diffusion.

Session 3 (chaire O. Le Maître)

16h00 - 16h25   Présentation partenaire: Andra: L. Loth
                           Contribution de l'Andra à la prospective dans le domaine des mathématiques appliquées.

16h25 - 16h50   Présentation partenaire IRSN: M. Dymitrowska and H. Amor
                           Numerical tools for monophasic and biphasic flows and solute transport in porous media developed by IRSN.

16h50 - 17h30   PACEN, MoMaS et Discussion

(17h45 - 19h30  Réunion du bureau du GNR)

Session Posters (de 20h30 à 22h00)

Session 4 (chaire Ph. Montarnal)

09h00 - 09h45   Conférence invitée: F. Nobile, EPF-Lausanne.
                           Stochastic Polynomial approximation of PDEs with random coefficients.

09h45 - 10h10   N. Fajraoui, A. Younes et Th. Mara
                           Parameter identification and global sensitivity indices using sparse polynomial chaos expansions for reactive transport problems.

10h10 - 10h35   O. Le Maître and Ch. Soize
                           Non-parametric approach for modeling uncertainties in elliptic problems.

Session 5 (chaire G. Allaire)

11h00 - 11h45   Conférence invitée: T. Lelièvre, ENPC.
                           Numerical methods in molecular dynamics.

11h45 - 12h10   Ph. Ackerer
                           Multiscale approach for parameter identification.

Session 6 (chaire A. Mikelic)

14h00 - 14h45   Conférence invitée: A. Prohl, Universität Tübingen.
                           Structure-preserving discretizations of elektrokinetic flows.

14h45 - 15h10   J.-F. Dufrêche (avec GNR Paris)
                           To be announced.

15h10 - 15h35   G. Allaire
                           Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients .

15h35 - 16h00   Présentation partenaire EdF: Fernandes, Granet, Mondoloni, Santamaria, Rupp
                           Study of the Thermo-Hydro-mechanical couplings around a nuclear waste tunnel with Syrthes and Code_Aster.

Session 7 (chaire S. Granet)

16h25 - 16h50   J.-J. Marigo
                           De l'initiation à la rupture: les propriétés générales et quelques exemples d'utilisation des modèles à gradient d'endommagement.

16h50 - 17h15   Présentation Partenaire CEA: P. Omnès
                           A posteriori error estimation and domain decomposition: towards efficient computations for waste repositories.

17h15 - 17h40   D. Stemmelen
                           Hydrodynamique et dispersion en milieu poreux étudiées par IRM.

17h40 - 18h05   M.-C. Néel
                           Non-Fickian effects and fractional models for diffusion in porous media.

Session 8 (chaire A. Burnol)

09h00 - 09h45   Conférence invitée: B. Noetinger, IFPEN.
                           Modélisation avancée des réservoirs d'hydrocarbures souterrains, quelques problèmes ouverts.

09h45 - 10h10   M. Saad, F. Caro, K. Kahlil et B. Saad
                           Modèles diphasique bicomposant : analyse mathématique et numérique.

10h10 - 10h35   D. Hilhorst, K. Brenner et C. Cancès
                           Méthodes numériques pour les écoulements diphasiques en milieu poreux hétérogène.

Session 9 (chaire R. Herbin)

11h00 - 11h25   A. Pazdniakou et P.M. Adler
                           Modélisation des mélanges à deux phases à l'échelle du pore par méthode de Boltzmann.

11h25 - 11h45   I. Panfilova
                           Analyse hydrodynamique des régimes d'étalement et diffusion multi-composante des gaz en stockage souterrains de déchets radioactifs.

11h45 - 12h00   Présentation partenaire BRGM: A. Burnol et M. Parmentier
                           Problèmes de transfert de masse et d'énergie dans les milieux géologiques au BRGM: bilan et perspectives.

12h00 - 12h20   S. Granet
                           Benchmark multiphasique.

Session 10 (chaire A. Ern)

14h00 - 14h25   B. Amaziane et J. Jaffré
                           Modélisation mathématique et simulation numérique de la migration de Gaz dans le système d'un stockage souterrain de déchets radioactifs.

14h25 - 14h50   J. Bodin, M. Ghesmoune, A. Mikelic and M. Panfilov
                           Combination between the models of negative saturations and vector capillarity for multi-component fluids in tight porous media.

14h50 - 15h00   Clôture des journées: A. Ern

Abstracts of talks by invited speakers

R. Helmig
Flow and transport processes in porous media including multiple fluid phases are the governing processes in a large variety of geological and technical systems. In general, these systems include processes of varying complexity occurring in different parts of the domain of interest. The different processes mostly also take place on different spatial and temporal scales. It is extremely challenging to model such systems in an adequate way accounting for the spatially varying and scale-dependent character of these processes. In this presentation, we give a brief overview of existing upscaling, multiscale, and multiphysics methods, and we present mathematical models and model formulations for multiphase flow in porous media including compositional and non-isothermal flow. Finally, we show simulation results for two-phase flow using a multiphysics method and a multiscale multiphysics algorithm.

T. Lelièvre
Molecular dynamics is now a very widely used tool to study the matter at the molecular level. It is used in various fields, such as biology, chemistry or materials science. The aim is in particular to understand the relationships between the macroscopic properties of a molecular system and its atomistic features. For example, one would like to compute the constitutive relations for materials from molecular models, or predict the most likely conformations of a protein in a solvent from its amino acid sequence. One of the difficulty to reach this aim is related to timescales: the typical timescale of a molecular dynamics simulation is much smaller than the typical timescale at which the crucial events, from a macroscopic viewpoint, occur. This is related to the metastability of a molecular dynamics trajectory: the system stays for a very long time in some metastable state, before hopping to another one, and it is difficult to observe and simulate such rare events. An associated feature is the multimodality of the statistical ensemble (a probability measure) sampled by the molecular dynamics trajectories.
Many methods have been proposed in the molecular dynamics community to deal with these difficulties, and we will focus on two prototypical ones for which a mathematical analysis gives useful insights. We will first present adaptive importance sampling techniques, which have been proposed to sample efficiently statistical ensembles. Then, we will propose a mathematical analysis of the parallel replica algorithm which has been introduced by A.F. Voter to generate efficiently metastable dynamics.

F. Nobile
We consider the problem of numerically approximating statistical moments of the solution of a partial differential equation (PDE), whose input data (coefficients, forcing terms, boundary conditions, geometry, etc.) are uncertain and described by a finite or countably infinite number of random variables. This situation includes the case of infinite dimensional random fields suitably expanded in e.g Karhunen-Loève or Fourier expansions.
We focus on polynomial chaos approximations of the solution with respect to the underlying random variables by either Galerkin projection; or collocation on sparse grids of Gauss points.
We discuss in particular the proper choice of the polynomial space for linear elliptic PDEs with random diffusion coefficient. Numerical results showing the effectiveness and limitations of the approaches will be presented.
We will present also some recent results on discrete projection on polynomial spaces from random evaluations.

B. Noetinger
les coûts et les risques sans cesse croissants de l'exploitation des hydrocarbures souterrains justifient le recours à la modélisation numérique des écoulements. Ces modéles servent de réceptacle à la connaissance du géologue, du géophysicien et du spécialiste des écoulements. Ils permettent donc de prendre les décisions de forage ou d'exploitation les plus éclairées possibles. Des outils sont développés pour gérer le manque de connaissance exhaustive du réservoir, ce qui amène à la résolution de problèmes inverses et à gerer des incertitudes. Des problèmes fondamentaux de changement d'échelle sont aussi posés, en particulier dans le cas spécifique de roches fracturées. La présentation passera en revue ces problématiques, et quelques approches, tendances et résultats récents.

M. Ohlberger
In this talk we address a posteriori error estimation and adaptivity for the heterogeneous multiscale method applied to elliptic and parabolic multi-scale problems. Moreover, inspired by the reduced basis approach, we present a new framework for an efficient treatment of heterogeneous multiscale problems. The approach is based on the idea of considering heterogeneous multiscale problems as parametrized partial differential equations where the parameters are smooth functions. We then construct in an offline phase, a suitable localized reduced basis that is used in an online phase to efficiently compute approximations of the multiscale problem by means of a Discontinuous Galerkin method on a coarse grid. We present our new approach for elliptic multiscale problems and discuss an a posteriori error estimate that is used in the construction process of the localized reduced basis. Numerical experiments are given to demonstrate the efficiency of the new approach.

A. Prohl
Elektrokinetic flows of fluids dispersed with electric charges may be modelled by the Navier-Stokes equations coupled with classical semi-conductor equations. Corresponding solutions are non-negative, bounded charge concentrations, as well as an incompressible velocity field, which satisfy an energy- and an entropy principle.
In the talk we propose discretizations which inherit some of these properties, and report on difficulties to construct-preserving discretizations. - This is joint work with M. Schmuck (Imperial College London).

Présentation

Rencontres scientifiques

Projets

Benchmarks

Bibliographie

Logiciels

Liens Utiles

Liste de diffusion

Contacts

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