
Programme
Le workshop débutera lundi 5 à 14h30 et s'achèvera mercredi 7 à 16h30. Les présentations
sont de 30 mn.
Liste des orateurs
 Brahim Amaziane et Etienne Ahusborde (Université de Pau)
 Marie Billaud Friess (Ecole Centrale de Nantes)
 Konstantin Brenner (Université de Nice et INRIA Sophia Antipolis)
 Clément Cancès (Université Paris VI)
 Julia Charrier (Université Aix Marseille)
 Jean Raynald de Dreuzy (Université de Rennes)
 Anne Catherine Dieudonné (Université de Liège)
 Magdalena Dymitrowska (IRSN)
 Jocelyne Erhel (INRIA Rennes)
 Isabelle Faille (IFPEN)
 Yueyuan Gao (Université ParisSud)
 Sylvie Granet (EDF)
 Johann Guilleminot (Université Paris Est)
 Rainer Helmig (Université de Stuttgart)
 Julian Hennicker (Université Nice Sophia Antipolis)
 Raphaèle Herbin (Université d'AixMarseille)
 Michel Kern (INRIA Rocquencourt)
 Simon Lopez (BRGM)
 Anthony Nouy (Ecole Centrale de Nantes)
 Lionel Lenôtre (INRIA Rennes)
 Clémentine Prieur (Université Joseph Fourier)
 Michel Quintard (CNRS, IMFT)
 Mazen Saad (Ecole Centrale de Nantes)
 Laurent Trenty (Andra)
 Feng Xing (Université Nice Sophia Antipolis)
 Yumeng Zhang (Université de Nice et INRIA Sophia Antipolis)
 Lundi
 14h30  14h45: Introduction
 14h45  15h20: Isabelle Faille pdf
 15h20  15h55: Michel Kern pdf
 15h55  16h30: Jean Raynald de Dreuzy pdf
 16h30  17h00: Pause café
 17h00  17h35: Clément Cancès pdf
 17h35  18h10: Simon Lopez pdf
 Mardi
 9h00  9h35: Jocelyne Erhel pdf
 9h35  10h10: Johann Guilleminot pdf
 10h1010h40: Pause café
 10h40  11h15: Yueyuan Gao pdf
 11h15  11h50: Marie Billaud Friess pdf
 11h50  12h25: Anthony Nouy pdf
 12h25  14h00: Buffet
 14h00  14h35: Clémentine Prieur pdf
 14h35  15h10: Feng Xing pdf
 15h10  15h45: Julian Hennicker pdf
15h45  16h15: Pause café
 16h15  16h50: Laurent Trenty pdf
 16h50  17h25: Anne Catherine Dieudonné pdf
 17h25  18h00: Magdalena Dymitrowska pdf
 20h00 Diner
 Mercredi
 9h00  9h45: Rainer Helmig pdf
 9h45  10h20: Yumeng Zhang pdf
 10h20  10h50: Pause café
 10h50  11h25: Raphaèle Herbin pdf
 11h25  12h00: Etienne Ahusborde pdf
 12h00  12h35: Mazen Saad pdf
 12h35  14h00: Buffet
 14h00  14h15: Raphaèle Herbin: présentation du GDR MANU 20162019 pdf
 14h15  14h50: Michel Quintard pdf
 14h50  15h25: Sylvie Granet pdf
 15h25  16h00: Konstantin Brenner pdf
 16h00: Pause café et fin
Titres et résumés
 Brahim Amaziane et Etienne Ahusborde (Université de Pau)
 Titre: A sequential numerical simulator for twophase multicomponent flow with reactive transport in porous media
 Résumé:
In this talk, we will discuss a new numerical modeling of twophase multicomponent flow with reactive transport in porous media such as immiscible gas injection in oil reservoirs, gas migration in a nuclear waste repository or longterm fate of injected CO2 for geological sequestration.
We will focus on the numerical modeling of immiscible compressible twophase flow in porous media with geochemistry. The problem is modeled by the mass balance law for each phase, DarcyMuskat's law, the capillary pressure law and the coupling with chemistry occurs through reactions rates. In the case of kinetic reactions, these rates are nonlinear functions of the concentrations involved in ordinary differential equations, while for equilibrium reactions, these rates are unknown and replaced by the mass action laws that relate the activities of concerned species.
A sequential approach, consisting in solving firstly a twophase flow and then the reactive transport problem, is considered. In this context, we have implemented in the parallel opensource simulator DuMuX (http://www.dumux.org) a reactive transport module using an iterative approach where transport and chemistry are solved sequentially. To deal with the chemistry, we have developed a code in order to solve the chemical equilibrium problem involving mass actions laws and mass conservation laws coupled with ordinary differential equations. The nonlinear system is solved by means of the multidimensional rootfinding of GSL (http://www.gnu.org/software/gsl/).
Our reactive transport module has been validated for the reactive transport benchmark proposed by the MoMaS research group. The accuracy and effectiveness of this new simulator is demonstrated through numerical investigation. It is an ongoing longterm development effort, establishing a software framework, based on the C++ programming language, for the computation of multiphase multicomponent flow with reactive transport in porous media. Numerical simulations from two and three dimensional spaces including benchmarks tests will be presented.
This is a joint work with Etienne Ahusborde, Mustapha El Ossmani and Philippe Poncet.
 Marie Billaud Friess (Ecole Centrale de Nantes)
 Titre: Model reduction method for solving parameterdependent dynamical systems
 Résumé:
In this talk, we address the task of model reduction for solving parameter dependent nonlinear dynamical systems. In general, computing the full solution of such a problem can be very expensive and may be intractable when numerous simulations are needed for many values of the parameter. Model order reduction methods have been widely developed over the past years for solving parameterdependent problem using a surrogate model that can be rapidely evaluated.
The model reduction method proposed here can be seen as a reduced basis method where we seek the reduced approximation in a time dependent reduced space. Such an approach is well adapted to capture transient phenomenon contrary to an approach where the reduced space is time independent. In that context, the reduced approximation is obtained by a Galerkin projection of the full dynamical system on the reduced space. Here, the time dependency of the reduced space is taken into account through a modified reduced flux. To measure the accuracy of the reduced approximation, error analysis is achieved using the logarithmic Lipschitz constant associated to the flux for efficient majoration of the approximation error. The obtained error estimate is then used in a procedure for adaptive construction of the time dependent reduced spaces.
The applicability of our method and the effectiveness of the a posteriori error estimates are illustrated through numerical experiments on both linear and nonlinear test cases.
 Konstantin Brenner (Université de Nice et INRIA Sophia Antipolis)
 Titre: Immiscible twophase Darcy flow model accounting for vanishing and discontinuous capillary pressure: application to the flow in fractured porous media
 Résumé:
In the context of immiscible twophase Darcy flows in heterogeneous porous media the problem of choosing an appropriate set of primary unknowns may be challenging, especially when dealing with not strictly increasing capillary pressure curves and saturation jumps at rock type interfaces. We introduce a powerful variable substitution technique, which handles both mentioned difficulties, while using a single choice of primary unknowns. We illustrate this approach by a number of numerical test cases dealing with gaswater flow in fractured porous media.
 Clément Cancès (Université Paris VI)
 Titre: Discretization of unsaturated flows in heterogeneous anisotropic porous media on general grids preserving the gradient flow structure
 Résumé:
The Richards equation governing unsaturated flows in porous media has a formal gradient flow structure in a Riemannian setting. We first highlight the gradient flow structure, then we propose a numerical scheme that preserves it at the discrete level. The stability and the convergence of the scheme are then discussed. In collaboration with Cindy Guichard (LJLL, UPMC Paris 6).
 Julia Charrier (Université Aix Marseille)
 Titre: Convergence of monotone finite volume schemes for hyperbolic scalar conservation laws with multiplicative noise
 Résumé:
We consider nonlinear hyperbolic scalar conservation laws with multiplicative noise on R^{d}. After having presented the concept of stochastic entropy solution, I will quickly present an existence and uniqueness result for the stochastic entropy solution.
The main part of the talk will be devoted to the definition of stochastic monotone finite volume schemes and the proof of the convergence of these
schemes to the stochastic entropy solution under a stability condition. For the sake of clarity, I will present the proof in details only in the case of an upwind scheme and explain after that how to extend the proof to the general case.
This is a joint work with Caroline Bauzet and Thierry Gallouët.
 Jean Raynald de Dreuzy (Université de Rennes)
 Titre: Permeability scaling and flow structures in fracture networks
 Résumé:
After more than three decades of research, flows in fractured media have been shown to result from multiscale geological structures. Flows result nonexclusively from the damage zone of the large faults, from the percolation within denser networks of smaller fractures, from the aperture heterogeneity within the fracture planes and from some remaining permeability within the matrix. While the effect of each of these causes has been studied independently, global assessments of the main determinisms is still needed.
Based on an extensive analysis of 2D and 3D Discrete Fracture Networks (DFNs) as well as on reference connectivity structures, we investigate the relation between the local fracture structures and the effective permeability [de Dreuzy et al., 2012b]. Multiscale synthetic networks are reconstructed from field data and simplified mechanical modeling [Davy et al., 2010]. Highperformance numerical methods are developed to comply with the specificities of the geometry and physical properties of the fractured media [Pichot et al., 2010; Pichot et al., 2012]. And, based on a large MonteCarlo sampling, we determine the key determinisms of fractured permeability and flows.
We illustrate our approach on the respective influence of fracture apertures and fracture correlation patterns at large scale. We show the potential role of fracture intersections, so far overlooked between the fracture and the network scales. We also demonstrate how small fracture apertures and fracture closure reduce the bulk fracture permeability (Figure) [de Dreuzy et al., 2012a]. Using this analysis, we highlight the need for more specific insitu characterization of fracture flow structures.
Fracture modeling and characterization are necessary to meet the new requirements of a growing number of applications where fractures appear both as potential advantages to enhance permeability and drawbacks for safety, e.g. in energy storage, stimulated geothermal energy and nonconventional gas productions.
 Anne Catherine Dieudonné (Université de Liège)
 Titre: Hydromechanical modelling of bentonitebased materials
 Résumé:
Most concepts of deep geological disposal for radioactive waste involve a multibarrier system in which bentonitebased materials are used as engineered barriers. The objective is to create a zone of low permeability that is able to limit water flow around the excavated galleries, and thereby delay the release of radionuclides to the biosphere.
The behaviour of bentonitebased materials under in situ conditions is complex, owing to strong multiphysical and multiscale coupling taking place. Both hydraulic and mechanical behaviour are indeed strongly coupled, and the material exhibits important swelling upon hydration. In addition, the structure of bentonites is characterized by a bimodal pore size distribution created upon compaction. This structure evolves along hydromechanical stress paths and influences the material properties (hydraulic conductivity, retention capacities ...).
In this paper, a hydromechanical model for compacted bentonites is developed. While developed at the macroscale, the model includes important aspects of the material microstructure. More specifically, attention is paid to:
 The implementation of an elastoplastic mechanical model able to reproduce the large strains observed in compacted bentonites upon wetting
 The extension of the existing hydromechanical formulation to include coupling between
 The water retention behaviour and the evolving material micro and macrostructure
 The permeability and the material macrostructure
The model is implemented in the finite element code LAGAMINE developed at the University of Liège. The performance of the implementation is investigated through the modelling of laboratory infiltration tests. The importance of the various hydromechanical coupling is also highlighted.
Finally, the model is used to study the hydromechanical behaviour of a bentonite buffer submitted to hydration under in situ conditions. The investigated problem is directly related to the set of experiments PGZ2 developed in Andra's underground research laboratory.
 Magdalena Dymitrowska (IRSN)
 Titre: Lattice Boltzmann simulations of flow and transport in argillites at low gas saturation
 Résumé:
In the framework of radioactive waste disposal studies, behavior of hydrogen produced through anaerobic corrosion of the steel canisters is a key point. At the near and far field scale, the migration process of hydrogen is modelled using macroscopic twophase flow models requiring macroscopic data like relative permeability curves and effective diffusion coefficients. As these parameters for opaque and tight porous media are difficult to measure experimentally, twophase flow modelling at the pore scale appears as an interesting tool. The objective of this talk is to present a Lattice Boltzmann approach used to model twophase flow and transport in fractures with apertures of a few micrometers in low gas saturation context.
 Jocelyne Erhel (INRIA Rennes)
 Titre: Generation of a stationary Gaussian random field
 Résumé:
Uncertainty quantification often requires several samples of a stationary Gaussian random field over a regular grid.
We compare classical methods used to simulate the field defined by its covariance function, namely the Discrete Spectral method, the Circulant Embedding approach, and the Discrete KarhunenLoève approximation. We also discuss the efficiency of these methods and some parallel issues.
 Isabelle Faille (IFPEN)
 Titre: Modeling fluid flow in faulted basins
 Résumé:
Basin modeling is a tool used in petroleum system assessment that simulates the evolution of a sedimentary basin through geological time in order to obtain qualitative and quantitative descriptions of the fluids that fill the sedimentary rocks. In structurally complex settings, accounting for faults as a key controlling factor on fluid flows through time is of primary importance. In this talk, we will point out some of the difficulties that are encountered when modeling flow in faulted basins and discuss the numerical approaches that have been developed. In particular, we will present the doublelayer reduced fault model that is used to model flow along the fault zones and discuss different discretizations based on Finite Volume Methods.
 Yueyuan Gao (Université ParisSud)
 Titre: Finite volume methods for first order stochastic conservation laws
 Résumé:
We perform MonteCarlo simulations in the onedimensional torus for the first order Burgers equation forced by a stochastic source term with zero spatial integral. We suppose that this source term is a white noise in time, and consider various regularities in space. We apply a finite volume scheme combining the Godunov numerical flux with the EulerMaruyama integrator in time. It turns out that the empirical mean converges to the spaceaverage of the deterministic initial condition as time tends to infinity. The empirical variance also stabilizes for large time, towards a limit which depends on the space regularity and on the intensity of the noise. We then study a time explicit finite volume method with an upwind scheme for a conservation law driven by a multiplicative source term involving a QWiener process. We present some a priori estimates including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities for the discrete solution and show that it converges up to a subsequence to a stochastic measurevalued entropy solution of the conservation law in the sense of Young measures. The numerical part is joint work with E. Audusse and S. Boyaval while the convergence proof is joint work with T. Funaki and H. Weber.
 Sylvie Granet (EDF)
 Titre: Modelling of coupling problems in porous media: Goal and Issues in Geological Nuclear Waste Disposal application
 Résumé:
A great deal of attention is focused on mutiphysic problems in porous media in electricity industry. It concerns civil engineering works (dam construction, containment building, etc.) and radioactive waste management (feasibility of deep geological underground disposal, packaging of nuclear waste, etc.). General concept of an underground nuclear waste storage meets requirements of different kinds, variable with time. The integrity of constructions must be guaranteed during operating period and some difficulties are encountered because the set of galleries and the rock is complex. Consequently, deep knowledge of thermal, hydraulic and mechanical processes is necessary. First, an accurate description of mechanical behavior of geomaterials is a crucial issue. This is necessary to model excavation damaged zones (EDZ) which involves development of cracks and fractures in the rock. Those will modify the hydraulic properties of the soil creating preferred zones for water and radionuclides flow. Secondly, overpressures due to thermal loading or gas production (due to corrosion or radiolysis) have also to be taken into account. Moreover Chemical processes could occur in some special type of packages (bituminous packages for example). Therefore, and to describe the couplings and the transfers phenomena in these geological repositories, fully coupled thermohydromechanical models are developed in EDF’s homemade open source Finite Element software: Code_Aster (www.codeaster.org).
This models have numerical specificities: high nonlinearities, time dependency and physical variables multiplicity. All of that provides numerical difficulties and convergence problems. For this reason numerical schemes have been developed : adapted Finite Elements or Finite Volumes, regularization techniques, time and space adaptive schemes, etc. Moreover very complex studies are required today and we have to deal with HPC problems. For example, it is still difficult to provide a THM computation with a viscoplastic mechanical law on a real 3D structure in an acceptable time. For that, appropriated stopping criteria for the solvers and adaption criteria for the mesh and time step refinement have to be developed. Finally, comparing and fitting of numerical results with experimental tests constitute a crucial issue today. Specific strategy has to be developed.
 Johann Guilleminot (Université Paris Est)
 Titre: Stochastic representation of random positivedefinite tensorvalued properties: application to 3D anisotropic permeability random fields
 Résumé:
The study of fluid flows through porous media is an important field of both research and engineering, which has received a large attention from the scientific community during the past decades. Such an issue arises in various fields of applications, such as hydrogeology, petroleum engineering or composite manufacturing (in Liquid Composite Molding – LCM – processes). Predictive simulations of such flows generally require a very detailed description of both the mechanical and transport properties associated with the underlying medium, especially when random microstructures are involved. In this context, the construction and calibration of suitable stochastic representations for the properties of interest turns out to be critical in order to model inherent (e.g. soil) variability, as well as epistemic uncertainties (if need be). In this talk, emphasis is put on the construction, generation and statistical inverse identification of nonGaussian tensorvalued random field models. The latter are typically devoted to the representation of 3D nonisotropic permeability random fields, as well as to the representation of elasticity random fields (with arbitrary symmetries). A selfcontained theoretical treatment of informationtheoretic probabilistic models is first proposed along the lines detailed in [1, 3, 5] in elasticity, or in [2] for permeability random fields. Such models are particularly relevant when underdetermined statistical inverse problems are faced, hence making the identification of polynomial chaos representations (based on experimental measurements) hardly tractable. Algorithmic and sampling issues are then discussed. The numerical scheme is based on the definition of a family of Itô stochastic differential equations (indexed in space) [4], and involves a stochastic step sequence ensuring the convergence of the integration scheme. Numerical applications are finally provided so as to exemplify the proposed models and random generators.
References
[1] C. Soize, NonGaussian positivedefinite matrixvalued random fields for elliptic stochastic partial differential operators, Computer Methods in Applied Mechanics and Engineering, v.195(13), 2664 (2006)
[2] J. Guilleminot and C. Soize and R. Ghanem, Stochastic representation for anisotropic permeability tensor random fields, International Journal for Numerical and Analytical Methods in Geomechanics, v.36(13), 15921608 (2012)
[3] J. Guilleminot and C. Soize, Random fields with symmetry properties: Application to the mesoscopic modeling of elastic random media, SIAM Multiscale Modeling & Simulation, v.11(3), 840870 (2013)
[4] J. Guilleminot and C. Soize, Itô SDEbased generator for a class of nonGaussian vectorvalued random fields in uncertainty quantification, SIAM Journal of Scientific Computing, v.36(6), A2763A2786 (2014)
[5] B. Staber and J. Guilleminot, Approximate solutions of Lagrange multipliers for informationtheoretic random field models, SIAM/ASA Journal on Uncertainty Quantification, to appear (2015)
 Rainer Helmig (Université de Stuttgart)
 Titre: Modeling and Analysis of SoilMoisture Processes in the Subsurface: The Influence of Evaporation and Salt Precipitation in Groundwater
 Résumé:
During this presentation you will discover how soilmoisture processes in the subsurface play a crucial role in the hydrological cycle and the groundwater budget.
Understanding soilmoisture conditions in this zone is of interest in various applications in hydrology, such as landatmospheric interaction, soil evaporation and evapotranspiration, and climate modeling, as well as emerging problems in assessing the risk of, for example, the leakage of carbon dioxide or methane from deep geological formations to the shallow subsurface that affects groundwater quality and vegetation.
In this lecture you will learn about:
 Relevant processes of mass, momentum, and energy transfer at the interface between a freeflow and a porousmedia system
 Conceptual modeling for coupled singlephase free flow and twophase porousmedium flow with a detailed description of the models in the free flow and in the porous medium
 A new coupling concept for modeling coupled porousmedium and free flow with application to evaporation and saltprecipitation processes; a comparison study will show the advantages and disadvantages in comparison with classical approaches
 Three model combinations for evaporation processes and how to use them to study the effects of various quantities and processes—a porousmedium model coupled with a laminar freeflow model, a simple boundarylayer model, and a Reynoldsaveraged turbulence model that uses algebraic expressions to account for the turbulent flow behavior.
 Raphaèle Herbin (Université d'AixMarseille)
 Titre: Mathematical analysis of the MAC scheme for incompressible flows
 Résumé:
The scheme MarkerAndCell (MAC) introduced by Harlow and Welch in 1965 is widely used in computational fluid mechanics for
of its simplicity and because it requires a minimum number of degrees of freedom.
We perform the mathematical study of its convergence for incompressible flows using compactness methods which are classical in the study of finite volume schemes for nonlinear problems.
The key challenge in this context comes from the existence of several dual meshes (one for each direction of space) and from the treatment of nonlinear convection term .
 Michel Kern (INRIA Rocquencourt)
 Titre: Spacetime domain decomposition methods for flow and transport in porous media
 Résumé:
Global in time, nonoverlapping domain decomposition methods have proven to be a convenient and robust way for handling highly varying physical properties that are defining features of subsurface models, in particular because they allow different time steps in the different subdomains.
This presentation will give an overview of the method, and how it can be adapted to different models. A common thread will be the reformulation of the multidomain model, through optimized transmission conditions and local subdomain solvers, as a (spacetime) interface problem.
After explaining in details the method for the case of one phase diffusion, we will show how it can be extended to handle advection, fractured media, and two phase flow with discontinuous capillary pressure (the last part is a work in progress).
 Lionel Lenôtre (INRIA Rennes)
 Titre: Lagrangian methods for parabolic partial differential equations with discontinuous coecients: analytical computation of transition's densities and simulation algorithms
 Résumé:
Parabolic partial differential equations with discontinuous coefficients are involved in a large variety of applications (physic, biology, etc... See e.g. [4, 5]). However, reliable approximations using Lagrangian methods are still a challenge both theoretically and numerically, especially in presence of interfaces. In this talk, we present some recent work consisting in the computation of analytical solutions of such equations. Precisely, we will detail the link between parabolic partial differential equations and stochastic processes, a method for the computation of the solution using TitchmarshKodaira theory [3] and Feller work [1, 2]. We also propose Lagrangian stochastic simulation schemes.
Bibliography
[1] William Feller. Generalized second order dierential operators and their lateral conditions. Illinois J. Math.,1,459:504, 1957.
[2] William Feller. On the intrinsic form for second order dierential operator. Illinois J. Math., 2(1),1:18, 1959.
[3] K. Kodaira. Eigenvalue problem for ordinary dierential equations of second order and Heisenberg’s theory of smatrices.
Amer. J. Math., 71,921:945, 1949.
[4] A. Lejay and G. Pichot. Simulating diusion processes in discontinuous media: a numerical scheme with constant time steps. Journal of Computational Physics,231, 7299:7314, 2012.
[5] J. M. Ramirez, E. A. Thomann, and E. C. Waymire. Advectiondispersion across interfaces. Statist. Sci.,28(4), 487:509, 2013.
 Simon Lopez (BRGM)
 Titre: Some aspects and current needs for geothermal reservoir modeling
 Résumé:
Geothermal energy is a carbonfree steady subsurface energy source with low environmental impact. Depending on the resource temperature level, it can be used to generate electricity and/or provide direct use for numerous applications. In countries with a favorable geological context, high temperature geothermal energy can make a significant contribution to power production. In France, geothermal power production is already an attractive option in volcanic islands compared to importing fossil fuel. More generally, the development of Enhanced Geothermal Systems is expected to considerably widen the range of geological settings where geothermal power production is possible, but this will require a sound understanding and quantification of deep fluids circulation. We will briefly review different forms of geothermal energy and focus on some current needs for geothermal reservoir modeling in volcanic settings.
Numerical modeling has become essential in all phases of geothermal operations. It is used in the exploration phases to assess the geothermal potential, validate conceptual hypothesis and help well siting. Static conceptual models are built to bring together all the available information into one single consistent model of the subsurface. Then, dynamic modeling is performed to reproduce the natural state of the system and quantitatively compare different exploitation strategies. Considering the current geothermal modeling state of the art there is an established need for a better integration of static and dynamic models opening the door for a new generation of conceptual geothermal reservoir models. These new models must be larger and deeper with the possibility to model both the roots of geothermal systems and surface features. The dynamic behavior of such systems involves highly nonlinear physics and fluid equations of state describing physical and thermodynamic properties over a very wide range of pressures (1 Pa100 MPa) and temperature (10°C1000°C).
 Anthony Nouy (Ecole Centrale de Nantes)
 Titre: Preconditioners for parameterdependent equations and projectionbased model reduction methods
 Résumé:
We present a method for the construction of preconditioners for large systems of parameterdependent equations, where an interpolation of the matrix inverse is computed through a projection of the identity with respect to random approximations of the Frobenius norm. Adaptive interpolation strategies are then proposed for different objectives in the context of projectionbased model order reduction methods: error estimation, projection on a given approximation space, or recycling of computations.
 Clémentine Prieur (Université Joseph Fourier)
 Titre: Goaloriented error estimation for the reduced
basis method, application to sensitivity analysis
 Résumé:
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of
parametrized partial differential equations. We consider a quantity of interest, which is a functional of the PDE solution, and we propose a probabilistic error bound for the reduced model. We discuss the need of accurate, explicitly computable error bounds for sensitivity analysis.
 Michel Quintard (CNRS, IMFT)
 Titre: TwoPhase Flow and Heat Transfer in Highly Permeable Porous Media
 Résumé:
Twophase flows in highly permeable porous media depart easily from the classical slow, quasistatic behavior that is behind the use of the classical generalized Darcy's law. Indeed,
capillary, Bond and Reynolds number can reach important values which requires new specific treatments. Such flows happen in many applied fields like in chemical engineering (structured
media, trickle beds, …), nuclear safety (debris bed reflooding, …), geothermy (hot springs, maar orphreatic explosions, ...).
In a first part of the paper, hybrid mesoscale models and macroscale models are presented to deal with highly dynamic porescale twophase flows with large Bond numbers or large Reynolds numbers as well as large Capillary numbers. Hybrid mesoscale models are based on a combination of porescale local simulations embedded in a networkscale modeling. It is shown that the resulting models have all the necessary ingredients to account for dynamic spreading of twophase plumes as opposed to quasistatic capillary spreading triggered by capillary pressure gradients. For pure macroscale models, several candidate models designed to account for liquid retention due to the drag force of a countercurrent flow are discussed from a theoretical and experimental perspective. Models are then coupled to heat transfer to account for intense boiling such as in reflooding of a debris bed after a severe nuclear reactor accident. It is shown that a local nonequilibrium model is necessary and that the heat exchange term has a complex dependence on saturation and flow conditions. In particular, it requires the introduction of Nukiyamalike boiling curves specific to porous media.
 Mazen Saad (Ecole Centrale de Nantes)
 Titre: Mathematical analysis of compressible multifluid flows in porous media
 Résumé:
We consider a porous media model describing the evolution of pressures and saturations of nonmiscible and compressible phases in porous media. In the case of multifluid flow and under the assumption that the densities are bounded, we introduce the notion of total differential condition and we establish energy estimates to obtain weak solutions for such a model. Next, our interest is the case of slightly compressible phases for which the density of each phase follows an exponential law with a small compressibility factor. A degenerate weighted weak formulation is introduced to take into account the compressibility and the degeneracy. Existence results of degenerate weak solutions are introduced.
 Laurent Trenty (Andra)
 Titre: Complex multiphysics multilayers modelling approach for ironenvironment interactions and upscaling to an HLW cell scale of geological repository radioactive wastes.
 Résumé:
Engineered barrier system designed for deep geological repository for high and intermediatelevel longlived radioactive wastes (HLW, ILWLL) consists of a complex system of different underground structures where metallic materials have a major role in reversibility and safety performance. The evaluation of their physicochemical behaviour (corrosion) and mechanical may allow to optimize steel grades selection and to size the overpack and liners, as well as to identify their role in the process of degradation of components in concrete. The liner and overpack will be exposed to a chemical environment evolving in time. Concentrations of oxygen, hydrogen, relative humidity, water saturation and temperature will fluctuate significantly during the time of geological disposal which could be favour or disfavour to steel passivation conditions and modify corrosion kinetics.
Modelling of coupled effects between electrochemistry and geochemistry at cell scale is primordial to improve knowledge of corrosion processes and to optimise metallic components design according to safety performance. Difficulties of such modelling are to simulate both nano, micro and metric scales respectively representative of oxide layer at the iron surface, corrosion products layer and environment.
Today we are developping in collaboration with CEA, Inria, LHyGeS (Strasbourg University) and ICB (Bourgogne University) software and coupling approaches able to simulate a part of each problem. An integrated work is carried out to simulate in a coupled way oxidation of iron, appearance or not of the different layers and geochemical evolution of the porous media.
 Yumeng Zhang (Université de Nice et INRIA Sophia Antipolis)
 Titre: Coupling of a liquid gas compositional 2D Darcy flow with a 2D compositional free gas flow
 Résumé:
In this talk we present an efficient algorithm to solve coupled gas liquid Darcy and free gas flows at the porous and free flow domain interface. A reduced model using a 1D approximation of the gas free flow is also introduced and compared to the full model. The algorithms are applied to the modeling of mass exchanges at the interface between the storage and the ventilation galleries in radioactive waste disposals.
Contact
