Robust Newton solver based on variable switch for a finite volume discretization of Richards equation

International audienceWe propose an efficient nonlinear solver for the resolution of the Richards equation. It is based on variable switching and is easily implemented thanks to a fictitious variable allowing to describe both the saturation and the pressure. Numerical experiments show that our method enables to use Newton's method with large time steps, reasonable number of iterations and in regions where the pressure-saturation relationship is given by a graph

A Priori Error Estimate of a Multiscale Finite Element Method for Transport Modeling

International audienceThis work proposes an \textit{a priori} error estimate of a multiscale finite element method to solve convection-diffusion problems where both velocity and diffusion coefficient exhibit strong variations at a scale which is much smaller than the domain of resolution. In that case, classical discretization methods, used at the scale of the heterogeneities, turn out to be too costly. Our method, introduced in~\cite{ECCOMAS}, aims at solving this kind of problems on coarser grids with respect to the size of the heterogeneities by means of particular basis functions. These basis functions are defined using cell problems and are designed to reproduce the variations of the solution on an underlying fine grid. Since all cell problems are independent from each other, these problems can be solved in parallel, which makes the method very efficient when used on parallel architectures. This article focuses on the proof of an \textit{a priori} error estimate of this method

Approximating the vanishing capillarity limit of two-phase flow in multi-dimensional heterogeneous porous medium

International audienceNeglecting capillary pressure effects in two-phase flow models for porous media may lead to non-physical solutions: indeed, the physical solution is obtained as limit of the parabolic model with small but non-zero capillarity. In this paper, we propose and compare several numerical strategies designed specifically for approximating physically relevant solutions of the hyperbolic model with neglected capillarity, in the multi-dimensional case. It has been shown in [Andreianov&Canc'es, Comput. Geosci., 2013, to appear] that in the case of the one-dimensional Buckley-Leverett equation with distinct capillary pressure properties of adjacent rocks, the interface may impose an upper bound on the transmitted flux. This transmission condition may reflect the oil trapping phenomenon. We recall the theoretical results for the one-dimensional case which are used to motivate the construction of multi- dimensional finite volume schemes. We describe and compare a coupled scheme resulting as the limit of the scheme constructed in [Brenner & Canc'es & Hilhorst, HAL preprint no.00675681, 2012) and two IMplicit Pressure - Explicit Saturation (IMPES) schemes with different level of coupling

A Cell-Centred CVD-MPFA Finite Volume Method for Two-Phase Fluid Flow Problems with Capillary Heterogeneity and Discontinuity

A novel finite-volume method is presented for porous media flow simulation that is applicable to discontinuous capillary pressure fields. The method crucially retains the optimal single of freedom per control-volume being developed within the flux-continuous control-volume distributed multi-point flux approximation (CVD-MPFA) framework (Edwards and Rogers in Comput Geosci 02(04):259–290, 1998; Friis et al. in SIAM J Sci Comput 31(02):1192–1220, 2008) . The new methods enable critical subsurface flow processes involving oil and gas trapping to be correctly resolved on structured and unstructured grids. The results demonstrate the ability of the method to resolve flow with oil/gas trapping in the presence of a discontinuous capillary pressure field for diagonal and full-tensor permeability fields. In addition to an upwind approximation for the saturation equation flux, the importance of upwinding on capillary pressure flux via a novel hybrid formulation is demonstrated

A Priori Error Estimate of a Multiscale Finite Element Method for Transport Modeling

International audienceThis work proposes an \textit{a priori} error estimate of a multiscale finite element method to solve convection-diffusion problems where both velocity and diffusion coefficient exhibit strong variations at a scale which is much smaller than the domain of resolution. In that case, classical discretization methods, used at the scale of the heterogeneities, turn out to be too costly. Our method, introduced in~\cite{ECCOMAS}, aims at solving this kind of problems on coarser grids with respect to the size of the heterogeneities by means of particular basis functions. These basis functions are defined using cell problems and are designed to reproduce the variations of the solution on an underlying fine grid. Since all cell problems are independent from each other, these problems can be solved in parallel, which makes the method very efficient when used on parallel architectures. This article focuses on the proof of an \textit{a priori} error estimate of this method

Modèles et schémas numériques pour la simulation de genèse de bassins sédimentaires

M. Damien Lamberton, Président du jury,M. Robert Eymard, Directeur de thèse,M. Jacques Blum, Rapporteur,M. Pierre Fabrie, Rapporteur,M. Jürgen Fuhrmann, Rapporteur,Mme Raphaèle Herbin, Examinateur,M. Roland Masson, Membre invité.This work presents some results concerning the modelling and the simulationof sedimentary basins.We first describe the mathematical models and the numerical schemes used inthe Institut Français du Pétrole within the framework of the Temisproject. This first part is illustrated by numerical tests dealing with 1D/2D basins.We then study an upwind scheme commonly used for the resolution of Darcy's equations and we establish new mathematical results for a Dead-Oil model. We also show how to design a scheme with a variable Péclet number in presence of capillary pressure. Again, we complete a mathematical study and we prove the convergence of the scheme for a simplified case. Numerical tests achieved on a model problem show that the use of a variable Péclet number improves the precisionof the calculations.Finally, in a last part, we consider a flow problem where the rock changes and the changes of capillary pressure curves are coupled. We precise the physical condition that the solutions in saturation must satisfy on the interfaces where the type of rock changes and we deduce from this condition an original weak problem. The existence of a solution to this problem is obtained by proving the convergence of a finite volume scheme. Numerical examples showthe effects of the interface condition on the capillary trapping.Ce travail présente quelques contributions à la modélisationet à la simulation de genèse de bassins sédimentaires.Nous présentons tout d'abord les modèles mathématiques et les schémas numériques mis en oeuvre à l'Institut Françaisdu Pétrole dans le cadre du projet Temis. Cette première partie est illustrée à l'aide de tests numériques portant sur des bassins 1D/2D.Nous étudions ensuite le schéma amont des pétroliers utilisé pour la résolution des équations de Darcy et nous établissons des résultats mathématiques nouveauxdans le cas d'un écoulement de type Dead-Oil.Nous montrons également comment construire un schéma à nombrede Péclet variable en présence de pression capillaire. Là encore, nous effectuons une étude mathématiquedétaillée et nous montrons la convergence du schémadans un cas simplifié. Des tests numériques réaliséssur un problème modèle montrent que l'utilisation d'un nombrede Péclet variable améliore la précision des calculs.Enfin nous considérons dans une dernière partie un modèle d'écoulement où les changements de lithologie et les changements de courbes de pression capillaire sont liés.Nous précisons la condition physique que doivent vérifierles solutions en saturation aux interfaces de changement de roche etnous en déduisons une formulation faible originale.L'existence d'une solution à ce problème est obtenuepar convergence d'un schéma volumes finis.Des exemples numériques montrent l'influence de la conditiond'interface sur le passage ou la retenue des hydrocarbures

Application of the mixed multiscale finite element method to parallel simulations of two-phase flows in porous media

The Mixed Multiscale Finite Element method (MMsFE) is a promising alternative to traditional upscaling techniques in order to accelerate the simulation of flows in large heterogeneous porous media. Indeed, in this method, the calculation of the basis functions which encompass the fine-scale variations of the permeability field, can be performed in parallel and the size of the global linear system is reduced. However, we show in this work that a two-level MPI strategy should be used to adapt the calculation resources at these two steps of the algorithm and thus obtain a better scalability of the method. This strategy has been implemented for the resolution of the pressure equation which arises in two-phase flow models. Results of simulations performed on complex reservoir models show the benefits of this approach

Understanding the interaction between henipaviruses and their natural host, fruit bats: Paving the way toward control of highly lethal infection in humans

International audienceHendra virus and Nipah virus (NiV) are highly pathogenic zoonotic paramyxoviruses, from henipavirus genus, that have emerged in late 1990s in Australia and South-East Asia, respectively. Since their initial identification, numerous outbreaks have been reported, affecting both domestic animals and humans, and multiple rounds of person-to-person NiV transmission were observed. Widely distributed fruit bats from Pteropodidae family were found to be henipavirus natural reservoir. Numerous studies have reported henipavirus seropositivity in pteropid bats, including bats in Africa, thus expanding notably the geographic distribution of these viruses. Interestingly, henipavirus infection in bats seems to be asymptomatic, in contrast to severe disease induced in numerous other mammals. Unique among the mammals by their ability to fly, these intriguing animals are natural reservoir for many other emerging and remerging viruses highly pathogenic for humans. This feature, combined with absence of clinical symptoms, has attracted the interest of scientific community to virus-bat interactions. Therefore, several bat genomes were sequenced and particularities of the bat immune system have been intensively analyzed during the last decade to understand their coexistence with viruses in the absence of disease. The peculiarities in inflammasome activation, a constitutive expression of interferon alpha, and some differences in adaptive immunity have been recently reported in fruit bats. Studies on virus-bat interactions have thus emerged as an exciting novel area of research that should shed new light on the mechanisms that regulate viral infection and may allow development of novel therapeutic approaches to control this highly lethal emerging infectious disease in humans