%0 Journal Article
%T Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media*
%A Brenner Konstantin
%J ESAIM : Proceedings
%D 2012
%I EDP Sciences
%R 10.1051/proc/201235016
%X We propose a finite volume method on general meshes for the numerical simulation of an incompressible and immiscible two-phase flow in porous media. We consider the case that can be written as a coupled system involving a degenerate parabolic convection-diffusion equation for the saturation together with a uniformly elliptic equation for the global pressure. The numerical scheme, which is implicit in time, allows computations in the case of a heterogeneous and anisotropic permeability tensor. The convective fluxes, which are non monotone with respect to the unknown saturation and discontinuous with respect to the space variables, are discretized by means of a special Godunov scheme. We prove the existence of a discrete solution which converges, along a subsequence, to a solution of the continuous problem. We present a number of numerical results in space dimension two, which confirm the efficiency of the numerical method. Nous proposons un sch¨¦ma de volumes finis hybrides pour la discr¨¦tisation d¡¯un probl¨¨me d¡¯¨¦coulement diphasique incompressible et immiscible en milieu poreux. On suppose que ce probl¨¨me a la forme d¡¯une ¨¦quation parabolique d¨¦g¨¦n¨¦r¨¦e de convection-diffusion en saturation coupl¨¦e ¨¤ une ¨¦quation uniform¨¦ment elliptique en pression. On consid¨¨re un sch¨¦ma implicite en temps, o¨´ les flux diffusifs sont discr¨¦tis¨¦s par la m¨¦thode des volumes finis hybride, ce qui permet de pouvoir traiter le cas d¡¯un tenseur de perm¨¦abilit¨¦ anisotrope et h¨¦t¨¦rog¨¨ne sur un maillage tr¨¨s g¨¦n¨¦ral, et l¡¯on s¡¯appuie sur un sch¨¦ma de Godunov pour la discr¨¦tisation des flux convectifs, qui peuvent ¨ºtre non monotones et discontinus par rapport aux variables spatiales. On d¨¦montre l¡¯existence d¡¯une solution discr¨¨te, dont une sous-suite converge vers une solution faible du probl¨¨me continu. On pr¨¦sente finalement des cas test bidimensionnels.
%U http://dx.doi.org/10.1051/proc/201235016