Geodesic
Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media
Konstantin Brenner1
1 Laboratoire de Mathématiques, Université de Paris-Sud 11, F-91405 Orsay Cedex, France
ESAIM. Proceedings, Tome 35 (2012), pp. 210-215.

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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.
DOI : 10.1051/proc/201235016

Konstantin Brenner 1

1 Laboratoire de Mathématiques, Université de Paris-Sud 11, F-91405 Orsay Cedex, France 
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Konstantin Brenner. Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media. ESAIM. Proceedings, Tome 35 (2012), pp. 210-215. doi : 10.1051/proc/201235016. http://geodesic.mathdoc.fr/articles/10.1051/proc/201235016/

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