Hybrid finite volume scheme for a two-phase flow in heterogeneous porous media

Abstract

We apply a finite volume method on general meshes for the discretization of an incompressible and immiscible two-phase flow in porous media. The problem is considered in the global pressure formulation. Mathematically, it amounts to solve an elliptic equation for the global pressure, with an anisotropic and heterogeneous permeability ten-sor coupled to a parabolic degenerate convection-diffusion equation for a saturation, again with the same permeability tensor. Extending ideas which we had previously developed for the numerical solution of a degenerate parabolic convection-reaction-diffusion equation we discretize the diffusion terms by means of a hybrid finite volume scheme, while we use a Godunov scheme for the non monotone convection flux. We prove the convergence of the numerical scheme in arbitrary space dimension and we present results of a number of numerical tests in space dimension two.