Numerical Approximation of a Two-phase Flow Problem in a Porous Medium with Discontinuous Capillary Forces

Abstract

We consider a simplified model of a two-phase flow through a heterogeneous porous medium. Focusing on the capillary forces motion, a nonlinear degenerate parabolic problem is approximated in a domain shared in two homogeneous parts, each of them being characterized by its relative permeability and capillary curves functions of the phase saturations. We first give a weak form of the conservation equations on the whole domain, with a new general expression of the conditions at the interface between the two regions. We then propose a finite volume scheme for the approximation of the solution, which is shown to converge to a weak solution in one-, two-, or three-dimensional domains. We conclude with some numerical tests.