On Approximating Solutions of a Class of Systems of Equations Modeling Immiscible two-phase Flow through a Porous Medium

Dr. Koffi Fadimba

Department of Mathematics
University of Rhode Island, Kingston

March 27, 2002

Abstract

We consider the pressure/saturation system obtained by modeling immiscible two-phase flow (water/oil, for instance) through a porous medium. One obtains a coupled nonlinear degenerate system of advection-diffusion equations. In trying to solve such a problem, one is confronted with three major difficulties: the "coupledness", the non-linearity, and the degeneracy. Each of these difficulties requires that one approximates the problem by a family of problems. In this presentation we focus on the degenerate nature of this class of problems: regularize the problem to get a nondegenerate problem, then approximate the solution of the regularized problem numerically. We consider the different steps for approximating the solution of the initial problem (regularization, discretization in the space variable, full discretization, and linearization of the scheme obtained). We go over some techniques for deriving error estimates for these different steps of approximation