Finite Difference Methods for Two-Phase Incompressible Flow in Porous Media

Two-phase, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. Convection physically dominates diffusion, and the object of this paper is to develop a finite difference procedure that reflects this dominance. The pressure equation, which is elliptic in appearance, is discretized by a standard five-point difference method. The concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms. A convergence analysis is given for the method.