A numerical method for two phase flow with an unstable interface

The random choice method is used to compute the oil-water interface for two dimensional porous media equations. The equations used are a pair of coupled equations: the (elliptic) pressure equation and the (hyperbolic) saturation equation. The equations do not include the dispersive capillary pressure term and the computation does not introduce numerical diffusion. The method resolves saturation discontinuities sharply. The main conclusion of this paper is that the random choice is a correct numerical procedure for this problem even in the highly fingered case. Two methods of inducing fingers are considered: deterministically, through choice of Cauchy data and heterogeneity, through maximizing the randomness of, the random choice method.