... ABSTRACT A modified random choice method is described for solving simultaneously the Buckley-Leverett, incompressibility, and Darcy's Law equations for immiscible displacement in a porous medium. The main idea of the numerical method is to modify the one-dimensional Riemann solvers in the split...

... accounts for the diffusive part of the convection-diffusion equation. Unlike conventional finite difference methods, which approximate the convection term by some form of upwind differencing scheme, the present approach calculates the convective flow by the random choice method in the first fractional step...