Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation

We present an accurate numerical method for a large class of scalar, strong ly degenerate convection-diffusion equations. Important subclasses are hype rbolic conservation laws, porous medium type equations, two-phase reservoir how equations, and strongly degenerate equations coming from the recent th eory of sedimentation-consolidation processes. The method is based on split ting the convective and the diffusive terms. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlin ear diffusion part is solved by an implicit-explicit finite difference sche me. In addition, one version of the implemented operator splitting method h as a mechanism built in for detecting and correcting unphysical entropy los s, which may occur when the time step is large. This mechanism helps us gai n a large time step ability for practical computations. A detailed converge nce analysis of the operator splitting method was given in Part I. Here we present numerical experiments with the method for examples modelling second ary oil recovery and sedimentation-consolidation processes. We demonstrate that the splitting method resolves sharp gradients accurately, may use larg e time steps, has first order convergence, exhibits small grid orientation effects, has small mass balance errors, and is rather efficient.