A Characteristic Difference Method for 2D Nonlinear Convection-Diffusion Problems

Abstract

In this paper we construct a characteristic difference method for two-dimensional nonlinear convection-diffusion problems. These problems arise in the modeling of fluid flow and transport in porous media, for example. The method is analysed mathematically and an error bound is derived. Convergence of the method can be achieved under a milder restriction in the temporal stepsize and spatial stepsize than those required by existing methods.