CENTRAL DIFFERENCE-LIKE APPROXIMATION FOR THE SOLUTION OF THE CONVECTION-DIFFUSION EQUATION

Abstract

A method was developed for the numerical solution of the convection-diffusion equation. It is based on a central difference-like approximation and the requirement that cell face values of the convected variable must be bounded by their adjacent cell center values. To evaluate its performance, a two-dimensional problem that has bean used in the literature to test a large number of methods was used as a benchmark. The predictions of the proposed method are in very good agreement with the benchmark for all Péclet numbers. They are free of oscillations and far superior to those of the upwind scheme. At high Péclet numbers, spatial oscillations are the weakness of central difference schemes and Galerkin finite-element methods. Also, at high Péclet values, due to false diffusion, the accuracy of first-order upwind and hybrid schemes in practical meshes is poor.