The Weighted Upwinding Finite Volume Method for the Convection Diffusion Problem on a Nonstandard Covolume Grid

Abstract

In this paper we propose a weighted upwinding finite volume method on a nonstandard covolume grid for the variable coefficient convection-diffusion problems. We give a simple method of choosing the optimal weighted factors depending on the local Peclet's numbers of the original problem. With the optimal factors the method overcomes numerical oscillation and avoids the numerical dispersion and has high-order computing accuracy. The conservation law and the maximum principle are proved. The second-order error estimates in L2 and discrete H1 norms are obtained for the optimal weighted upwinding finite volume method. Numerical experiments are given to illustrate the performance of the method. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)