An extremum-preserving finite volume scheme for convection-diffusion equation on general meshes

Abstract

We present an extremum-preserving finite volume scheme for the convection-diffusion equation on general meshes in this article. The harmonic averaging point locating at the interface of heterogeneity are utilized to define the auxiliary unknowns. The second-order upwind method with a slope limiter is used for the discretization of convection flux. This scheme has only cell-centered unknowns and possesses a small stencil. The extremum-preserving property of this scheme is proved by standard assumption. Numerical results demonstrate that the extremum-preserving scheme is an efficient method in solving the convection-diffusion equation on distorted meshes.