A positivity-preserving finite volume scheme for convection–diffusion equation on general meshes

Abstract

A new positivity-preserving finite volume scheme is proposed for solving the convection–diffusion equation on 2D or 3D distorted meshes. The nonlinear two-point flux approximation is applied to the discretization of diffusion flux. The discretization of convection flux is based on the second-order upwind method with a slope limiter. The cell centres are employed to define the primary unknowns. The cell vertexes are devoted to define the auxiliary unknowns, which can be computed from the primary unknowns. And the interpolation method of this scheme is not required to be positivity-preserving. Numerical results illustrate that the scheme is effective in solving the convection–diffusion problem and has second-order convergence rate on the distorted meshes.