A novel cell-centered finite volume scheme with positivity-preserving property for the anisotropic diffusion problems on general polyhedral meshes

Abstract

In this paper, we propose a novel cell-centered positivity-preserving finite volume scheme for the anisotropic diffusion problems. The discretization of diffusion flux is based on the standard nonlinear two-point flux approximation. The cell vertexes are employed to define auxiliary unknowns. A positivity-preserving vertex interpolation algorithm is constructed to get the value of auxiliary unknowns. This interpolation algorithm has almost second order convergence rate on the distorted meshes. Numerical results illustrate that our scheme is efficient and practical in solving the 3D anisotropic diffusion problems.