The cell-centered positivity-preserving finite volume scheme for 3D anisotropic diffusion problems on distorted meshes

Abstract

In this paper, a new cell-centered positivity-preserving finite volume scheme is proposed for the 3D anisotropic diffusion problems on distorted meshes. The primary unknowns and auxiliary unknowns are used in this scheme. First, the one-sided flux on each cell facet is discretized by a fixed stencil. Then, the nonlinear two-point flux approximation is applied to get the cell-centered discrete scheme. Besides, a second-order interpolation algorithm is constructed to eliminate the auxiliary unknowns in flux expressions. Furthermore, an improved Anderson acceleration method is given to accelerate the convergence of Picard iterations. Finally, several numerical examples are presented to show the accuracy and efficiency of the proposed scheme.