Finite-Volume Methods for Anisotropic Diffusion Problems on Skewed Meshes

Abstract

A direct numerical method for the anisotropic diffusion equation is presented and the balance-point method and adaptive method are also derived. All these methods are formulated and implemented in the in-house fluid flow solver GTEA. Two test cases, an isotropic problem and an anisotropic problem with exact solution on a skewed mesh, are chosen for comparison and validation. The error and computation time are illustrated. It is concluded that the direct method has the least computation time among all the diffusion problems and that all the methods meet the precision requirement in engineering computation even on skewed meshes.