Stabilized semi-implicit finite volume scheme for parabolic tensor diffusion equations

Abstract

We introduce a new stabilized nite volume method for solving tensor diusion equations. The new scheme is based on the classical diamond-cell nite volume method and on the idea of in ow-implicit/out ow-explicit (or forward-backward diusion) splitting accompanied by a suitable stabilization. Comparisons with known exact solution and numerical experiments investigating stability of the proposed method in case of highly anisotropic diusion tensor are discussed.