Benchmark 3D: A Monotone Nonlinear Finite Volume Method for Diffusion Equations on Polyhedral Meshes

Abstract

We propose a new monotone FV method based on a nonlinear two-point flux approximation scheme. The original idea belongs to C. LePotier [2] who proposed a monotone FV scheme for the discretization of parabolic equations on triangular meshes, which was extended to steady-state diffusion problems with full anisotropic tensors on triangulations or scalar diffusion coefficients on shape regular polygonal meshes [3]. Later a new interpolation-freemonotone cell-centered FV method with nonlinear two-point flux approximation was proposed for full diffusion tensors and unstructured conformal polygonal 2D meshes [4]. In this paper, we extend the last approach to the case of 3D conformal polyhedral meshes [1]. © Springer-Verlag Berlin Heidelberg 2011.