A simple and high accurate finite volume scheme for diffusion equations

Abstract

Most of numerical methods for diffusion equations, refer to vertex unknowns directly or indirectly, and their accuracy is ultimately determined by the approximation to vertex unknowns. Based on the “twin-fitting” method, a simple and high accurate treatment for the vertex unknowns is developed and is applied to the nine-point scheme for diffusion problem. Numerical experiments show that the resulting nine-point scheme is high accurate for diffusion problems with discontinuous diffusion coefficients on distorted meshes.