General fully implicit discretization of the diffusion term for the finite volume method

Abstract

In this paper, a fully implicit method for the discretization of the diffusion term is presented in the context of the cell-centered finite volume method. The newly developed fully implicit method is denoted by the modified implicit nonlinear diffusion (MIND) scheme. The method is used to solve several isotropic and anisotropic diffusion problems in two-dimensional domains covered with structured (quadrilateral elements) and unstructured (triangular elements) grid systems. The comparison of generated results with similar ones obtained using the semi-implicit scheme demonstrates the superior robustness and accuracy of the MIND scheme and its good convergence characteristics for all types of meshes. © 2017 Taylor & Francis.