A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes

A new finite volume method is presented for discretizing general linear or nonlinear elliptic second-order partial-differential equations with mixed boundary conditions. The advantage of this method is that arbitrary distorted meshes can be used without the numerical results being altered. The resulting algorithm has more unknowns than standard methods like finite difference or finite element methods. However, the matrices that need to be inverted are positive definite, so the most powerful linear solvers can be applied. The method has been tested on a few elliptic and parabolic equations, either linear, as in the case of the standard heat diffusion equation, or nonlinear, as in the case of the radiation diffusion equation and the resistive diffusion equation with Hall term.