A Local Support-Operators Diffusion Discretization Scheme for Quadrilateralr-zMeshes

Abstract

We derive a cell-centered 2-D diffusion differencing scheme for arbitrary quadrilateral meshes inr-zgeometry using a local support-operators method. Our method is said to be local because it yields a sparse matrix representation for the diffusion equation, whereas the traditional support-operators method yields a dense matrix representation. The diffusion discretization scheme that we have developed offers several advantages relative to existing schemes. Most importantly, it offers second-order accuracy even on meshes that are not smooth, rigorously treats material discontinuities, and has a symmetric positive-definite coefficient matrix. The only disadvantage of the method is that it has both cell-center and face-center scalar unknowns as opposed to just cell-center scalar unknowns. Computational examples are given which demonstrate the accuracy and cost of the new scheme relative to existing schemes.