A Local Support-Operators Diffusion Discretization Scheme for Quadrilateral r-z Meshes

We derive a cell-centered 2-D diffusion differencing scheme for arbitrary quadrilateral meshes in r-z geometry 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 secondorder 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. c © 1998 Academic Press