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 second-order accuracy even on meshes that ale 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.