A LOCAL SUPPORT-OPERATORS DIFFUSION DISCRETIZATION SCHEME FOR QUADRILATERAL R-Z MESHES

We derive a cell-centered 2-D diffusion differencing scheme for arbitr ary quadrilateral meshes in r-z geometry using a local support-operato rs method. Our method is said to be local because it yields a sparse m atrix representation for the diffusion equation, whereas the tradition al 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 s econd-order accuracy even on meshes that ale not smooth, rigorously tr eats material discontinuities, and has a symmetric positive-definite c oefficient matrix. The only disadvantage of the method is that it has both cell-center and face-center scalar unknowns as opposed to just ce ll-center scalar unknowns. Computational examples are given which demo nstrate the accuracy and cost of the new scheme relative to existing s chemes. (C) 1998 Academic Press.