A Local Support-Operators Di usion Discretization Scheme for Hexahedral Meshes

We derive a cell-centered 3-D di usion di erencing scheme for arbitrary hexahedral meshes using the local support-operators method. Our method is said to be local because it yields a sparse matrix representation for the di usion equation, whereas the traditional support-operators method yields a dense matrix representation. The di usion discretization scheme that we have developed o ers several advantages relative to existing schemes. Most importantly, it o ers second-order accuracy even on meshes that are not smooth, rigorously treats material discontinuities, and has a symmetric positive-de nite coe cient matrix. The only disadvantage of the method is that it has both cell-centered and face-centered scalar unknowns as opposed to just cell-center scalar unknowns. Computational examples are given which demonstrate the accuracy and cost of the new scheme.