A Local Support-operator di€usion discretization scheme for quadrilateral r±z meshes

We derive a cell-centered 3-D diusion dierencing 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 diusion equation, whereas the traditional support-operators method yields a dense matrix representation. The diusion discretization scheme that we have developed oers several advantages relative to existing schemes. Most importantly, it oers second-order accuracy even on meshes that are not smooth, rigorously treats material discontinuities, and has a symmetric positive-de nite coecient 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. 2