A Local Support-Operators Diffusion Discretization
Scheme for Hexahedral Meshes


J. E. Morel, Michael L. Hall, and Mikhail J. Shashkov
University of California
Los Alamos National Laboratory
Los Alamos, NM 87545


Submitted to the Journal of Computational Physics, Summer 1999

Abstract:

We derive a cell-centered 3-D diffusion differencing 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 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 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-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.

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