on A Local Support-Operators Diffusion Discretization Scheme for

We derive a cell-centered 3-D diffusion differencing scheme for unstructured hex-ahedral 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 represen-tation. The diffusion discretization scheme that we have developed offers several advantages relative to existing schemes. Most importantly, it offers second-order accuracy on reasonably well-behaved nonsmooth meshes, rigorously treats material discontinuities, and has a symmetric positive-definite coefficient matrix. The order of accuracy is demonstrated computationally rather than theoretically. Rigorous treat-ment of material discontinuities implies that the normal component of the flux is continuous across such discontinuities while the parallel components may be either continuous or discontinuous in accordance with the exact solution to the problem be-ing considered. 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. c ° 2001 Academic Press Key Words: diffusion; support-operators method; unstructured mesh