Multipoint Schemes for the Solution of the Diffusion Equation by Vectorial Computation

The discretized diffusion equation is structured in a formalism embodying in the left side all the terms involving the group fluxes at the generic point under calculation, and in the right side containing all the terms involving the fluxes at neighbor points. This formalism is especially suited for vectorial computation and also presents very good computing performance in scalar computers. The computing methodology includes an acceleration technique, “coarse-mesh precalculation,” to minimize computing times, particularly for cases with very large numbers of points. The algorithm is stable and positive, and it is improved by a discretization of the Laplacian operator using five points in each coordinate.