Parallelization of an unstructured grid, hydrodynamic-diffusion code

Abstract

We describe the parallelization of a three dimensional, unstructured grid, finite element code which solves hyperbolic conservation laws for mass; momentum, and energy, and diffusion equations modeling heat conduction and radiation transport. Explicit temporal differencing advances the cell-based gasdynamic equations. Diffusion equations use fully implicit differencing of nodal variables which leads to large, sparse; symmetric, and positive definite matrices. Because of the unstructured grid, the off-diagonal non-zero elements appear in unpredictable locations. The linear systems are solved using parallelized conjugate gradients. The code is parallelized by domain decomposition of physical space into disjoint subdomains (SDs). Each processor receives its own SD plus a border of ghost cells. Results are presented on a problem coupling hydrodynamics to non-linear heat conduction.

Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48.