Linear Solution Preservation and Diffusive Solutions for S_N Radiation Transport

Heath Hanshaw, University of Michigan

Deterministic radiation transport discretizations mimic, to various degrees, properties of the analytic transport equation. No deterministic scheme accurately mimics all of these properties, and one must generally choose a method that prioritizes, based on properties important to the problem at hand. When the problem contains optically-thick diffusive regions, for example, the importance of meeting the asymptotic thick diffusion limit is well known.

We demonstrate that linear-solution-preservation (in space and angle) is also vitally important to obtaining accurate solutions in diffusive regions. Though this quality is achieved by modern Corner Balance / Discontinuous Finite Element Methods on triangular/tetrahedral grids, the state-of-the-art Upstream Corner Balance method fails to preserve linear solutions on quadrilateral grids. We develop a new Multidimensional Multiple Balance method, which is linear-solution-preserving on skewed quadrilateral grids. We demonstrate the new method’s success in diffusive regions on non-orthogonal quadrilateral grids, and we compare it to Upstream Corner Balance on a variety of other problems.

Abstract Author(s): Heath L. Hanshaw