Consistent Second Moment Methods with Scalable Linear Solvers for Radiation Transport

TL;DR

This paper introduces consistent Second Moment Methods (SMMs) aligned with Discontinuous Galerkin discretizations for radiation transport, improving accuracy and scalability in complex multi-material simulations.

Contribution

It develops SMMs that are consistent with high-order DG discretizations, enabling scalable parallel solutions and better solution quality in radiation transport problems.

Findings

Consistent SMMs improve solution accuracy over independent discretizations.

The methods preserve the diffusion limit.

LDG and IP consistent SMMs are scalable in parallel computing environments.

Abstract

Second Moment Methods (SMMs) are developed that are consistent with the Discontinuous Galerkin (DG) spatial discretization of the discrete ordinates (or \Sn) transport equations. The low-order (LO) diffusion system of equations is discretized with fully consistent \Pone, Local Discontinuous Galerkin (LDG), and Interior Penalty (IP) methods. A discrete residual approach is used to derive SMM correction terms that make each of the LO systems consistent with the high-order (HO) discretization. We show that the consistent methods are more accurate and have better solution quality than independently discretized LO systems, that they preserve the diffusion limit, and that the LDG and IP consistent SMMs can be scalably solved in parallel on a challenging, multi-material benchmark problem.