Efficient, Nonlinear Second Moment Methods for Multigroup Thermal Radiative Transfer
Abstract
Thermal radiative transfer (TRT) presents significant computational challenges due to the stiff, nonlinear coupling between radiation and material energy, particularly in multigroup, high-fidelity transport models. In this work, we develop an efficient nonlinear acceleration framework for TRT based on the Second Moment (SM) method. Our approach couples high-order discrete ordinates transport to a gray, diffusion-based low-order system that implicitly resolves the stiff absorption-emission physics, isolating this stiffness from the high-order system. The resulting algorithm alternates between transport sweeps and a Newton-type solution of the coupled low-order and material energy balance equations, utilizing nonlinear temperature elimination for improved robustness. Crucially, our approach is the first moment-based TRT algorithm with a symmetric and positive definite (SPD) low-order system enabling scalable linear solves via algebraic multigrid-preconditioned conjugate gradient. We investigate both consistent and independent low-order discretizations within a discontinuous Galerkin framework and assess their performance on one and two-dimensional gray and multigroup benchmark problems.
Cite
@article{arxiv.2504.21784,
title = {Efficient, Nonlinear Second Moment Methods for Multigroup Thermal Radiative Transfer},
author = {Samuel Olivier and James S. Warsa and HyeongKae Park},
journal= {arXiv preprint arXiv:2504.21784},
year = {2026}
}