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. Crucially, our approach is the first moment-based TRT algorithm with a symmetric and positive definite (SPD) low-order system enabling scalable linear solves. 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. A discrete reference approach is used to assess numerical error in space-time convergence studies of challenging TRT problems. Results demonstrate that these algorithms achieve robust nonlinear convergence and significant reductions in transport iterations compared to unaccelerated schemes, resulting in large speedups in overall runtime. While the independent formulation offers improved iteration counts on under-resolved meshes, the consistent method provides superior solution quality and robustness. Overall, this work establishes the SM method as an effective and scalable approach for nonlinear multigroup TRT and provides insight into the interplay between discretization consistency, accuracy, and solver performance arising in moment-based acceleration algorithms.