A Comparison of the Consistent and Independent Second Moment Methods Applied to Thermal Radiative Transfer

The design of efficient numerical methods for modeling thermal radiative transfer (TRT) is challenging due to the stiff, nonlinear coupling between radiation and material energies, especially at the time scales of interest in high energy density physics and astrophysics. Here, we investigate the use of the Second Moment Method (SMM) to accelerate absorption-emission within the context of the multigroup, Discrete Ordinates transport equations with discontinuous Galerkin spatial discretization. SMM employs a reduced-dimensional, diffusion-based model of radiation transport that, when coupled with suitable discrete closures, serves as a proxy for the transport equation, isolating the transport equation from the stiff absorption-emission physics. We use a gray low-order system to reduce the cost of solving the low-order system and leverage SMM low-order discretizations specifically designed to be scalably solvable with existing linear solver technology. Our algorithm robustly resolves the nonlinear TRT system while only relying on transport sweeps, linearly solving symmetric and positive definite, gray diffusion systems, and nonlinearly solving the spatially pointwise energy balance equation. This algorithm is used as a vehicle to compare the efficacy of low-order discretizations developed for steady-state, linear transport on gray and multigroup TRT problems in one and two spatial dimensions.