Proper orthogonal decomposition based reduced-order modeling of flux-Limited gray thermal radiation

•A reduced-order modeling approach for radiation penetration problems is shown to be competitive with a full-order model in both accuracy and speed.•The wave initialization regime is highly reducible while the reducibility of the wave propagation regime is more limited.•When combined with slow singular value decay of advective problems and that thermal radiation penetration problems typically span many orders of magnitude, many singular modes are required.•Nonlinear propagation of error is found to exist between the radiation energy density and flux-limited diffusion coefficient.•Typical indicators for truncation of the radiation energy density and flux-limited loss operator are insufficient in practice due to nonlinear propagation of error. In this work, a proper orthogonal decomposition (POD) based reduced-order model (ROM) is developed to solve gray, flux-limited thermal radiation diffusion. We focus on the variable opacity radiation penetration benchmark posed by Olson, Auer, and Hall. The T−3 relationship for opacity in conjunction with high-temperature radiation penetrating an initially cold material produces a strong thermal radiation shock. This class of problems is particularly challenging for standard POD-based reduced-order modeling due to the nonlinearities presented by 1) the T4 source term, and 2) flux-limited diffusion operator. To address these challenges and develop a cost competitive ROM, we employ a “hyper-reduction” technique through discrete empirical interpolation (DEIM) and allow for adaptive reduced-order projections through principal interval decomposition (PID). Performance of the proposed methodology is quantified by comparing the cost savings and accuracy relative to a full-order computation. Reference solutions and snapshot data are obtained through a full-order calculation performed by the University of Chicago maintained astrophysics code, FLASH. For consistency and potential extensibility, the developed ROM is also implemented in FLASH. We find that in the initialization regime, where the thermal radiation wave is initially created by the warming of the material, this class of problems is highly reducible and suitable for POD-based ROMs. However, the strong convective nature of the wave propagation regime is less reducible and more challenging to create an efficient ROM.