A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure based on Data-Driven Shape Function

A new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is a data-driven one that acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) with opacities and emission source evaluated at the known material temperatures. The solution to this RTE approximates the specific intensity distribution for the problem in all phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup $P_1$, $P_{1/3}$, and flux-limited diffusion radiative transfer (RT) models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The presented VEF model is shown to reliably improve accuracy by 1-2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.