Reduced-Order Models for Thermal Radiative Transfer Based on POD-Galerkin Method and Low-Order Quasidiffusion Equations

Abstract: This paper presents a new technique for developing reduced-order models (ROMs) for nonlinear radiative transfer problems in high-energy density physics. The proper orthogonal decomposition (POD) of photon intensities is applied to obtain global basis functions for the Galerkin projection (POD-Galerkin) of the time-dependent multigroup Boltzmann transport equation (BTE) for photons. The POD-Galerkin solution of the BTE is used to determine the quasidiffusion (Eddington) factors that yield closures for the nonlinear system of (i) multilevel low-order quasidiffusion (VEF) equations and (ii) material energy balance equation. Numerical results are presented to demonstrate accuracy of the ROMs obtained with different low-rank approximations of intensities.