An Approximation Method for Time-Dependent Problems in High Energy Density Thermal Radiative Transfer

Abstract

We analyze a computational method for solving multidimensional thermal radiative transfer (TRT) problems based on the radiative transfer equation (RTE) with approximate time evolution operator. The variation in the specific intensity of radiation over each time interval is approximated by an exponential function. This approximation reduces the RTE to an equation of steady-state form with time-dependent coefficients and a modified collision rate density term. This enables one to avoid storage of the high-dimensional solution from the previous time level. The numerical method for TRT problems applies the RTE with the time-dependent approximation as a high-order problem in multilevel system of low-order quasidiffusion (LOQD) equations. The change rate in the intensity is evaluated by the solution of the LOQD equations for the moments of the specific intensity. We study the accuracy of the approximate method in modeling the evolution of temperature and radiation waves in TRT problems.