A Variable Eddington Factor method for the 1-D grey radiative transfer equations with discontinuous Galerkin and mixed finite-element spatial differencing

Abstract

The purpose of this paper is to present a Variable Eddington Factor (VEF) method for the 1-D grey radiative transfer equations that uses a lumped linear discontinuous Galerkin spatial discretization for the Snequations together with a constant-linear mixed finite-element discretization for the VEF moment and material temperature equations. The use of independent discretizations can be particularly useful for multiphysics applications such as radiation-hydrodynamics. The VEF method is quite old, but to our knowledge, this particular combination of differencing schemes has not been previously investigated for radiative transfer. We define the scheme and present computational results. As expected, the scheme exhibits second-order accuracy for the directionally-integrated intensity and material temperature, and behaves well in the thick diffusion limit. An important focus of this study is the treatment of the strong temperature dependence of the opacities and the spatial dependence of the opacities within each cell, which are not explicitly defined by the basic discretization schemes.