A variable Eddington factor method with different spatial discretizations for the radiative transfer equation and the hydrodynamics/radiation-moment equations

Abstract

The purpose of this paper is to present a High-Order/Low-Order radiation-hydrodynamics method that is second-order accurate in both space and time and uses the Variable Eddington Factor (VEF) method to couple a high-order set of 1-D slab-geometry grey Sn radiation transport equations with a low-order set of radiation moment and hydrodynamics equations. The Sn equations are spatially discretized with a lumped linear-discontinuous Galerkin scheme, while the low-order radiation-hydrodynamics equations are spatially discretized with a constant-linear mixed finite-element scheme. Both the high-order and low-order equations are discretized in time using a trapezoidal BDF-2 method. One manufactured solution is used to demonstrate that the scheme is second-order accurate for smooth solutions, and another one is used to demonstrate that the scheme is asymptotic-preserving in the equilibrium-diffusion limit. Calculations are performed for radiative shock problems and compared with semi-analytic solutions. In a previous paper it was shown that the pure radiative transfer scheme (the Sn equations coupled to the radiation moment equations and a material temperature equation rather than the hydrodynamics equations) is asymptotic-preserving in the equilibrium-diffusion limit, is well-behaved with unresolved spatial boundary layers in that limit, and yields accurate Marshak wave speeds even with strongly temperature-dependent opacities and relatively coarse meshes. These same properties carry over to our radiation-hydrodynamics scheme.