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

We present a High-Order/Low-Order radiation-hydrodynamics method that is second-order accurate in space and time and uses the Variable Eddington Factor (VEF) method to couple a high-order set of 1-D slab-geometry grey S_n radiation transport equations with a low-order set of radiation moment and hydrodynamics equations. The S_n 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. We computationally demonstrate by comparison with a manufactured solution that our scheme is second-order accurate in time and space. We also computationally demonstrate that our method is asymptotic preserving in the thick equilibrium-diffusion limit. Finally, we demonstrate that our method yields excellent results for two radiative shock solutions. (authors)