Asymptotic Accuracy of the Equilibrium Diffusion Approximation and Semi-analytic Solutions of Radiating Shocks

Abstract

Radiation hydrodynamics (RH) provides a theoretical description for many astrophysical events spanning a wide range of observable phenomena. It is the goal of high-energy-density laboratory astrophysics (HEDLA) to reproduce some of these events in terrestrial settings. Computational models exist to aide our understanding of these subjects by reproducing astrophysical observations and laboratory experiments via simulations, and potentially furthering our understanding by mak- ing predictions which guide the experiments and their observations. It is the goal of this thesis to contribute to our understanding of computational models in RH. Two problems are solved that aide this understanding: 1) we showed that the equilibrium diffusion approximation (EDA) of RH is correct through first-order in the asymptotic equilibrium diffusion limit (EDL), in agreement with other transport models; and, 2) we produced semi-analytic radiative shock solutions using grey Sn transport. The first problem establishes the limits of the EDA in RH. The EDA for radiation transport without material motion has already been shown to preserve the EDL through first-order. The second problem extends the semi-analytic solution method of Lowrie and Edwards [LE08] for radiative shocks to include grey Sn transport.