| 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 making 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 angularly discretized (S[subscript n]) transport. The first problem establishes the asymptotic limits of the EDA in RH, which will have direct applications to discretizations of RH models. The second problem extends previous semi-analytic solution methods for radiative shocks to include grey S[subscript n] transport. Previous semi-analytic methods relied on nonequilibrium diffusion theory to describe the radiation, which assumes that while the radiation is out of equilibrium with the material, the angular dependence of the radiation field is isotropic over the extended spatial domain of the radiative shock, and that the radiation energy density is monotonic over the shock's spatial domain. The purpose of using grey S[subscript n] transport is to determine the angular dependence of the radiation field. It is shown that the anisotropy of the radiation field can cause the radiation energy density to be nonmonotonic and exhibit a local maximum if a spike in the material temperature, called a Zel'dovich spike, near the shock discontinuity exists. This local maximum of the radiation energy density is termed "anti-diffusive" radiation because the radiation flux and the gradient of the radiation energy density may have the same sign in this region, which is in stark contrast to diffusion theory wherein the radiation flux is proportional to the negative gradient of the radiation energy density. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/152454 |
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