Nonrelativistic grey Sn-transport radiative-shock solutions

TL;DR

This paper develops semi-analytic grey Sn-transport radiative-shock solutions with variable Eddington factors, revealing complex precursor structures, nonmonotonic radiation energy density, and differences from diffusion models, advancing understanding of radiative shock physics.

Contribution

It introduces new semi-analytic solutions with variable Eddington factors for radiative shocks, including temperature- and density-dependent cross sections, and compares them to diffusion models to reveal novel physical features.

Findings

Evidence of a spike in the variable Eddington factor upstream

Identification of an adaptation zone near the embedded shock

Nonmonotonic radiation energy density indicating anti-diffusive flow

Abstract

We present semi-analytic radiative-shock solutions in which grey Sn-transport is used to model the radiation, and we include both constant cross sections and cross sections that depend on temperature and density. These new solutions solve for a variable Eddington factor (VEF) across the shock domain, which allows for interesting physics not seen before in radiative-shock solutions. Comparisons are made with the grey nonequilibrium-diffusion radiative-shock solutions of Lowrie and Edwards [1], which assumed that the Eddington factor is constant across the shock domain. It is our experience that the local Mach number is monotonic when producing nonequilibrium-diffusion solutions, but that this monotonicity may disappear while integrating the precursor region to produce Sn-transport solutions. For temperature- and density-dependent cross sections we show evidence of a spike in the VEF in the far upstream portion of the radiative-shock precursor. We show evidence of an adaptation zone in the precursor region, adjacent to the embedded hydrodynamic shock, as conjectured by Drake [2, 3], and also confirm his expectation that the precursor temperatures adjacent to the Zeldovich spike take values that are greater than the downstream post-shock equilibrium temperature. We also show evidence that the radiation energy density can be nonmonotonic under the Zeldovich spike, which is indicative of anti-diffusive radiation flow as predicted by McClarren and Drake [4]. We compare the angle dependence of the radiation flow for the Sn-transport and nonequilibrium-diffusion radiation solutions, and show that there are considerable differences in the radiation flow between these models across the shock structure. Finally, we analyze the radiation flow to understand the cause of the adaptation zone, as well as the structure of the Sn-transport radiation-intensity solutions across the shock structure.