Self-similar solution of the subsonic radiative heat equations using a binary equation of state

TL;DR

This paper develops a semi-analytic model for subsonic radiative heat waves and shock waves, demonstrating that using region-specific binary equations of state improves accuracy over a single ideal gas EOS.

Contribution

The paper introduces a binary EOS approach with two ideal gas models for different regions, enhancing the accuracy of self-similar solutions for radiative heat waves.

Findings

Binary EOS improves shock wave description accuracy.

Semi-analytic solutions match numerical simulations well.

Using a single ideal gas EOS causes large errors.

Abstract

Radiative subsonic heat waves, and their radiation driven shock waves, are important hydro-radiative phenomena. The high pressure, causes hot matter in the rear part of the heat wave to ablate backwards. At the front of the heat wave, this ablation pressure generates a shock wave which propagates ahead of the heat front. Although no self-similar solution of both the ablation and shock regions exists, a solution for the full problem was found in a previous work. Here, we use this model in order to investigate the effect of the equation of state (EOS) on the propagation of radiation driven shocks. We find that using a single ideal gas EOS for both regions, as used in previous works, yields large errors in describing the shock wave. We use the fact that the solution is composed of two different self-similar solutions, one for the ablation region and one for the shock, and apply two ideal gas EOS (binary-EOS), one for each region, by fitting a detailed tabulated EOS to power laws at different regimes. By comparing the semi-analytic solution with a numerical simulation using a full EOS, we find that the semi-analytic solution describes both the heat and the shock regions well.