Self-similar Solution of the Subsonic Radiative Heat Equations Using a Binary Equation of State

Shay I. Heizler*, Tomer Shussman, Elad Malka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


ABSTRACT: Radiative subsonic heat waves, and their 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 our 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.

Original languageAmerican English
Pages (from-to)256-267
Number of pages12
JournalJournal of Computational and Theoretical Transport
Issue number4
StatePublished - 6 Jun 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Taylor & Francis Group, LLC.


  • Radiative transfer; self-similar; shock wave; subsonic heat wave; subsonic Marshak wave


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