Full self-similar solutions of the subsonic radiative heat equations

Tomer Shussman, Shay I. Heizler

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We study the phenomenon of diffusive radiative heat waves (Marshak waves) under general boundary conditions. In particular, we derive full analytic solutions for the subsonic case that include both the ablation and the shock wave regions. Previous works in this regime, based on the work of R. Pakula and R. Sigel [Phys. Fluids. 28, 232 (1985)], present self-similar solutions for the ablation region alone, since, in general, the shock region and the ablation region are not self-similar together. Analytic results for both regions were obtained only for the specific case in which the ratio between the ablation front velocity and the shock velocity is constant. In this work, we derive a full analytic solution for the whole problem in general boundary conditions. Our solution is composed of two different self-similar solutions, one for each region, that are patched at the heat front. The ablative region of the heat wave is solved in a manner similar to previous works. Then, the pressure at the front, which is derived from the ablative region solution, is taken as a boundary condition to the shock region, while the other boundary is described by Hugoniot relations. The solution is compared to full numerical simulations in several representative cases. The numerical and analytic results are found to agree within 1% in the ablation region, and within 2%-5% in the shock region. This model allows better prediction of the physical behavior of radiation induced shock waves, and can be applied for high energy density physics experiments.

Original languageAmerican English
Article number082109
JournalPhysics of Plasmas
Issue number8
StatePublished - 1 Aug 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 AIP Publishing LLC.


Dive into the research topics of 'Full self-similar solutions of the subsonic radiative heat equations'. Together they form a unique fingerprint.

Cite this