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We study the phenomenon of diffusive radiative heat waves (Marshak waves)under general boundary conditions. In particular, we derive full analyticsolutions for the subsonic case, that include both the ablation and the shockwave regions. Previous works in this regime, based on the work of [R. Pakulaand R. Sigel, Phys. Fluids. 443, 28, 232 (1985)], present self-similarsolutions for the ablation region alone, since in general, the shock region andthe ablation region are not self-similar together. Analytic results for bothregions were obtained only for the specific case in which the ratio between theablation front velocity and the shock velocity is constant. In this work, wederive a full analytic solution for the whole problem in general boundaryconditions. Our solution is composed of two different self-similar solutions,one for each region, that are patched at the heat front. The ablative region ofthe heat wave is solved in a manner similar to previous works. Then, thepressure at the front, which is derived from the ablative region solution, istaken as a boundary condition to the shock region, while the other boundary isdescribed by Hugoniot relations. The solution is compared to full numericalsimulations in several representative cases. The numerical and analytic resultsare found to agree within $1\%$ in the ablation region, and within $2-5\%$ inthe shock region. This model allows better prediction of the physical behaviorof radiation induced shock waves, and can be applied for high energy densityphysics experiments.

Full self-similar solutions of the subsonic radiative heat equations