Supersonic-subsonic transition region in radiation heat flow via self-similar solutions

We examine the supersonic-subsonic transition region in radiation heat flow. The extreme supersonic and subsonic regions were both examined in previous works, mainly through analytic self-similar solutions. Such solutions may use to evaluate the energy absorption in a layer of a given material (gold, for example) for various initial densities [Rosen & Hammer, PRE 2005], and show that there is an optimal foam density, for which the energy absorption is minimal. This result may be useful for choosing specific hohlraums materials and densities [Young et al., PRL 2008]. However, there is no exact self-similar solution for the full radiative heat flow equations for the transition region, that is for Mach numbers around 1. In [Garnier et al., PoP 2006] a unique self-similar solution was introduced for a specific boundary condition, which is valid for any Mach number. Using this exact solution, we analyze the transition region for different materials and parameters (temperature, density, time), and examine its sensitivity to the time dependence of the boundary condition. In addition, we extend the validity of the approximate solutions for a general boundary condition, comparing it to the exact one, when available. The results are also compared against 1D full numerical simulations.