Conditions for supersonic bent Marshak waves
  Supersonic radiation diffusion approximation is a useful way to study the
radiation transportation. Considering the bent Marshak wave theory in
2-dimensions, and an invariable source temperature, we get the supersonic
radiation diffusion conditions which are about the Mach number
$M>8(1+\sqrt{\ep})/3$, and the optical depth $\tau>1$. A large Mach number
requires a high temperature, while a large optical depth requires a low
temperature. Only when the source temperature is in a proper region these
conditions can be satisfied. Assuming the material opacity and the specific
internal energy depend on the temperature and the density as a form of power
law, for a given density, these conditions correspond to a region about source
temperature and the length of the sample. This supersonic diffusion region
involves both lower and upper limit of source temperature, while that in
1-dimension only gives a lower limit. Taking $\rm SiO_2$ and the Au for
example, we show the supersonic region numerically.
