Shock wave structure in astrophysical flows with an account of photon   transfer
  For an accurate treatment of the shock wave propagation in high-energy astrophysical phenomena, such as supernova shock breakouts, gamma-ray bursts and accretion disks, knowledge of radiative transfer plays a crucial role. In this paper we consider one-dimensional (1D) special relativistic radiation hydrodynamics by solving the Boltzmann equation for radiative transfer. The structure of a radiative shock is calculated for a number of shock tube problems, including strong shock waves, and relativistic- and radiation-dominated cases. Calculations are performed using an iterative technique that consistently solves the equations of relativistic hydrodynamics and relativistic comoving radiative transfer. A comparison of radiative transfer solutions with the Eddington approximation and the M1 closure is made. A qualitative analysis of moment equations for radiation is performed and the conditions for the existence of jump discontinuity for non-relativistic cases are investigated numerically. 
Alexey Tolstov, Sergey Blinnikov, Shigehiro Nagataki, Ken'ichi Nomoto
astro-ph.HE