  We calculate the quasi-stationary structure of a radiating shock wave
propagating through a spherically symmetric shell of cold gas by solving the
time-dependent equations of radiation hydrodynamics on an adaptive grid. We
show that this code successfully resolves the shock wave in both the
subcritical and supercritical cases and, for the first time, we have reproduced
all the expected features -- including the optically thin temperature spike at
a supercritical shock front -- without invoking analytic jump conditions at the
discontinuity. We solve the full moment equations for the radiation flux and
energy density, but the shock wave structure can also be reproduced if the
radiation flux is assumed to be proportional to the gradient of the energy
density (the diffusion approximation), as long as the radiation energy density
is determined by the appropriate radiative transfer moment equation.
  We find that Zel'dovich and Raizer's analytic solution for the shock wave
structure accurately describes a subcritical shock but it underestimates the
gas temperature, pressure, and the radiation flux in the gas ahead of a
supercritical shock. We argue that this discrepancy is a consequence of
neglecting terms which are second order in the minimum shock compression ratio
[$\eta_1 = (\gamma-1)/(\gamma+1)$, where $\gamma$ is the adiabatic index] and
the inaccurate treatment of radiative transfer near the discontinuity. In
addition, we verify that the maximum temperature of the gas immediately behind
the shock is given by $T_{+} = 4 T_1/(\gamma+1)$, where $T_1$ is the gas
temperature far behind the shock.
