  Similarity solutions to the nonlinear non-equilibrium Marshak wave problem
with a time dependent radiation driving source are presented. The radiation
transfer model used is the gray, non-equilibrium diffusion approximation in the
supersonic regime. These solutions constitute an extension of existing
non-equilibrium supersonic Marshak wave solutions which are linear, to the
nonlinear regime, which prevails in realistic high energy density systems. The
generalized solutions assume a material model with power law temperature
dependent opacities and a material energy density which is proportional to the
radiation energy density, as well as a surface radiation temperature drive
which obeys a temporal power-law. The solutions are analyzed in detail and it
is shown that they take various qualitatively different forms according to the
values of the opacity exponents. The solutions are used to construct a set of
standardized benchmarks for supersonic non-equilibrium radiative heat transfer,
which are nontrivial but straightforward to implement. These solutions are
compared in detail to implicit Monte-Carlo and discrete-ordinate transport
simulations as well gray diffusion simulations, showing a good agreement, which
demonstrates the usefulness of these solutions as a code verification test
problem.
