  In this paper, a high-order gas-kinetic scheme is developed for the equation
of radiation hydrodynamics in equilibrium-diffusion limit which describes the
interaction between matter and radiation. To recover RHE, the
Bhatnagar-Gross-Krook (BGK) model with modified equilibrium state is
considered. In the equilibrium-diffusion limit, the time scales of radiation
diffusion and hydrodynamic part are different, and it will make the time step
very small for the fully explicit scheme. An implicit-explicit (IMEX) scheme is
applied, in which the hydrodynamic part is treated explicitly and the radiation
diffusion is treated implicitly. For the hydrodynamics part, a time dependent
gas distribution function can be constructed by the integral solution of
modified BGK equation, and the time dependent numerical fluxes can be obtained
by taking moments of gas distribution function. For the radiation diffusion
term, the nonlinear generalized minimal residual (GMRES) method is used. To
achieve the temporal accuracy, a two-stage method is developed, which is an
extension of two-stage method for hyperbolic conservation law. For the spatial
accuracy, the multidimensional weighted essential non-oscillation (WENO) scheme
is used for the spatial reconstruction. A variety of numerical tests are
provided for the performance of current scheme, including the order of accuracy
and robustness.
