(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
In this paper, we study an implicit-explicit scheme for the radiation hydrodynamics in the equilibrium diffusion limit and in the grey nonequilibrium diffusion limit. We extend a popular Godunov-type method, the MUSCL-Hancock scheme, to the convective part of the radiation hydrodynamics, while a cell centered finite volume scheme is used for the radiative heat transfer. Moreover, the implicit-explicit scheme is easier to implement. Numerical simulations show the character of the radiative shock wave and the accuracy of the scheme.