  The radiation magnetohydrodynamics (RMHD) system couples the ideal
magnetohydrodynamics equations with a gray radiation transfer equation. The
main challenge is that the radiation travels at the speed of light while the
magnetohydrodynamics changes with the time scale of the fluid. The time scales
of these two processes can vary dramatically. In order to use mesh sizes and
time steps that are independent of the speed of light, asymptotic preserving
(AP) schemes in both space and time are desired. In this paper, we develop an
AP scheme in both space and time for the RMHD system. Two different scalings
are considered. One results in an equilibrium diffusion limit system, while the
other results in a non-equilibrium system. The main idea is to decompose the
radiative intensity into three parts, each part is treated differently with
suitable combinations of explicit and implicit discretizations guaranteeing the
favorable stability conditionand computational efficiency. The performance of
the AP method is presented, for both optically thin and thick regions, as well
as for the radiative shock problem.
