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.

翻译：辐射磁力动力学(RMHD)系统将理想的磁力动力学方程式与灰色辐射转移方程式相配。主要的挑战在于,辐射以光速飘移,而磁力动力学则随着流体的时间尺度的变化而变化。这两个过程的时间尺度可以大相径庭。为了使用与光速无关的网状尺寸和时间步骤,需要在空间和时间上使用无光保护(AP)系统。在本文中,我们为RMHD系统开发了空间和时间的AP方案。考虑了两种不同的缩放。一个是平衡扩散限制系统,另一个是非平衡系统。主要的想法是将辐射强度分解为三个部分,每个部分都用不同的明确和隐含的离散式组合处理,以保证有利的稳定性条件和计算效率。AP方法的性能,对于光密度和厚度区域,以及辐射冲击问题,都作了介绍。