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 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. The performances of the semi-implicit method are presented, for both optically thin and thick regions, as well as for the radiative shock problem. Comparisons with the semi-analytic solution are given to verify the accuracy and asymptotic properties of the method.

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,辐射在光速下流动,而磁力动力学则随着液体的变化而变化。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,需要同时在空间和时间上使用无线保护(AP)系统。在本文中,我们为RMHD系统在空间和时间上制定了一个AP方案。考虑了两个不同的比例,一个是平衡扩散限制系统,另一个是非等离子系统。主要想法是将辐射强度分解成三个部分,每个部分都得到不同的处理。对光薄和厚地区的半隐蔽方法的性能以及辐射性冲击问题都作了介绍。与半分析性解决办法的比较是为了核实该方法的准确性和防腐蚀性。