A Spatial-Temporal asymptotic preserving scheme for radiation magnetohydrodynamics in the equilibrium and non-equilibrium diffusion limit

TL;DR

This paper introduces a novel asymptotic preserving scheme for radiation magnetohydrodynamics that remains stable and efficient across different regimes, including equilibrium and non-equilibrium diffusion limits, by decomposing radiative intensity.

Contribution

It develops a new AP scheme in space and time for RMHD, handling multiple scalings and decomposing radiative intensity for improved stability and efficiency.

Findings

Effective in both optically thin and thick regions.

Maintains stability across different regimes.

Improves computational efficiency for RMHD simulations.

Abstract

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.