标题： 全局高阶数值格式用于广义相对论辐射磁流体力学方程的时间演化 显示英文标题

标题： Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations

摘要： 正确模拟中微子的输运在一些天体物理场景中至关重要，例如核心坍缩超新星和双中子星合并。 在本文中，我们专注于截断矩形式，在灰近似下仅考虑前两个矩（M1方案），这将玻尔兹曼七维方程简化为一组与流体力学方程密切相似的$3+1$方程。 求解M1方案仍然是数学上具有挑战性的，因为在辐射-物质相互作用的区域中，演化方程变得刚性，并表现出对流-扩散问题的行为。 在此，我们提出了基于隐式-显式龙格-库塔（IMEX）方法的不同全局、高阶时间积分方案，旨在克服由于这种行为引起的时间步长限制，同时允许我们使用通常用于MHD和爱因斯坦方程的显式RK方法。 最后，我们在多个数值测试中分析了它们的性能。 显示英文摘要

摘要： Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of $3+1$ equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, high-order time integration schemes based on Implicit-Explicit Runge-Kutta (IMEX) methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit RK commonly employed for the MHD and Einstein equations. Finally, we analyze their performance in several numerical tests.