标题： 关于广义相对论辐射磁流体力学方程时间演化的一种高阶数值格式 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： 在某些天体物理场景（如核心坍缩超新星和双中子星合并）中，正确建模中微子的输运至关重要。 本文集中于截断矩形式主义，在灰色近似下仅考虑前两个矩（M1方案），这将Boltzmann的七维方程简化为一组接近流体力学方程的 $3+1$ 方程。 求解M1方案在数学上仍然具有挑战性，因为在这些情况下需要模拟辐射与物质的相互作用，而此时演化方程变得刚性，并表现为一个对流-扩散问题。 在这里，我们提出了基于隐式-显式Runge-Kutta（IMEX）方法的不同全局高阶时间积分方案，旨在克服这种行为引起的步长限制，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.