论文标题
一般相对论辐射磁力动力学方程的时间演变的全局高阶数值
Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations
论文作者
论文摘要
正确建模中微子的转运在某些天体物理场景中至关重要，例如核心 - 循环超新星和二元中子星星合并。在本文中，我们专注于截短的正式主义，考虑到灰色近似中的前两个时刻（M1方案），这将Boltzmann的七维方程式减少到了$ 3+1 $方程的系统，与流体动力学方程非常相似。解决M1方案在数学上仍然具有挑战性，因为有必要在进化方程变得僵硬并作为对流扩散问题的状态中建模辐射 - 物体相互作用。在这里，我们提出了基于隐式解释runge-kutta（IMEX）方法的不同全局高阶时间集成方案，旨在克服由这种行为引起的时间步长限制，同时允许我们使用MHD和Einstein方程通常使用的显式RK。最后，我们在几个数值测试中分析了它们的性能。
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.
