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.

翻译：正确模拟中微子输运对于某些天体物理场景（如核塌缩超新星和双中子星并合）至关重要。本文聚焦于截断矩形式，在灰色近似下仅考虑前两阶矩（M1格式），将玻尔兹曼七维方程简化为一个与流体动力学方程高度相似的$3+1$方程组。求解M1格式在数学上仍具有挑战性，因为需要在演化方程变为刚性且表现为对流扩散问题的区域中建模辐射与物质的相互作用。本文提出了基于隐式-显式龙格-库塔（IMEX）方法的不同全局高阶时间积分格式，旨在克服由该行为引起的时间步长限制，同时允许使用常用于磁流体动力学方程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其性能。