Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next-higher-order in {\epsilon}/mc2 correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. Our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

中文翻译：

---

超新星模拟中非弹性中微子-核子散射的广义 Kompaneets 形式主义

基于 Kompaneets 近似，我们开发了一种稳健的方法，在核心坍缩超新星模拟的背景下，通过非弹性中微子 - 核子散射来计算光谱重新分布。由此产生的方程将轻子数守恒到机器精度和线性标度，而不是二次方，与能量组的数量。形式主义还提供了一种优雅的方法来推导出能量转移到物质的速率，当中微子辐射场处于热平衡时，它必须自动变为零。此外，我们推导出了对中微子 Kompaneets 方程的 {\epsilon}/mc2 校正中的下一个更高阶。与其他 Kompaneets 模式不同，我们的模式还推广到各向异性角分布的情况，同时保留了作为经典 Kompaneets 方程标志的保守形式。