基于离散纵坐标的多群辐射磁流体力学（含康普顿散射）
Multi-group Radiation Magneto-hydrodynamics based on Discrete Ordinates including Compton Scattering
摘要：
我们提出了一个公式和数值算法，以扩展由Jiang（2021）开发的灰辐射磁流体动力学（MHD）方案，通过多群方法包括频率依赖性。整个频率空间可以在实验室框架中被划分为任意数量的组，并且我们沿着每个组内的离散射线跟踪频率积分比强度的时间依赖性演化。光子的空间输运在实验室坐标系中进行，而所有的耦合项在流体静止坐标系中求解。洛伦兹变换用于连接不同的框架。辐射输运方程在时间上完全隐式求解，而MHD方程则显式演化，使得时间步长不受光速的限制。有限体积法用于空间和频率空间中的传输，以保持辐射能量密度和动量。该算法包括光子吸收，电子散射以及康普顿散射，这是通过求解Kompaneets方程计算。该算法是准确的光学深度条件下的广泛范围内，可以处理辐射压力和气体压力为主的流动。它适用于具有自适应网格细化的笛卡尔和曲线坐标系。我们提供了各种各样的测试问题，包括辐射球，阴影测试，移动气体的吸收，邦迪型流以及热和散装康普顿散射的测试问题的集合。我们还讨论了频率依赖性的例子，可以使一个很大的差异相比，灰色的方法。
英文摘要：
We present a formulation and numerical algorithm to extend the scheme for grey radiation magneto-hydrodynamics (MHD) developed by Jiang (2021) to include the frequency dependence via the multi-group approach. The entire frequency space can be divided into arbitrary number of groups in the lab frame, and we follow the time dependent evolution of frequency integrated specific intensities along discrete rays inside each group. Spatial transport of photons is done in the lab frame while all the coupling terms are solved in the fluid rest frame. Lorentz transformation is used to connect different frames. Radiation transport equation is solved fully implicitly in time while the MHD equations are evolved explicitly so that time step is not limited by the speed of light. A finite volume approach is used for transport in both spatial and frequency spaces to conserve radiation energy density and momentum. The algorithm includes photon absorption, electron scattering as well as Compton scattering, which is calculated by solving the Kompaneets equation. The algorithm is accurate for a wide range of optical depth conditions and can handle both radiation pressure and gas pressure dominated flows. It works for both Cartesian and curvilinear coordinate systems with adaptive mesh refinement. We provide a variety of test problems including radiating sphere, shadow test, absorption of a moving gas, Bondi type flows as well as a collection of test problems for thermal and bulk Compton scattering. We also discuss examples where frequency dependence can make a big difference compared with the grey approach.
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