We describe a new algorithm to implicitly solve the time-dependent, frequency-integrated radiation transport (RT) equation, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using Athena++. The radiation field is represented by specific intensities along discrete rays, which are evolved using a conservative finite volume approach for both Cartesian and curvilinear coordinate systems. All terms for spatial transport of photons and interactions between gas and radiation are calculated implicitly together. An efficient Jacobi-like iteration scheme is used to solve the implicit equations. This removes any time-step constraint due to the speed of light in RT. We evolve the specific intensities in the lab frame to simplify the transport step. The lab frame specific intensities are transformed to the comoving frame via Lorentz transformation when the source term is calculated. Therefore, the scheme does not need any expansion in terms of v/c. The radiation energy and momentum source terms for the gas are calculated via direct quadrature in the angular space. The time step for the whole scheme is determined by the normal Courant–Friedrichs–Lewy condition in the MHD module. We provide a variety of test problems for this algorithm, including both optically thick and thin regimes, and for both gas and radiation pressure-dominated flows to demonstrate its accuracy and efficiency.

我们描述了一种新算法来隐式求解时间相关的频率积分辐射传输 (RT) 方程，该方程与使用 Athena++ 的磁流体动力学 (MHD) 方程的显式求解器耦合。辐射场由沿离散射线的特定强度表示，这些强度是使用笛卡尔坐标系和曲线坐标系的保守有限体积方法演变而来的。光子的空间传输以及气体和辐射之间的相互作用的所有项都隐含地计算在一起。一种有效的类雅可比迭代方案用于求解隐式方程。由于 RT 中的光速，这消除了任何时间步长约束。我们改进了实验室框架中的特定强度以简化传输步骤。计算源项时，实验室坐标系特定强度通过洛伦兹变换转换为共移动坐标系。因此，该方案不需要任何扩展v / c。气体的辐射能量和动量源项通过角空间中的直接求积计算。整个方案的时间步长由 MHD 模块中的正常 Courant-Friedrichs-Lewy 条件确定。我们为此算法提供了各种测试问题，包括光学厚和薄区域，以及气体和辐射压力主导的流动，以证明其准确性和效率。