We present a numerical code for radiation hydrodynamics designed as a module for the freely available PLUTO code. We adopt a gray approximation and include radiative transfer following a two-moment approach by imposing the M1 closure to the radiation fields. This closure allows for a description of radiative transport in both the diffusion and free-streaming limits, and is able to describe highly anisotropic radiation transport as can be expected in the vicinity of an accreting planet in a protoplanetary disk. To reduce the computational cost caused by the timescale disparity between radiation and matter fields, we integrate their evolution equations separately in an operator-split way, using substepping to evolve the radiation equations. We further increase the code's efficiency by adopting the reduced speed of light approximation (RSLA). Our integration scheme for the evolution equations of radiation fields relies on implicit-explicit schemes, in which radiation-matter interaction terms are integrated implicitly while fluxes are integrated via Godunov-type solvers. The module is suitable for general astrophysical computations in 1, 2, and 3 dimensions in Cartesian, spherical and cylindrical coordinates, and can be implemented on rotating frames. We demonstrate the algorithm performance on different numerical benchmarks, paying particular attention to the applicability of the RSLA for computations of physical processes in protoplanetary disks. We show 2D simulations of vertical convection in disks and 3D simulations of gas accretion by planetary cores, which are the first of their kind to be solved with a two-moment approach.

中文翻译：

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适用于环绕恒星盘中行星形成模拟的两矩辐射流体动力学方案

我们提出了辐射流体动力学的数字代码，设计为免费提供的 PLUTO 代码的模块。我们采用灰色近似，并通过将 M1 闭合强加到辐射场来包括遵循两时刻方法的辐射转移。这种闭合允许在扩散和自由流动极限下描述辐射传输，并且能够描述高度各向异性的辐射传输，正如在原行星盘中的吸积行星附近可以预期的那样。为了减少辐射场和物质场之间时间尺度差异导致的计算成本，我们以算子分裂的方式分别整合它们的演化方程，使用子步法来演化辐射方程。我们通过采用降低的光速近似 (RSLA) 进一步提高了代码的效率。我们辐射场演化方程的积分方案依赖于隐式-显式方案，其中辐射-物质相互作用项是隐式积分的，而通量是通过 Godunov 型求解器积分的。该模块适用于笛卡尔坐标系、球坐标系和圆柱坐标系中的一维、二维和三维的一般天体物理计算，并且可以在旋转框架上实现。我们展示了不同数值基准上的算法性能，特别关注 RSLA 在计算原行星盘物理过程中的适用性。我们展示了圆盘中垂直对流的 2D 模拟和行星核心气体吸积的 3D 模拟，这是同类中第一个用两矩方法解决的问题。