Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and nonlinear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. We prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3--5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.

翻译：辐射流体力学是一组具有挑战性的多尺度与多物理耦合方程。为捕捉目标物理过程，通常需要在流体力学时间尺度上进行时间推进，这使得显式积分成为自然选择。另一方面，耦合的辐射方程在非相对论区域具有特定的尺度特性，使得隐式积分实际上成为必要。一阶类李-特罗特算子分裂是目前实践中最常用的时间积分方案，通过在显式流体力学步骤与隐式辐射求解及能量沉积步骤之间交替进行。然而，此类方案仅具有一阶精度，且辐射方程与流体力学方程之间的非线性耦合使得更一般的方程加性分解变得十分复杂。本文针对灰扩散模型下的辐射流体力学，提出了一种新的方程表述与分解方法，使得（线性）隐显式龙格-库塔时间积分方案得以应用。我们在新框架中证明了总能量守恒，并在多个辐射激波问题上展示了时间方向上的二阶收敛性。即使在李-特罗特分裂法对流体力学方程采用三阶TVD龙格-库塔格式的情况下，本方法在流体力学CFL条件下仍能获得比一阶李-特罗特算子分裂法低3-5个数量级的误差。