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场方程组。为捕捉相关物理现象，通常需以流体力学时间尺度进行时间步进，这使得显式积分成为显然选择。另一方面，耦合的辐射方程具有特定标度关系，使得在非相对论性体系中隐式积分实际上成为必要。一阶Lie-Trotter型算子分裂是实践中应用最普遍的时间积分方案，交替执行显式流体力学步与隐式辐射求解及能量沉积步。然而，此类方案受限于一阶精度，且辐射与流体力学方程间的非线性耦合使得方程的通用加法分裂难以实现。本文针对灰体扩散辐射流体力学问题，提出一种新的公式化建模与分裂方法，从而允许应用（线性）隐式-显式龙格-库塔时间积分方案。我们证明了新框架下总能量的守恒性，并在多个辐射激波问题上实现了时间二阶收敛性。在流体力学CFL条件下，即使Lie-Trotter方法对流体力学方程采用三阶TVD龙格-库塔格式，新方法的误差仍比一阶Lie-Trotter算子分裂小3至5个数量级。