  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.
