Equations and Algorithms for Astrophysical Radiation Hydrodynamics in All Non-relativistic Regimes

We analyze the equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading order in any regime of non-relativistic radiation hydrodynamics. Our equations are accurate to first order in v/c in the static diffusion regime. We give the equations in a conservation law form well-suited to implementation in numerical algorithms. Our work improves on previous zeroth order derivations of the equations by retaining differences between laboratory frame and comoving frame quantities, which are neglected at zeroth order. We compare our equations to the zeroth order equations, and show that in certain regimes the zeroth order equations omit terms that are formally of leading order. We discuss the circumstances under which this will produce significant errors. For systems in the static diffusion regime, our analysis of the equations suggests an algorithm for numerical solution that is both simpler and faster than earlier methods. We implement this algorithm in the Orion adaptive mesh refinement code, and demonstrate it in a few simple test problems. Subject headings: hydrodynamics — methods: numerical — radiative transfer