An asymptotically correct implicit-explicit time integration scheme for finite volume radiation-hydrodynamics

Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of time-scales, and where the relative importance of these processes often varies by orders of magnitude across the computational domain. Here, we present a new implicit-explicit method for numerical RHD that has a number of desirable properties that have not previously been combined in a single method. Our scheme is based on moments and allows machine-precision conservation of energy and momentum, making it highly suitable for adaptive mesh refinement applications; it requires no more communication than hydrodynamics and includes no non-local iterative steps, making it highly suitable for massively parallel and Graphics Processing Unit (GPU)-based systems where communication is a bottleneck; and we show that it is asymptotically accurate in the streaming, static diffusion, and dynamic diffusion limits, including in the so-called asymptotic diffusion regime where the computational grid does not resolve the photon mean-free path. We implement our method in the GPU-accelerated RHD code quokka and show that it passes a wide range of numerical tests.