AREPO-IDORT: Implicit Discrete Ordinates Radiation Transport for Radiation Magnetohydrodynamics on an Unstructured Moving Mesh

Radiation is crucial not only for observing astrophysical objects, but also for transporting energy and momentum. However, accurate on-the-fly radiation transport in astrophysical simulations is challenging and computationally expensive. Here we introduce AREPO-IDORT (Implicit Discrete Ordinates Radiation Transport), a scheme coupled to the explicit magnetohydrodynamic (MHD) solver in the 3D moving-mesh code AREPO. The discrete ordinates scheme means we directly solve for the specific intensities along discrete directions. We solve the time-dependent relativistic radiation transport equation via an implicit Jacobi-like iterative finite-volume solver, which overcomes the small radiation time-steps needed by explicit methods. Compared to commonly-used moment-based methods, e.g. flux-limited diffusion or M1 closure, this scheme has the advantage of correctly capturing the direction of radiation in both optically-thick and thin regions. It is based on the scheme by Jiang 2021 for the adaptive mesh refinement code ATHENA++, but we generalize the scheme to support (1) an unstructured moving-mesh, (2) local time-stepping, and (3) general equations of state. We show various test problems that commonly-used moment-based methods fail to reproduce accurately. To apply the scheme to a real astrophysics problem, we show the first global 3D radiation hydrodynamic simulation of the entire convective envelope of a red supergiant star. (abridged) For this problem, the radiation module only takes less than half of the total computational cost. Our current scheme assumes grey radiation, is first-order accurate in both time and space (abridged). We expect our scheme will enable more accurate multi-scale radiation MHD simulations involving supersonic bulk motions, ranging from planet formation in protoplanetary disks, stars and associated transients, to accretion flows near black holes.