AREPO-IDORT: Implicit discrete ordinate radiation transport For radiation magnetohydrodynamics on an unstructured moving mesh

Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany

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Received: 20 March 2025
Accepted: 23 May 2026

Abstract

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 ordinate radiation transport), a scheme coupled to the explicit magnetohydrodynamic (MHD) solver in the 3D moving-mesh code AREPO. The discrete ordinate scheme means that we directly solve the specific intensities in 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, such as flux-limited diffusion (FLD) or M1 closure, this scheme has the advantage of correctly capturing the directions of radiation in both optically thick and thin regions. It is based on the scheme developed for the adaptive mesh refinement code ATHENA++, but we generalise 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. We even marginally resolve the photosphere, which is a known challenge for global 3D simulations of stars. 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, and is memory-intensive (especially for large cosmological simulations), but we discuss potential avenues for future improvements. We expect that 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.