A radiation-hydrodynamics scheme valid from the transport to the diffusion limit

TL;DR

This paper introduces a numerical scheme for radiation-hydrodynamics that accurately models the coupling of fluid dynamics and radiative transfer across regimes from transport to diffusion, ensuring robustness and correctness in complex astrophysical scenarios.

Contribution

It presents an asymptotic preserving modification of the HLLE scheme for the grey moment M1 system, enabling accurate simulations from free-streaming to diffusive limits.

Findings

The scheme performs well across different regimes.

It remains stable and accurate in complex astrophysical cases.

Successfully models steep opacity gradients in gas cloud collapse.

Abstract

We present in this paper the numerical treatment of the coupling between hydrodynamics and radiative transfer. The fluid is modeled by classical conservation laws (mass, momentum and energy) and the radiation by the grey moment $M_1$ system. The scheme introduced is able to compute accurate numerical solution over a broad class of regimes from the transport to the diffusive limits. We propose an asymptotic preserving modification of the HLLE scheme in order to treat correctly the diffusion limit. Several numerical results are presented, which show that this approach is robust and have the correct behavior in both the diffusive and free-streaming limits. In the last numerical example we test this approach on a complex physical case by considering the collapse of a gas cloud leading to a proto-stellar structure which, among other features, exhibits very steep opacity gradients.