On the application of Jacobian-free Riemann solvers for relativistic radiation magnetohydrodynamics under M1 closure

TL;DR

This paper introduces a novel Jacobian-free Riemann solver for relativistic radiation magnetohydrodynamics under M1 closure, demonstrating robustness and accuracy in various test scenarios, with promising applications in high-energy astrophysics.

Contribution

It presents the first implementation of Jacobian-free Riemann solvers in radiation MHD, enhancing stability and applicability for complex astrophysical simulations.

Findings

Robustness demonstrated in 1D and multi-dimensional tests

Effective in both free-streaming and diffusion limits

Potential for studying photon-matter interactions in astrophysics

Abstract

Radiative transfer plays a major role in high-energy astrophysics. In multiple scenarios and in a broad range of energy scales, the coupling between matter and radiation is essential to understand the interplay between theory, observations and numerical simulations. In this paper, we present a novel scheme for solving the equations of radiation relativistic magnetohydrodynamics within the parallel code L\'ostrego. These equations, which are formulated taking successive moments of the Boltzmann radiative transfer equation, are solved under the gray-body approximation and the M1 closure using an IMEX time integration scheme. The main novelty of our scheme is that we introduce for the first time in the context of radiation magnetohydrodynamics a family of Jacobian-free Riemann solvers based on internal approximations to the Polynomial Viscosity Matrix, which were demonstrated to be robust and accurate for non-radiative applications. The robustness and the limitations of the new algorithms are tested by solving a collection of one-dimensional and multi-dimensional test problems, both in the free-streaming and in the diffusion radiation transport limits. Due to its stable performance, the applicability of the scheme presented in this paper to real astrophysical scenarios in high-energy astrophysics is promising. In future simulations, we expect to be able to explore the dynamical relevance of photon-matter interactions in the context of relativistic jets and accretion discs, from microquasars and AGN to gamma-ray bursts.