Semi-implicit scheme for treating radiation under M1 closure in general relativistic conservative fluid dynamics codes

TL;DR

This paper introduces a semi-implicit numerical scheme for incorporating radiation into general relativistic fluid dynamics codes using the M1 closure, effectively handling various optical regimes and demonstrating robustness through multiple test problems.

Contribution

It presents a covariant M1 closure scheme with semi-implicit treatment of radiation source terms, implemented in the KORAL code, improving simulation accuracy in relativistic radiation hydrodynamics.

Findings

Successfully tested on relativistic shock tubes and atmospheres

Demonstrated ability to model shadows and beams in curved spacetime

Validated against static and accretion flow scenarios

Abstract

A numerical scheme is described for including radiation in multi-dimensional general-relativistic conservative fluid dynamics codes. In this method, a covariant form of the M1 closure scheme is used to close the radiation moments, and the radiative source terms are treated semi-implicitly in order to handle both optically thin and optically thick regimes. The scheme has been implemented in a conservative general relativistic radiation hydrodynamics code KORAL. The robustness of the code is demonstrated on a number of test problems, including radiative relativistic shock tubes, static radiation pressure supported atmosphere, shadows, beams of light in curved spacetime, and radiative Bondi accretion. The advantages of M1 closure relative to other approaches such as Eddington closure and flux-limited diffusion are discussed, and its limitations are also highlighted.