Explicit-Implicit Scheme for Relativistic Radiation Hydrodynamics

TL;DR

This paper introduces an explicit-implicit numerical scheme for relativistic radiation hydrodynamics that conserves energy and momentum, enabling efficient simulations of high-speed astrophysical phenomena without restrictive time step constraints.

Contribution

The paper presents a novel explicit-implicit scheme for RRHD that avoids FLD approximation and relaxes CFL conditions in optically thick media, improving simulation accuracy and efficiency.

Findings

Successfully passes 1D and 2D test problems.

Conserves total energy and momentum in simulations.

Applicable to relativistic astrophysical scenarios.

Abstract

We propose an explicit-implicit scheme for numerically solving Special Relativistic Radiation Hydrodynamic (RRHD) equations, which ensures a conservation of total energy and momentum (matter and radiation). In our scheme, 0th and 1st moment equations of the radiation transfer equation are numerically solved without employing a flux-limited diffusion (FLD) approximation. For an hyperbolic term, of which the time scale is the light crossing time when the flow velocity is comparable to the speed of light, is explicitly solved using an approximate Riemann solver. Source terms describing an exchange of energy and momentum between the matter and the radiation via the gas-radiation interaction are implicitly integrated using an iteration method. The implicit scheme allows us to relax the Courant-Friedrichs-Lewy condition in optically thick media, where heating/cooling and scattering timescales could be much shorter than the dynamical timescale. We show that our numerical code can pass test problems of one- and two-dimensional radiation energy transport, and one-dimensional radiation hydrodynamics. Our newly developed scheme could be useful for a number of relativistic astrophysical problems. We also discuss how to extend our explicit-implicit scheme to the relativistic radiation magnetohydrodynamics.