A Multidimensional Relativistic Hydrodynamics Code with a General Equation of State

TL;DR

This paper introduces a new general equation of state for relativistic gases and a multidimensional hydrodynamics code that accurately models relativistic astrophysical flows, improving upon previous methods.

Contribution

The authors develop a novel general equation of state compatible with the Synge model and implement a robust multidimensional relativistic hydrodynamics code using the HLL scheme.

Findings

The new code accurately simulates relativistic flows with non-zero tangential velocities.

Relativistic jet simulations show morphology depends on the equation of state and gas composition.

The proposed methods outperform previous approaches in accuracy and robustness.

Abstract

The ideal gas equation of state with a constant adiabatic index, although commonly used in relativistic hydrodynamics, is a poor approximation for most relativistic astrophysical flows. Here we propose a new general equation of state for a multi-component relativistic gas which is consistent with the Synge equation of state for a relativistic perfect gas and is suitable for numerical (special) relativistic hydrodynamics. We also present a multidimensional relativistic hydrodynamics code incorporating the proposed general equation of state, based on the HLL scheme, which does not make use of a full characteristic decomposition of the relativistic hydrodynamic equations. The accuracy and robustness of this code is demonstrated in multidimensional calculations through several highly relativistic test problems taking into account nonvanishing tangential velocities. Results from three-dimensional simulations of relativistic jets show that the morphology and dynamics of the relativistic jets are significantly influenced by the different equation of state and by different compositions of relativistic perfect gases. Our new numerical code, combined with our proposed equation of state is very efficient and robust, and unlike previous codes, it gives very accurate results for thermodynamic variables in relativistic astrophysical flows.