A multidimensional relativistic hydrodynamic code with a general equation of state

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 hydrodynamic 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 threedimensional 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. © 2010. The American Astronomical Society.