  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.
