Numerical Relativistic Hydrodynamics Based on the Total Variation Diminishing Scheme

This paper describes a multidimensional hydrodynamic code which can be used for studies of relativistic astrophysical flows. The code solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based on the total variation diminishing (TVD) scheme. It uses a new set of conserved quantities and employs an analytic formula for transformation from the conserved quantities in the reference frame to the physical quantities in the local rest frame. Several standard tests, including relativistic shock tubes, a relativistic wall shock, and a relativistic blast wave, are presented to demonstrate that the code captures discontinuities correctly and sharply in ultrarelativistic regimes. The robustness and flexibility of the code are demonstrated through test simulations of the relativistic Hawley-Zabusky shock and a relativistic extragalactic jet.