3 - D Relativistic SPH

In this paper we present the equations and some basic applications of relativistic SPH. The equations are generated under the assumption that there are no interaction terms between the fluid modelled and the background space-time, i.e. we are neglecting the perturbations to the metric produced by the modelled fluid. This corresponds to a stationary metric, which for this work, we further limit to be static as well. The equations use a new signal velocity term and artificial viscosity to smear out the effects of strong shocks and are tested here against Newtonian and relativistic shocks.