GENERAL-RELATIVISTIC HYDRODYNAMICS WITH A ROE SOLVER

We present a numerical method to solve the equations of general relati vistic hydrodynamics in a given external gravitational field. The meth od is based on a generalization of Roe's approximate Riemann solver fo r the non relativistic Euler equations in Cartesian coordinates. The n ew method is applied to a set of standard test problems for general re lativistic hydrodynamics, and is shown to perform well in comparison t o existing numerical schemes. In contrast to existing explicit methods the present method can cope with strong relativistic shocks. By-produ cts are: the characteristic form of the general relativistic Euler equ ations, a numerical method for special relativity that can deal with s trong discontinuities, a numerical scheme for the integration of the E uler equations in an arbitrary coordinate system, possibly under the i nfluence of (external) gravity, and a novel method to incorporate sour ce terms in numerical schemes.