A kinetic beam scheme for relativistic gas dynamics

An extension of the beam scheme of Sanders and Prendergast (Astrophys. J.188,489, 1974) for the Newtonian gas dynamics to relativistic gas dynamics is presented. It is found that the relativistic Euler equations are split into a set of discrete conservation laws with beam split conservative state vectors and flux vectors. High-order accurate schemes using essentially nonoscillatory concept are devised. Formulations for two space dimensions are also included. Numerical experiments with relativistic one-dimensional shock tube flows and two-dimensional Kelvin-Helmholtz instability flow to illustrate the method are given.