Simple and efficient Godunov scheme for computational relativistic gas dynamics

The governing equations of relativistic computational fluid dynamics (CFD) are integrated numerically. The equation of state (EOS) for a gas at relati vistic temperature (the thermal energy of a gas particle is on the order of its rest mass energy) is obtained as a polynomial approximation for a gas with the Maxwellian distribution function. In contrast to previous investig ations by other authors, in which the polytropic index of a gas was accepte d to be constant, here the relativistic dependence of the specific heat is taken into account. The use of the proposed EOS facilitates the relativisti c CFD. The Riemann invariants are expressed in terms of elementary function s so that the characteristic decomposition of the governing equations is ef ficient and natural. The full solution of the Riemann problem (Riemann solv er) is also given by elementary functions. In order to construct it numeric ally, a simple transcendent equation, which relates the pressure and the ve locity at the contact discontinuity, should be solved using an iteration pr ocedure, just as in nonrelativistic CFD. So the Godunov scheme based upon t he exact Riemann solver becomes simple and efficient. 1D test results are p resented, as well as an example of a 2D simulation. (C) 2001 Academic Press .