THE ANALYTICAL SOLUTION OF THE RIEMANN PROBLEM IN RELATIVISTIC HYDRODYNAMICS

We consider the decay of an initial discontinuity in a polytropic gas in a Minkowski space-time (the special relativistic Riemann problem). In order to get a general analytical solution for this problem, we ana lyse the properties of the relativistic flow across shock waves and ra refactions. As in classical hydrodynamics, the solution of the Riemann problem is found by solving an implicit algebraic equation which give s the pressure in the intermediate states. The solution presented here contains as a particular case the special relativistic shock-tube pro blem in which the gas is initially at rest. Finally, we discuss the im pact of this result on the development of high-resolution shock-captur ing numerical codes to solve the equations of relativistic hydrodynami cs.