The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics

We have generalized the exact solution of the Riemann problem in special re lativistic hydrodynamics (Marti & Muller 1994) for arbitrary tangential flo w velocities. The solution is obtained by solving the jump conditions acros s shocks plus an ordinary differential equation arising from the self-simil arity condition along rarefaction waves, in a similar way as in purely norm al flow. The dependence of the solution on the tangential velocities is ana lysed, and the impact of this result on the development of multi-dimensiona l relativistic hydrodynamic codes (of Godunov type) is discussed.