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We have generalised the exact solution of the Riemann problem in specialrelativistic hydrodynamics for arbitrary tangential flow velocities. Thesolution is obtained by solving the jump conditions across shocks plus anordinary differential equation arising from the self-similarity condition alongrarefaction waves, in a similar way as in purely normal flow. The dependence ofthe solution on the tangential velocities is analysed, and the impact of thisresult on the development of multidimensional relativistic hydrodynamic codes(of Godunov type) is discussed.Comment: 26 pages, 4 figures. Accepted for publication in Journal of Fluid  Mechanic

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