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We present a second-order upwind numerical scheme for equations ofrelativistic hydrodynamics with a source term. A new non-linear Riemann solveris constructed. Solution of a Riemann problem on a cells boundary is based onexact relations in case of zero tangential velocities. In this sense our solveris "exact". In case of non-zero tangential velocities a reasonableapproximation is made that allows to avoid solution of very complicated exactequations. The scheme is tested on several one- and three-dimensional solutionsdemonstrating a good performance for both strong shocks and strongrarefactions.

A new Godunov-type numerical code with a non-linear Riemann solver for equations of relativistic hydrodynamics