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In this work we present a formulation of the Riemann solver for relativistic hydrodynamics. The Riemann solver presented here is an extension to the relativistic regeime of the high quality, two shock Riemann solver for non-relativistic hydrodynamics presented by Van Leer (1979) and Colella (1982). It, therefore, shows the same advantages that the previously mentioned reimann solvers show for non-relativistic hydrodynamics, viz. exact treatment for strong shocks and accurate treatment of contact discontinuities. We then incorporate the riemann solver into a multidimensional TVD algorithm and show that the algorithm allows one to calculate with precision several flows with very high Lorenz factors ( i.e. flows with speeds very close to the speed of light). Applications to astrophysical flows will be presented.
