2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157117We present a second-order upwind numerical scheme for equations of relativistic hydrodynamics with a source term. A new non-linear Riemann solver is constructed. Solution of a Riemann problem on a cells boundary is based on exact relations in case of zero tangential velocities. In this sense our solver is "exact". In case of non-zero tangential velocities a reasonable approximation is made that allows to avoid solution of very complicated exact equations. The scheme is tested on several one- and three-dimensional solutions demonstrating a good performance for both strong shocks and strong rarefactions.38 pages, submitted to J.Comp. PhysAstrophysicsHigh Energy Physics - PhenomenologyNuclear Theorytext