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

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

2008-03-18

arxiv.org/abs/0803.2556v1

Astronomy and Astrophysics

Astrophysics

38 pages, submitted to J.Comp. Phys

Scientific paper

We 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.

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