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arXiv · 0803.2556

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

Pavlo V. Tytarenko·Iurii A. Karpenko·Yury M. Sinyukov
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Abstract

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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Pavlo V. Tytarenko, Iurii A. Karpenko, Yury M. Sinyukov. 2008-03-18. A new Godunov-type numerical code with a non-linear Riemann solver for equations of relativistic hydrodynamics. https://arxiv.org/abs/0803.2556

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