Yukinao Akamatsu, Shu-ichiro Inutsuka, Chiho Nonaka, Makoto Takamoto
In this article, we present a state-of-the-art algorithm for solving the relativistic viscous hydrodynamic equation with QCD equation of state. The numerical method is based on the second-order Godunov method and has less numerical dissipation, which are crucial in describing of quark-gluon plasma in high energy heavy-ion collisions. We apply the algorithm to several numerical test problems such as sound wave propagation, shock tube and blast wave problems. In the sound wave propagation, the intrinsic {\em numerical} viscosity is measured and its explicit expression is shown, which is the second-order of spatial resolution both in the presence and absence of {\em physical} viscosity. The expression of the numerical viscosity can be used to determine the maximum cell size in order to accurately measure the effect of physical viscosity in the numerical simulation.
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http://arxiv.org/abs/1302.1665
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