A new scheme of causal viscous hydrodynamics for relativistic heavy-ion
  collisions: A Riemann solver for quark-gluon plasma
  In this article, we present a state-of-the-art algorithm for solving the
relativistic viscous hydrodynamics equation with the QCD equation of state. The
numerical method is based on the second-order Godunov method and has less
numerical dissipation, which is 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 sound wave propagation, the intrinsic 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 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.
