Hydrodynamic modeling of QGP expansion using an exact solution of Riemann problem

Hydrodynamic modelling of quark-gluon plasma requires sophisticated numerical schemes that have low numerical viscosity and are able to cope with high gradients of energy density that may appear in initial conditions. We propose to use the Godunov method with an exact Riemann solver for ideal hydrodynamic modelling to meet these conditions. We present the results of numerical tests of the method, such as the sound wave propagation and the shock tube problem, which show both high precision and low numerical viscosity. (paper)