Relativistic Hydrodynamics for Heavy–Ion Collisions II. Compression of Nuclear Matter and the Phase Transition to the Quark–Gluon Plasma†

We investigate the compression of nuclear matter in relativistic hydrodynamics. Nuclear matter is described by a σ − ω–type model for the hadron matter phase and by the MIT bag model for the quark–gluon plasma, with a first order phase transition between both phases. In the presence of phase transitions, hydrodynamical solutions change qualitatively, for instance, one-dimensional stationary compression is no longer accomplished by a single shock but via a sequence of shock and compressional simple waves. We construct the analytical solution to the “slab-on-slab” collision problem over a range of incident velocities. The performance of numerical algorithms to solve relativistic hydrodynamics is then investigated for this particular test case. Consequences for the early compressional stage in heavy–ion collisions are pointed out. This work was supported by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract No. DE-FG02-93ER-40764. Partially supported by the Alexander von Humboldt–Stiftung under the Feodor–Lynen program.