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 $\sigma-\omega$--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.