Relativistic Hydrodynamics for Heavy–Ion Collisions I. General Aspects and Expansion into Vacuum

We present algorithms to solve relativistic hydrodynamics in 3+1–dimensional situations without apparent symmetry to simplify the solution. In simulations of heavy–ion collisions, these numerical schemes have to deal with the physical vacuum and with equations of state with a first order phase transition between hadron matter and a quark–gluon plasma. We investigate their performance for the one–dimensional expansion of baryon-free nuclear matter into the vacuum, which is an analytically solvable test problem that incorporates both the aspect of the vacuum as well as that of a phase transition in the equation of state. The dependence of the lifetime of the mixed phase on the initial energy density is discussed. 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. 1