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, i.e. rather special conditions fluid-dynamical algorithms are usually not confronted with. Therefore, prior to applying them directly to the simulation of heavy-ion collisions, one should investigate their performance in well-controlled situations. We consider here 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.