  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.
