The collision of two ultra-relativistic, heavy-ions is simulated by so
lving the time dependent relativistic hydrodynamics equations on an Eu
lerian grid. A high resolution second order upwind scheme based on the
Harten Lax Van Leer (HLLE) method is used in the calculations. We hav
e extended this method for simulating ultra-relativistic, heavy-ion co
llisions. This strategy is shown to be faster and/or more accurate tha
n other published methods for the simulation of ultra-relativistic hea
vy-ion collisions. (C) Elsevier Science Inc., 1998.