Relativistic hydrodynamics in a global fashion

After a long and controversial tradition of applications to high-energy hadron-hadron and hadron-nucleus collisions, relativistic hydrodynamics may finally become a convincing concept when applied to ultrarelativistic nuclear collisions with large projectiles and targets. We propose a new method, which we call global hydrodynamics, for solving the hydrodynamic equations, with two objectives in mind: first to make the calculations easier by using an approximate but very efficient scheme, and second to gain new insights into the dynamics by establishing the global expansion characteristics as a new viewpoint. The method consists of integrating the partial differential equations of hydrodynamics over an azimuthally symmetric region to obtain global conservation laws from the local ones. Assuming specific thermal and velocity profiles we derive ordinary differential equations for the most relevant dynamical quantities which are easy to solve. This enables us to do large numbers of runs easily and thus to perform a systematic scan of the whole range of possible initial conditions, following each case individually until freeze-out. By comparing the computed particle spectra to experiments it is possible to restrict the initial conditions and obtain quantitative information on the early dynamics of relativistic nuclear collisions.