Idrodinamica viscosa e relativistica per le collisioni di ioni pesanti con ECHO-QGP

A deeper understanding of the experimental data from the heavy-ion experiments performed at RHIC (Relativistic Heavy Ion Collider) and LHC (Large Hadron Collider), where the Quark Gluon Plasma (QGP) is supposed to be produced, is actually one of the main goals of the theoretical research in Quantum Chromodynamics (QCD) in the high temperature and low density regime. Relativistic hydrodynamics represents a useful tool to understand heavy-ion collisions (HIC), being used to study the hot and dense medium created and to explain several independent experimental observable in the soft sector. In this work we display how a relativistic viscous hydrodynamical theory consistently satisfying causality can be developed. This theory finds an efficient numerical implementation in the ECHO-QGP code, specifically designed to simulate heavy ion collisions. We have followed the latest stages of the development of ECHO-QGP, performing an activity of testing and debugging of the code before its public release. In some special cases the numerical solution of the hydrodynamic equations can be compared to exact analytic results, thus providing an important validation of the code. Among the above exact solutions the major role is played by the so-called Gubser flow, which allowed us to test the code in a very non trivial case (in the presence of viscosity and transverse and longitudinal expansion).