  We present ECHO-QGP, a numerical code for $(3+1)$-dimensional relativistic
viscous hydrodynamics designed for the modeling of the space-time evolution of
the matter created in high energy nuclear collisions. The code has been built
on top of the \emph{Eulerian Conservative High-Order} astrophysical code for
general relativistic magneto-hydrodynamics [\emph{Del Zanna et al., Astron.
Astrophys. 473, 11, 2007}] and here it has been upgraded to handle the physics
of the Quark-Gluon Plasma. ECHO-QGP features second-order treatment of causal
relativistic viscosity effects in both Minkowskian or Bjorken coordinates;
partial or complete chemical equilibrium of hadronic species before kinetic
freeze-out; initial conditions based on the optical Glauber model, including a
Monte-Carlo routine for event-by-event fluctuating initial conditions; a
freeze-out procedure based on the Cooper-Frye prescription. The code is
extensively validated against several test problems and results always appear
accurate, as guaranteed by the combination of the conservative
(shock-capturing) approach and the high-order methods employed. ECHO-QGP can be
extended to include evolution of the electromagnetic fields coupled to the
plasma.
