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

Relativistic viscous hydrodynamics for heavy-ion collisions with ECHO-QGP