  We present a fully Lagrangian conservation form of the general relativistic
hydrodynamic equations for perfect fluids with artificial viscosity in a given
arbitrary background spacetime. This conservation formulation is achieved by
choosing suitable Lagrangian time evolution variables, from which the generic
fluid variables rest-mass density, 3-velocity, and thermodynamic pressure have
to be determined. We present the corresponding equations for an ideal gas and
show the existence and uniqueness of the solution. On the basis of the
Lagrangian formulation we have developed a three-dimensional general
relativistic Smoothed Particle Hydrodynamics (SPH) code using the standard SPH
formalism as known from non-relativistic fluid dynamics. One-dimensional
simulations of a shock tube and a wall shock are presented. With our method we
can model ultra-relativistic fluid flows including shocks with relativistic
gamma-factors of even 1000.
