Covariant smoothed particle hydrodynamics on a curved background

We show that the smoothed-particle-hydrodynamics discretization technique is compatible with the principles of general relativity if the contact interactions are modeled by spatial smoothing functions in the local frame comoving with the fluid. We then develop a smoothed-particle-hydrodynamics algorithm to model a non-self-gravitating isentropic fluid on a curved background. The equations of the fluid are discretized using a kernel whose spatial support is of a constant proper width in the local comoving frame. The one-dimensional relativistic shock problem is used for testing this algorithm