Conservative, special-relativistic smoothed particle hydrodynamics

We derive a new special-relativistic version of Smooth Particle Hydrodynamics (SPH) from the Lagrangian of an ideal fluid. The new formulation accounts for the terms that stem from non-constant smoothing lengths, in SPH usually called ”grad-h terms”. To handle shocks a refined artificial viscosity scheme is applied. The performance of this new equation set is explored in a variety of benchmark tests and the results of the new formulation are compared against an earlier specialrelativistic SPH version. The new approach generally yields excellent results. As expected from a Lagrangian method, it performs extremely well in supersonic advection tests, but also for strong relativistic shocks, usually considered a particular challenge for SPH, the method yields convincing results. It is, for example, able to handle Lorentz-factors as large as γ = 50 000 in the so-called wall shock test.