Inviscid smoothed particle hydrodynamics

In smoothed particle hydrodynamics (SPH), artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks. We present a novel method of controlling the amount of artificial viscosity, which uses the total time derivative of the velocity divergence as shock indicator and aims at completely eliminating viscosity away from shocks. We subject the new scheme to numerous tests and find that the method works at least as well as any previous technique in the strong-shock regime, but becomes virtually inviscid away from shocks, while still maintaining particle order. In particular sound waves or oscillations of gas spheres are hardly damped over many periods.