Inviscid smoothed particle hydrodynamics

• Published in: Monthly notices of the Royal Astronomical Society Vol. 408; no. 2; pp. 669 - 683
• Main Authors: Cullen, Lee, Dehnen, Walter
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 21.10.2010; Wiley-Blackwell; Oxford University Press
• Subjects: Astronomy; Astrophysics; Earth, ocean, space; Exact sciences and technology; Fluid mechanics; hydrodynamics; methods: numerical; Particle physics; Shock waves; methods: numerical; hydrodynamics; Viscosity; Divergences; Smoothed particle hydrodynamics method; Gas sphere; Numerical method; Acoustic waves
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2010.17158.x

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.