Controlling artificial viscosity in smoothed particle hydrodynamics simulations of accretion disks

A. Cartwright and D. Stamatellos

School of Physics and Astronomy, Cardiff University, 5, The Parade, Cardiff CF24 3AA, UK e-mail: Annabel.Cartwright@astro.cf.ac.uk

Received: 19 March 2010
Accepted: 15 April 2010

Abstract

Context. The fidelity of smoothed particle hydrodynamics (SPH) simulations of accretion disks depends on how artificial viscosity (AV) is formulated.

Aims. We investigate whether standard methodology is reliable in this regard.

Methods. We test the operation of two methods for selective application of AV in SPH simulations of Keplerian accretion disks, using a ring spreading test to quantify effective viscosity, and a correlation coefficient technique to measure the formation of unwanted prograde alignments of particles.

Results. Neither the Balsara switch (B) nor time dependent viscosity (TDV) work effectively, as they leave AV active in areas of smooth shearing flow, and do not eliminate the accumulation of alignments of particles in the prograde direction. The effect of both switches is periodic, the periodicity dependent on radius and unaffected by the density of particles. We demonstrate that a very simple algorithm activates AV only when truly convergent flow is detected and reduces the unwanted formation of prograde alignments. The new switch works by testing whether all the neighbours of a particle are in Keplerian orbit around the same point, rather than calculating the divergence of the velocity field, which is very strongly affected by Poisson noise in the positions of the SPH particles.