A turbulence model for smoothed particle hydrodynamics

The aim of this paper is to describe a turbulence model for the particle method Smoothed Particle Hydrodynamics (SPH). The model makes few assumptions, conserves linear and angular momentum, satisfies a discrete version of Kelvin s circulation theorem, and is computationally efficient. Furthermore, the results from the model are in good agreement with the experimental and computational results of Clercx and Heijst for two-dimensional turbulence inside a box with no-slip walls. The model is based on a Lagrangian similar to that used for the Lagrangian averaged Navier-Stokes (LANS) turbulence model, but with a different smoothed velocity. The smoothed velocity preserves the shape of the spectrum of the unsmoothed velocity, but reduces the magnitude for short length scales by an amount which depends on a parameter epsilon. We call this the SPH-epsilon model. The effectiveness of the model is indicated by the fact that the second and fourth order velocity correlation functions calculated using the smoothed velocity and a coarse resolution, are in good agreement with a calculation using a resolution which is finer by a factor 2, and therefore requires 8 times as much work to integrate to the same time