A Turbulence Model for Smoothed Particle Hydrodynamics

The aim of this paper is to devise a turbulence model for the particle method Smoothed Particle Hydrodynamics (SPH) which makes few assumptions, conserves linear and angular momentum, satisfies a discrete version of Kelvin’s circulation theorem, and is computationally efficient. These aims are achieved. Furthermore, the results from the model are in good agreement with the experimental and com-putational 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 differ-ent 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 . We call this the SPH- model. The effectiveness of the model is indicated by the fact that the second order velocity correlation function calculated using the smoothed velocity and a coarse resolution, 1 a