2009/11/13 by J. J. Monaghan, Monaghan, J. J.
Engineering · Physics and Astronomy · #Angular velocity #Classical mechanics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics Simulations and Interactions #Fluid Dynamics and Heat Transfer #Function (biology) #K-epsilon turbulence model #K-omega turbulence model #Lattice Boltzmann Simulation Studies #Mechanics #Physics #Smoothed-particle hydrodynamics #Statistical physics #Turbulence #Work (physics) #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.0911.2523
34 pages, 11 figures
arxiv created 2009/11/13 · openalex publication_date 2009/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 ε. We call this the SPH-ε 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, is 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.