A turbulence model for smoothed particle hydrodynamics

TL;DR

This paper introduces a new turbulence model for Smoothed Particle Hydrodynamics (SPH) that conserves momentum, aligns with experimental data, and is computationally efficient, improving the simulation of two-dimensional turbulence.

Contribution

The paper presents the SPH-$ extepsilon$ model, a turbulence model for SPH that preserves key physical properties and reduces computational cost while matching experimental results.

Findings

Model agrees well with experimental and computational results.

Reduces short-scale velocity magnitudes effectively.

Achieves similar accuracy with half the resolution, saving computational resources.

Abstract

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 $\epsilon$. We call this the SPH-$\epsilon$ 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.