Direct Numerical Simulation of decaying two-dimensional turbulence in a no-slip square box using Smoothed Particle Hydrodynamics

TL;DR

This study applies Smoothed Particle Hydrodynamics (SPH) to simulate decaying 2D turbulence in a no-slip square domain, comparing results with pseudo-spectral methods and analyzing vortex formation, energy spectra, and boundary effects.

Contribution

It demonstrates the feasibility of using SPH for DNS of wall-bounded turbulence and compares its performance with established spectral methods, highlighting differences in vortex generation.

Findings

SPH results match pseudo-spectral in energy and enstrophy evolution

No long-lived boundary-generated vortices observed in SPH simulations

Kinetic energy spectrum exhibits expected k-3 inertial range scaling

Abstract

This paper explores the application of SPH to a Direct Numerical Simulation (DNS) of decaying turbulence in a two-dimensional no-slip wall-bounded domain. In this bounded domain, the inverse energy cascade, and a net torque exerted by the boundary, result in a spontaneous spin up of the fluid, leading to a typical end state of a large monopole vortex that fills the domain. The SPH simulations were compared against published results using a high accuracy pseudo-spectral code. Ensemble averages of the kinetic energy, enstrophy and average vortex wavenumber compared well against the pseudo-spectral results, as did the evolution of the total angular momentum of the fluid. However, while the pseudo-spectral results emphasised the importance of the no-slip boundaries as generators of long lived coherent vortices in the flow, no such generation was seen in the SPH results. Vorticity filaments produced at the boundary were always dissipated by the flow shortly after separating from the boundary layer. The kinetic energy spectrum of the SPH results was calculated using a SPH Fourier transform that operates directly on the disordered particles. The ensemble kinetic energy spectrum showed the expected k-3 scaling over most of the inertial range. However, the spectrum flattened at smaller length scales (initially less than 7.5 particle spacings and growing in size over time), indicating an excess of small-scale kinetic energy.