A study of time correlations in lattice Boltzmann-based large-eddy simulation of isotropic turbulence

Abstract

As one of statistical characteristics of turbulent flow, space-time correlation is important when studies contribute to understanding of the mechanism of sound radiation and wave scattering by turbulence. This paper combines large-eddy simulations (LES) with the lattice Boltzmann method (LBM) to study the effects of subgrid models on time correlations in decaying isotropic turbulence. The performance of the inertial-range (IR) consistent model and the classical Smagorinsky model is evaluated in terms of two-time Eulerian velocity correlations at the LBM framework. The present study compares the correlations evaluated by LES and the direct numerical simulations based on the lattice Boltzmann equation and Navier–Stokes (NS) equations, respectively. It shows that the lattice Boltzmann subgrid models yield an underestimation of the magnitude of the time correlation on different time intervals and on a variety of wavenumber modes, similar to NS subgrid models. It is also observed that the calculated decorrelation time scale is in good agreement with the theoretical analysis for the Eulerian time microscale and scales nearly as τ(k)∝(Vk)−1. It appears that τ(k) may be either underestimated or overestimated depending on the shape of initial energy spectrum to some extent. Furthermore, compared to the classical Smagorinsky model with different initial spectra, the IR consistent subgrid model shows promising performance on the prediction of the time-space correlations in turbulent flows.