Large-eddy Simulation of Isotropic Homogeneous Decaying Turbulence

Abstract

Simulations of three dimensional freely decaying homogeneous turbulence in a periodic cube have been used to examine in a detailed and quantitative manner the behaviour of a Large Eddy Simulation (LES) using implicit subgrid modelling. This paper details the form and behaviour of the implicit subgrid models for the Minmod and third order limiting methods at several mesh resolutions. It is shown that for simulations above 32^3 the decay of kinetic energy follows a power law with a decay exponent between 1:2 and 1:4, except in the case of turbulence with a constrained length scale for which the decay exponent is 2:1. This is in very good agreement with experimental data and theoretical analysis where the exponent ? 1:2 ? 1:4 unconstrained, and 2:0 when constrained. At a resolution of 32^3 the number of degrees of freedom are not sufficient to allow a turbulent flow, and velocity derivative statistics are Gaussian. The skewness of the velocity derivative is lower than existing explicit LES and Direct Numerical Simulation (DNS) simulations, but in good agreement with the most recent experimental results. There is a limited sub-inertial range with the three-dimensional Kolmogorov constant ? 1:9, also in agreement with DNS. The less dissipative nature of the third order limiter gives better skewness at a lower grid resolutions, however both give good results in terms of energy dissipation and growth of the length scales.