Tutorial Title: Time-accuracy in large-eddy simulation


Guowei He

14:10:00 - 15:20:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Large-eddy simulation (LES) is emerging as a next-generation tool for computation fluid dynamics, in company with many new challenges. In LES of turbulent flows, large-scale eddies are directly solved from the filtered Navier-Stokes (NS) equations, while the effects of small-scale eddies on the large-scale ones have to be modeled using a so-called sub-grid scale (SGS) model. The important developments to achieve the goals are the filter approach, the SGS models and the energy conservative schemes. The recently increasing application of LES to predict non-equilibrium properties of turbulent flows requires that LES should correctly predict two-point, two-time correlations or space-time correlations. For example, turbulence-generated noise requires that a LES with a SGS model could accurately predicts space-time correlations, since the acoustic intensity radiated by turbulent flows depends on space-time correlations according to the Lighthill analogy. In turbulent two-phase flows, space-time correlations determine particle dispersions. Most of the currently existing SGS models are based on the energy budget equations. Therefore, they are able to correctly predict energy spectra at large scales, but they may not accurately predict other statistic quantities, such as space-time correlations. In the first lecture, I will present an introduction on large-eddy simulation, including the filter approach, the SGS models and the energy conservative scheme. These relevant concepts and methods are clearly explained in the fashion different from the Reynolds-Averaged NS method. In the second lecture, I will introduce our recent studies on time accuracy in LES. A new assessment quantity, space-time correlation, is introduced to evaluate the performance of the SGS models. It is found that a LES with the Smagorinsky SGS model may under-predict the correlation magnitudes and over-predict the decorrelation time scales (PoF 14 2186 2002). This may lead to an inaccurate prediction on sound power spectra. Based on those observations, we further develop a non-frozen flow model for the space-time correlations in turbulent shear flows (PRE 79 046319 2009). It is used to explain why the energy-based SGS model is not able to correctly predict space-time correlations. Finally, I will discuss possible SGS models to improve the LES prediction on space-time correlations. Those SGS models are especially useful to turbulence-generated noise and particle dispersion in turbulent flows.