Abstract
The present study is aimed at enhancing the effectiveness of the large eddy simulation (LES) approach to the computation of turbulent flows by these two methods: i) developing a superior subgrid scale (SGS) model and ii) improving the economy of LES. First of all, the various existing SGS models are extensively investigated, and their advangages and disadvantages are addressed to highlight the areas requiring improvements. This study leads to the construction of a modified SGS dynamic model. In addition, a detailed derivation of the second-order velocity structure function SGS model is made, correcting an error found in that model. A new multiple mesh method is also designed to accelerate LES. After the above theoretical studies, several low-Reynolds-number channel flow simulations have been performed. Firstly, simulations with varying model constants are carried out, and the results agree with those of Deardorff [14], showing that a model constant of about 0.1 is optimum for channel flows. Secondly, simulations with varying numerical resolutions have been carried out. They reveal that the refinement of the mesh in the direction normal to the wall improves all the turbulence statistics, both higher- and lower-order statistics, over the whole channel, while the refinement of the resolution in the streamwise and spanwise directions improves lower-order statistics over the whole channel, but only improves higher-order turbulence statistics in the central region of the channel. Thirdly, a dissipation-range SGS model (i.e. the Smagorinsky model with low- Reynolds-number modification [67]) is, for the first time, tested and compared with the standard Smagorinsky model. The results obtained show some promise for automatically adjusting the SGS model with Reynolds number. Fourthly, the performance of the modified dynamic SGS model is assessed through a comparison of length scales computed respectively by this modified model, the Germano- Lilly dynamic SGS model and two empirical wall damping functions in conjunction with an optimum model coefficient, which have been successfully used in many simulations of channel flows. Two values of the ratio of filter widths are set for each of the dynamic models. The results have confirmed that the modified dynamic SGS model can be successfully extended to simulate low-Reynolds-number channel flows. Of great promise is that the modified SGS dynamic model gives the correct behaviour of the subgrid eddy viscosity in the region of a plane wall to an accuracy that exceeds the best-tuned wall damping function, and almost collapses with the theoretical behaviour of the length scale near the wall without any tuning and adjustment. In addition, the impact of the choice of the ratio of filter widths on the modified dynamic SGS model is much less than that on the Germano-Lilly model. Finally, simulations using the new and old multiple mesh methods are performed. The instantaneous results just after the interpolation of the coarse mesh velocity field onto the fine mesh show that the fine mesh velocity field created by the new multiple mesh method contains the information of the residual field. In contrast, there is no difference between the fine mesh results obtained by the old method and those from a simulation on the coarse mesh.