The effect of filtering on truncated Navier–Stokes equations

The large-eddy simulation (LES) equations are obtained by spatially filtering the Navier–Stokes equations. The nature of the LES solution strongly depends on the filtering operation. In this paper, the effect of some smooth and discrete filters on the LES is studied with the truncated Navier–Stokes (TNS) equations model. These filters are tested with the k ^{− 5/3} spectrum and LES of the three-dimensional homogeneous flow. Through the comparisons of the energy spectrum, the evolution of the total energy as well as the subgrid scale (SGS) dissipation with the filtered direct numerical simulation (DNS) data, the filter shape is understood to have strong influence on the final results. It is shown in this study that the physical filter is the best among the smooth filters while for the discrete filters the Pade filter delivers better results. The results of the low-order Vasilyev filter can also be improved with the same idea of the smooth physical filter.

Keywords:

• Filter
• TNS
• LES
• SGS model

Acknowledgements

Special thanks goes to the reviewers who inspected the entire manuscript and made valuable suggestions. This research is supported by China Postdoctoral Science Foundation No. 2005037335, NSF China Grants No. 10232020, 10502029, and 90505005.