Large eddy simulations of turbulent flow based on a removal of energy production through nonlinear interactions

Abstract

In large eddy simulations (LES), nonlinear dispersive subgrid scale (SGS) models are usually found to be not sufficiently dissipative. In this work, a new model is proposed to directly remove the unphysical energy accumulation due to the nonlinear terms. The model can be obtained from two approaches, either based on the energy transfer in multi-level scales or derived from the kinetic energy equation. Moreover, a gradient-type modification is included to ensure Galilean invariance and generate extra dissipative effect, which is found to have negligible impact on the ideal energy removal. We compare the present model with other structural models and regularization techniques both theoretically and numerically. We show that because of the reduction of energy production at desired scales, the collective effect of our new model was able to provide sufficient SGS transfer in energy cascade without the help of extra dissipative terms. The scale separation is facilitated by a smooth low-pass filter, which becomes increasingly more active for higher wavenumbers. Since filtering already takes the grid size into account, the model is capable of consistently produce accurate results for all the test cases of wall-bounded turbulence. We believe our results further emphasized the importance of attenuating the energy pileup in LES and showed that it is possible to overcome the issue through a simple but effective modification of the nonlinear term.