SGS small scales == fluctuant scales ??
dear all
when filter is used in LES, the small scale occured, i.e unresolved scale. the fluctuant scales is small scale too. can i think the unresolved small scale as the same as fluctuant scales? thanks 
Re: SGS small scales == fluctuant scales ??
Hi,
No, you can't assume that unresolved scales are equal to fluctuant scales. In fact, energy related to fluctuant scales is equal to the energy contained in all the LES scales, unresolved one as well as resolved ones (minus the steady part). However, if you average LES results over time, the fluctuating energy comes from the resolved scales only since the unresolved scales have been filtered out. Generally, there is no problem because it is assumed that the cutoff is located far in the inertial subrange of the TKE spectrum. Therefore the SGS TKE is very small compare to the resolved scales TKE. IF you really want to obtain SGS TKE, you can for instance use a model with an extra equation for it, or evaluate both cutoff and Kolmogorov length scales and use an analytic formula for the shape of the spectrum (Heisenberg, Pao, ...) to perform integration. You can also use deconvolution so as to obtain an estimation of U_total from U_resolved. Regards 
Re: SGS small scales == fluctuant scales ??
I think you have explained this very clearly. Do you have any idea about my question downstairs ? or I will have to go for high order upwind scheme ? High order scheme is not flexible enough for complex geometry simulation though.

Re: SGS small scales == fluctuant scales ??
Hi
I'm not convinced that high order upwind schemes are a solution to your problem. As you've noticed, they are still dissipative with a quite high computational cost (ENO/WENO for instance). If there is no shock, a common way is to use high order central scheme with high order numerical filter to damp wiggles However, according to my experience, 2nd order centered scheme can perform really well. I never used Jameson scheme, rather a AUSM+(P) variant with no shock capturing component and a sensor that switch between upwind and centered formulation according to wiggles detection (see I. Mary and P. Sagaut, LES of a flow around an airfoil near stall, AIAA J. 40(6), pp. 11391145, 2002, for details). Using it, I obtained good results for high Reynolds number cavity flow. I'm also aware of a comparison between this scheme and Jameson's one for DES of dynamic stall of an airfoil: Jameson scheme was found to be too dissipative to obtain an acurate descrition of the unsteady flow. Finally, note that MILES (see J. P. Boris, F. F. Grinstein, E. S. Oran and R. L. Kolbe, New insights into largeeddy simulation, Fluid Dyn. Res. 10, pp. 199228, 1992) could be an option. This method has no explicit modelling for the subgrid scales and it is assumed that the intrinsic numerical dissipation of an upwind scheme is able to mimic the SGS dissipation. For complex configuration with high Reynolds number, MILES can sometime outperform classical LES. Regards 
Re: SGS small scales == fluctuant scales ??
Hi Lionel,
Thank you very much indeed for your info. It seems that a AUSM+(P) variant performs really good. This could be a good candidate for future LES simualtion. However, I still would like to see if there are some LES or DES work using a modified Jameson's scheme and how it works. From the paper you provided, I searched Ducros's work, unfortunately, his recent two papers are all published in the International Journal of Computational Fluid Dynamics, which I could not download straight away and may need a interlibrary loan later on. And I wonder if Jameson's scheme is used in these two papers. Do you know any recent conference papers on this issue ? As you said that "Jameson scheme was found to be too dissipative to obtain an acurate descrition of the unsteady flow", can we draw a conclusion that Jameson scheme is not good at all for LES ? Kind regards Li 
Re: SGS small scales == fluctuant scales ??
For some results using Ducros' Jameson+wiggle detector approach, you may have a look at: C. P. Mellen,J. Frohlich and W. Rodi: "Lessons from LESFOIL Project on LargeEddy Simulation of Flow Around an Airfoil", AIAA J. 41(4), 2003. Since F. Ducros no longer works in CERFACS, I'm not sure that its approach has been used recently.
I think that if you intend to use Jameson's scheme for LES, you have to cancel the shock capturing dissipative component at least. But I don't know if the DES results I've mentioned deal either with this modified Jameson's scheme or the full one. Regards 
Re: SGS small scales == fluctuant scales ??
Thanks a lot for your suggestions. I may contact those authors at certain stage when needed.

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