Cutoff wavenumbers, implicit filter LES
 

Dear experts,
I am studying the Energy spectrum acquired in a cfd LES software with an implicit filters. The cutoff wavenumbers is kC=pi/Dx. Does this cutoff correspond to the the point of the spectrum that deviates from the inertial range power low or to the end of the decrease? Or maybe it is a point in the middle of this region. I didn't find many papers that show this kind of analysis on implicit filters (maybe it is because I am not searching the right keyword). Can you help me?

No, using implicit filter, the cut-off frequency pi/dx is induced by the computational grid and is the highest frequency you can represent. In other words, it is the extrem value in the k-axis of the spectrum.

if I obtain the Wavenumber spectrum with the Taylor Hypotesis, starting from a Frequency spectrum, I can exceed this limit if I have a very fine time step, isnt'it? The wavenumber where the spectrum deviates from the -5/3 power law how is it called then? and how can be calculated?

It seems you are confusing numerical issues and physical issues.

You asked for the spatial resolution, why are you now talking about the computational time step? The time step introduces implicitly a further cut-off in terms of the (temporal) frequency pi/dt.
The change from the theoretical slope -5/3 is at the onset of the dissipation region, at a lenght scale denoted as Tayolr micro-scale. That is a physical lenght and, depending on your computational grid, you can (DNS) or not (LES) resolve up to it.

No. I don't think I am confusing. If you do the energy spectrum in a LES code with implicit filter you will realize that before the Nyquist limit the Energy will drop off definitely before the dissipation range. This is due to the filter operated by the grid

That does not depend on the implicit filter but on the specific shape of the numerically induced transfer function. If you take a DNS spectrum as reference, a LES spectrum can have a slight deviation from the inertial range (-5/3) in case a smooth transfer function (like a top-hat) acts. But an implicit filter is also acting in the case of an LES using spectral methods. In such a case there is no smoothing and the slope should be that of the theoretical one.
On the other hand, even for smooth filters, a slight deviation from the theoretical slope does not mean at all that this is the start of the physical dissipation range.

If you refine the grid, you will see that the dropoff point moves. This suggests that depends on the filter. If the filter is implied, the transfer function is implied, so nothing is added to the code, as far as I understood, and depends on the grid

The moving of the Nyquist frequency pi/dx (grid filter) is, indeed, grid size depending. But the implicit filter is not only the one due to the grid size being a superimposed effect due to the type of numerical discretization really in act.
Using FD is different form using FV and different from SM, each one underlying a different implicit filter shape at the same grid resolution.

I wrote some years ago an article about this topic, I know it is not simple to read but you can see for the main conclusions.

https://www.researchgate.net/publica...dy_Simulations

Thank you Prof. Denaro, I have been looking for paper like yours. Can you recommend me other paper that explore , for implicit filtering how the "drop-off" of the spectrum variates, changing size of the grid and using FV or FD?
Thank you

Of course you should consider the references in my paper. As further reading you could find useful also these papers and the related references:


https://www.researchgate.net/publica...dy_simulations


https://www.researchgate.net/publica...mes_simulation