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LES filter- frequency limit

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Old   July 1, 2019, 11:15
Default LES filter- frequency limit
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Ashish bhigah
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Hi,
I have a theorical doubt about the les filter.
The filter, in my software, is the cubic root of the the cell volume.
So if I use, for istance, the grid spacing delta=0,125 m, the resolved frequency should go from 0 to 2*pi/delta, which in this case is almost 50 Hz.

But now I have a doubt, since 2*pi/delta has the unit m^-1 , it should be wavenumber and not frequency.

So I am getting confused. Can you help me to understand which is the frequency limit of the resolved area.

Thank you in advance
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Old   July 1, 2019, 13:49
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Quote:
Originally Posted by bhigahAshish View Post
Hi,
I have a theorical doubt about the les filter.
The filter, in my software, is the cubic root of the the cell volume.
So if I use, for istance, the grid spacing delta=0,125 m, the resolved frequency should go from 0 to 2*pi/delta, which in this case is almost 50 Hz.

But now I have a doubt, since 2*pi/delta has the unit m^-1 , it should be wavenumber and not frequency.

So I am getting confused. Can you help me to understand which is the frequency limit of the resolved area.

Thank you in advance



You have an implicit filter, I suppose...You are doing confusion between the filter width (which is a lenght) and the cut-off wavenumber.

That is the filter is implicitly due to the grid and to the numerical scheme. In such s case, the cut-off frequency is simply due to the grid size. In a simple 1D example, a grid of step h introduces the cut-off spatial frequency (Nyquist) kc= pi/h. It is dimensional since the frequency is expressed as


k = n*2*pi/L


this way you see that n is the wavenumber and k is the frequency. Be aware that if L=2*pi then k=n*(1). This means that n is always a number but, to be trasformed in a frequency k, that requires to be multiplied by 1 that has the dimension 1/L. Of course, this is never explicitly written and you can read in papers n or k.
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Old   July 15, 2019, 09:01
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Ashish bhigah
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Hi, I have another question related to this. Is the cutoff related to the fact the we can considered the filter a top hat and doing the FT of a top hat function the first zero is at kc=pi/delta ??
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Old   July 15, 2019, 09:40
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Hi, I have another question related to this. Is the cutoff related to the fact the we can considered the filter a top hat and doing the FT of a top hat function the first zero is at kc=pi/delta ??

No, the transfer function of the top-hat filter has an infinite number of zeros and is a function going to zero only for k->+Inf.
The the cut-off is due the superimposition of the grid size.
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