LES box filter, filters big scales instead of small scales!

Moreza7 · February 16, 2021, 03:15

Hello,

As you know, in LES, the filter function must filter(remove) the small scales and keep the large scales.
But for the box filter in physical space(a), you can see that it keeps the values within range $(-\Delta/2,\Delta/2)$ which means that small scales from $(-\Delta/2,0)$ and $(0,\Delta/2)$ are kept and the scales bigger than $\Delta/2$ are set to zero.
I think this is in conflict with its spectral definition! In spectral space(b), it keeps the small wave numbers (big scales) and removes the large wavenumbers (small scales).
Can somebody explain this to me?

FMDenaro · February 16, 2021, 03:49

Quote:

Originally Posted by Moreza7

Hello,

As you know, in LES, the filter function must filter(remove) the small scales and keep the large scales.
But for the box filter in physical space(a), you can see that it keeps the values within range $(-\Delta/2,\Delta/2)$ which means that small scales from $(-\Delta/2,0)$ and $(0,\Delta/2)$ are kept and the scales bigger than $\Delta/2$ are set to zero.
I think this is in conflict with its spectral definition! In spectral space(b), it keeps the small wave numbers (big scales) and removes the large wavenumbers (small scales).
Can somebody explain this to me?

You are confusing the concepts. In the physical space the filter function is represented and you have the convolution product with the variable to produce the filtered variable. The more delta is greater, the more the variable is filtered.

The transfer function in spectral space will show the effects of the filter function along the wavenumbers.

Moreza7 · February 16, 2021, 05:27

Quote:

Originally Posted by FMDenaro

You are confusing the concepts. In the physical space the filter function is represented and you have the convolution product with the variable to produce the filtered variable. The more delta is greater, the more the variable is filtered.

The transfer function in spectral space will show the effects of the filter function along the wavenumbers.

Ok. So it just performs a smoothing procedure by averaging the variables in the filter width. Then how can we say that the small scales are eliminated?

FMDenaro · February 16, 2021, 05:48

There are a lot of textbook you can use to see the filtering in physical space. It makes smoother the original function.
The concept is explained by the slide at page 8 in my lecture
https://www.researchgate.net/publica...extFileContent

February 16, 2021, 03:15	LES box filter, filters big scales instead of small scales!	#1
Moreza7 Senior Member Join Date: Jan 2018 Posts: 121 Rep Power: 8	Hello, As you know, in LES, the filter function must filter(remove) the small scales and keep the large scales. But for the box filter in physical space(a), you can see that it keeps the values within range $(-\Delta/2,\Delta/2)$ which means that small scales from $(-\Delta/2,0)$ and $(0,\Delta/2)$ are kept and the scales bigger than $\Delta/2$ are set to zero. I think this is in conflict with its spectral definition! In spectral space(b), it keeps the small wave numbers (big scales) and removes the large wavenumbers (small scales). Can somebody explain this to me?

February 16, 2021, 05:48		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	There are a lot of textbook you can use to see the filtering in physical space. It makes smoother the original function. The concept is explained by the slide at page 8 in my lecture https://www.researchgate.net/publica...extFileContent Moreza7 and aero_head like this.

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