Notes about implicit filtering in LES

FMDenaro · September 18, 2021, 06:05

For interested students, I uploaded this note

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

FMDenaro · September 23, 2021, 06:25

Please, consider that to fully understand this note, the reading of these companion ones can be useful.

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

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

lucamirtanini · September 23, 2021, 11:09

Dear @FMDenaro,
Thank you so much for this useful notes. These are very explanatory.

I am using a code that uses a FD scheme. I would like to plot the graph k-keff for my case study, imaginary and Real part, as you have done in Fig. 2. I used the Eq. 17 but the results is different. Can you please tell me what I am doing wrong?

FMDenaro · September 23, 2021, 11:19

Quote:

Originally Posted by lucamirtanini

Dear @FMDenaro,
Thank you so much for this useful notes. These are very explanatory.

I am using a code that uses a FD scheme. I would like to plot the graph k-keff for my case study, imaginary and Real part, as you have done in Fig. 2. I used the Eq. 17 but the results is different. Can you please tell me what I am doing wrong?

Are you talking about the second order backward derivative? Could you post your plot to see the differences? Or you have found a different mathematical expression?

lucamirtanini · September 23, 2021, 11:30

I simply did:

$Re(k_{eff})=\frac{(4sen(k\Delta x) -sen(2k \Delta x)}{2 \Delta x }$

FMDenaro · September 23, 2021, 11:40

Quote:

Originally Posted by lucamirtanini

I simply did:

$Re(k_{eff})=\frac{(4sen(k\Delta x) -sen(2k \Delta x)}{2 \Delta x }$

So, the expression is the same. I plot the function in Fig.2 only in the range k*dx<=pi, which is the limit prescribed by the Nyquist cut-off. It makes no sense to plot beyond that.
Note that for simplicity I assumed dx=1.

lucamirtanini · September 23, 2021, 11:52

Ok. Now it is the same. Thank you.

FMDenaro · October 4, 2021, 16:39

I uploaded a revised pdf file with some further observations about the topic

September 18, 2021, 06:05	Notes about implicit filtering in LES	#1
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	For interested students, I uploaded this note https://www.researchgate.net/publica...ddy_Simulation sbaffini, arjun, flotus1 and 1 others like this.

September 23, 2021, 06:25		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	Please, consider that to fully understand this note, the reading of these companion ones can be useful. https://www.researchgate.net/publica..._wave_equation https://www.researchgate.net/publica...ing_a_function lucamirtanini likes this.

September 23, 2021, 11:52		#7
lucamirtanini Senior Member luca mirtanini Join Date: Apr 2018 Posts: 165 Rep Power: 7	Ok. Now it is the same. Thank you. FMDenaro likes this.

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September 23, 2021, 11:09		#3
lucamirtanini Senior Member luca mirtanini Join Date: Apr 2018 Posts: 165 Rep Power: 7	Dear @FMDenaro, Thank you so much for this useful notes. These are very explanatory. I am using a code that uses a FD scheme. I would like to plot the graph k-keff for my case study, imaginary and Real part, as you have done in Fig. 2. I used the Eq. 17 but the results is different. Can you please tell me what I am doing wrong?

October 4, 2021, 16:39		#8
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	I uploaded a revised pdf file with some further observations about the topic