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Periodic boundary conditions for velocity in Staggered grids 

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August 21, 2022, 05:45 
Periodic boundary conditions for velocity in Staggered grids

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Divyaprakash
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Hi,
I am trying to implement periodic boundary conditions along the x direction. So far I am getting error in the approach I am using. https://drive.google.com/file/d/1E_z...ew?usp=sharing I want to confirm If I have correctly implement the BCs. I am attaching an image which shows how I have implemented periodicity. The first grid corresponds to pressure. The second grid corresponds to uvelocity. The hatched lines indicate the periodic boundary. Can someone confirm if this correct or correct them if wrong. Last edited by Divyaprakash; August 21, 2022 at 05:46. Reason: image was not visible 

August 21, 2022, 07:36 

#2  
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Filippo Maria Denaro
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Quote:


August 21, 2022, 09:37 

#3 
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Divyaprakash
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The x velocity is forward staggered.


August 21, 2022, 10:09 

#4 
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Filippo Maria Denaro
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I used your sketch to show the correct staggered colocation for all the u components superimposed to the pressure colocation.
However, you seems to show walls at the BCs, thus you cannot use periodicity. 

August 21, 2022, 10:36 

#5 
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Divyaprakash
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Thank you so much for your time. Actually the ends are not walls. I used hatched lines, just to indicate boundaries. I am trying to simulate a 2D case with the top and bottom walls moving and the left and right boundaries periodic.
Can you please tell me in terms of the notations that you used in the figure, how may I apply the pressure and velocity boundary conditions? I have been stuck at this problem for quite long. Last edited by Divyaprakash; August 21, 2022 at 10:38. Reason: More details 

August 21, 2022, 12:30 

#6  
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Filippo Maria Denaro
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Quote:
The pressure notation you wrote is correct. The uvelocity periodicity needs to set u1=u6. 

August 21, 2022, 13:27 

#7 
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Divyaprakash
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August 21, 2022, 13:31 

#8 
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Filippo Maria Denaro
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You have to compute the equation for one of them


August 21, 2022, 13:44 

#9 
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Divyaprakash
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Thank you so much. I'll try to implement it. Just one more question. I have seen in many places the BC being implemented as follows. how to implement periodic bc on a staggered grid Would this work too? Based on above I had implemented the BC in my original figure. 

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periodic bc, staggered grid 
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