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Periodic boundary conditions for velocity in Staggered grids

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Old   August 21, 2022, 05:45
Default 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 u-velocity.
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
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Old   August 21, 2022, 07:36
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Quote:
Originally Posted by Divyaprakash View Post
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 u-velocity.
The hatched lines indicate the periodic boundary.


Can someone confirm if this correct or correct them if wrong.
Why the x-velocity is differently colocated along x?
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Old   August 21, 2022, 09:37
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The x velocity is forward staggered.
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Old   August 21, 2022, 10:09
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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.
Attached Images
File Type: jpg 69008.jpg (39.0 KB, 10 views)
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Old   August 21, 2022, 10:36
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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
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Old   August 21, 2022, 12:30
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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.



The pressure notation you wrote is correct. The u-velocity periodicity needs to set u1=u6.
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Old   August 21, 2022, 13:27
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Originally Posted by FMDenaro View Post
The pressure notation you wrote is correct. The u-velocity periodicity needs to set u1=u6.



But u1 and u6 both are unknown. How can I specify one as another?
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Old   August 21, 2022, 13:31
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You have to compute the equation for one of them
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Old   August 21, 2022, 13:44
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Originally Posted by FMDenaro View Post
You have to compute the equation for one of them

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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