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May 26, 2012, 21:11 
drichlet boundary condition for pressure

#1 
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Mehdi
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I plan to apply constant pressure boundary condition in outlet in collocated arrangement. unfortunately, I could not find any book or paper that explain how to apply it. does any one know how I do it or introduce a reference to me.
thanks in advance
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May 26, 2012, 23:41 

#2 
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Chris DeGroot
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At volumes adjacent to the outlet, just take the integration point value of the pressure on the outlet faces to be equal to the desired pressure. Seems too simple. Is there some specific issue with this BC you are struggling with?


May 27, 2012, 13:11 

#3 
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Mehdi
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thank you for your help but in simpler method, when momentum equation is descritized, value of pressure in cells appear and not in faces. so I guess I should assume a guest cells and value of these cells set constant pressure that I wanted to apply in outlet. but problem is I should have mass flux and velocity of these cells, because they are required for momentum equation. and I don't know how to deal with.
I hope I can explain the problem good.
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May 28, 2012, 09:14 

#4 
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Chris DeGroot
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Yes ghost cells is one way to do it. Blazek's book "Computational Fluid Dynamics" has a detailed description of this approach. So does Versteeg and Malalasekera.
In my code I simply place a "volume" with its centroid at the integration point and calculate any quantities adjacent to the boundaries implicitly using this value. Then I apply a condition to the boundary volume and absorb it into the interior. It is similar to the ghost cell approach, but I place the centroid of ghost cell right at the integration point and the cell doesn't have any volume. It is more like a ghost point I guess. For example at the volume adjacent to the boundary you will have an equation like AP*UP = AW*UW + AE*UE +B in one dimension where 'E' happens to be a boundary volume. Then at the boundary volume, for a Dirichlet condition, you can write AP*UP = B. where AP=1 and B is your specified value. Then the second equation can be absorbed into the first. Hopefully this made sense and applies to your situation. 

May 31, 2012, 20:15 

#5 
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Dear cdegroot
thank you for your answer. in fact, I think I could not find it out how to apply it. in collocated arrangement, for applying simpler method we have P and p' (correction part). the equation in two step with applying mometum interpolation (Rhie and Choe) in continuity equation: ap*p=Aw*Pw+AE*Pe+B ; b=Uf*dyvf*dx+ ... ap*p'=Aw*P'w+AE*P'e+B ; b=Uf*dyvf*dx+ ... when we want to apply constant pressure in boundary, P'=0 and P=cont. so we will (assume E is guest cell): ap*p=Aw*Pw+AE*C+B ; b=Uf*dyvf*dx+ ... ; C=value of pressure in boundary ap*p'=Aw*P'w+B ; b=Uf*dyvf*dx+ ... but we should calculate Ae in guest cell P equation that need geometric and flow character of the cell. in fact I dont know how to deal with this part.
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Best Regards; Mehdi Email: mb.pejvak[at]Gmail[dot]com Last edited by mb.pejvak; May 31, 2012 at 20:57. 

June 1, 2012, 00:35 

#6 
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Chris DeGroot
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If P is a ghost cell and it has a Dirichlet condition, it does not depend on neighbouring values, so Ae=Aw=0 in the ghost cell, true?
Last edited by cdegroot; June 1, 2012 at 00:37. Reason: Mistake 

June 1, 2012, 00:41 

#7 
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Chris DeGroot
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With regards to my last comment, it is possible I misunderstood you. Are you talking about the equation in the ghost cell or the equation at a volume adjacent to the boundary and you are having trouble figuring out AE in that equation?


June 1, 2012, 03:26 

#8 
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I might have a similar problem and I have attached a working code in this thread:
Boundary condition, incompressible colocated code Perhaps we can help each other? 

June 1, 2012, 04:43 

#9 
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Mehdi
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dear cdegroot
I think I can convey my purpose well. in fact my problem is applying Dirichlet pressure boundary condition and for velocities I applied Dirichlet boundary by set face of boundary cells as but in pressure equation we need to add a guest cell to apply constant pressure condition in outlet. so in continuity equation in simpler method, we should have AE in collocated arrangement. so I don't know how to find it? If i made mistake about that I'd really appreciate it if you correct me.
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June 1, 2012, 04:49 

#10 
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Mehdi
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dear Simbelmynė
I'll be happy if I can help you. but in fact, I have not worked FDM. and I don't know I can help you. I think Hoffman book is based on FDM. Have you ever taken look at it?
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June 1, 2012, 05:02 

#11 
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Dear mb.pejvak,
If you are using a structured mesh then I believe the two approaches are similar enough. I have a ton of different books where my favorites are the ones by C.A.J. Fletcher, and by Ferziger and Peric. I have managed to write working codes but I have some doubts about my boundary conditions (similar to what you describe, although I have solved it by using extrapolation from interior). Ferziger and Peric suggests using extrapolation of pressure at boundaries if a colocated setup is used where the control volumes extend to the boundary. 

June 1, 2012, 15:41 

#12  
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Chris DeGroot
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