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June 8, 2012, 05:50 
zeroGradient bc at the wall for pressure

#1 
Senior Member
Andrea Ferrari
Join Date: Dec 2010
Posts: 296
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Hi all,
i have a question regarding the zeroGradient boundary condition that is normally imposed for pressure at wall, when noslip velocity is imposed. This approximation is not always valid for example with complex curvilinear boundaries, at moving walls or when large pressure gradients exist towards the wall. However i have the impression that this is the standard bc if noslip is imposed for velocity. So my question is which is the physical/numerical origin of this bc? Is it linked to the predictorcorrector splitting? or are there any other reasons? best regards andrea 

June 9, 2012, 14:56 

#2 
Senior Member
A_R
Join Date: Jun 2009
Posts: 118
Rep Power: 9 
Dear Andrea
it is derived from navierstocks. firstly, the conduction terms go to zero by order of magnitude method comparing to convection terms, and then the convection terms go to zero because the velocity value is zero. therefore, the pressure gradient goes to zero. but based on physique concept, it shows that there is no flux through wall. but I, like many students, believe that it is not a real boundary condition and it can affect some part of calculated parameter such as drag. 

June 10, 2012, 03:54 

#3 
Senior Member
Andrea Ferrari
Join Date: Dec 2010
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Hi and thanks for reply
If you take NS (steadystate, incompressible, singlephase, mu constant) equations dot product with normal vector at the wall you will get this condition for normal component of pressure gradient dP/dn = (1/Re) (n \cdot \nabla^2 u) + (n \cdot f) , with f any body force. Now what i am saying is that put to zero the laplacian term in the above expression is not always valid. If the flow is parallel to the surface (poiseuille flow for example) it is easy to show that this term is zero and the right condition is dP/dn = 0, but if the flow is not parallel to the surface it is not correct, and if you have gravity for example you have at least account for hydrodtatic pressure. however my impression is that this condition is always used without taking care about the type of flow. best andrea 

June 10, 2012, 04:05 

#4 
Senior Member
A_R
Join Date: Jun 2009
Posts: 118
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Dear Andrea
you can find your answer in this pdf. http://www.ualberta.ca/~madhavan/zer...nt_at_wall.pdf but I said that it predicts pressure a bit more than usual. you can test it by a cylinder and check pressure force to real cases. the best form for bc is that Patankar says "if the velocity is known, the pressure does not need bc." or p`(wall)=0. but we cannot develop it in of. 

June 10, 2012, 04:33 

#5 
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Andrea Ferrari
Join Date: Dec 2010
Posts: 296
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I totally agree with .pdf, for poiseuille flow in a channel it is the correct condition for pressure, as i said in the previous post. and i also agree with the fact that if the velocity is known at the boundary you don't need at all a pressure bc (the problem comes from laplace equation that instead needs a boundary condition for pressure). So, if i have understood well, even if you don't need and it is not correct for every type of situations, dp/dn=0 is the condition that must be assigned if noslip is used for velocity? and if there's gravity or other body forces, which is the condition that has to be used?
best andrea 

June 15, 2012, 04:44 

#6 
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Albrecht vBoetticher
Join Date: Aug 2010
Location: Zürich, Swizerland
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Hi Andrea,
have you looked ad this thread: interFoam  mass conservation I see that in the PISO algorithm if the flux throug the wall is zero the second derivate of pressure orthogonal to the wall must be zero, too. I changed from zeroGradient to buoyantPressure at my slope with noslip bc for velocity, and the results look the same, but I use quite coarse meshes for shallow landslide simulations. 

June 15, 2012, 05:33 

#7 
Senior Member
Andrea Ferrari
Join Date: Dec 2010
Posts: 296
Rep Power: 8 
HI,
yes, i have seen that. I think that if g=0 buoyantPressure and zeroGradient give the same conditions and the correction when there's gravity is consistent to my second post. what i am saying is that there are many other situation in which zeroGradient for pressure might give wrong results and what i don't undesrtand is if this condition is a consequence of the PISO implementation. If the 2° derivate of pressure must be zero at the wall if the flux is zero, this does not mean necessarily that the first derivate is zero.. best andrea 

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