[odellar]

Hi,

Since starting this thread I've come across Rempfer's 2006 paper 'On Boundary Conditions For Incompressible Navier-Stokes Problems' (http://appliedmechanicsreviews.asmed...icleid=1398501) which provides some interesting and helpful insights on using the dp/dn=0 (where n is the boundary normal unit vector) pressure boundary condition.

Section 3.1 is particularly useful, and essentially explains that dp/dn=0 CAN BE CORRECT in the setting of a projection method numerical procedure (where the 'pressure' is in fact not the physical, thermodynamic quantity, but instead an 'artificial' numerical parameter), however it is in general not true for the physical, continuous (in time and space) Navier-Stokes equations.

[murx]

Thanks, that sounds helpful. I don't have a license for this journal, but I'll try to get a hold of it.

[Blanco]

Originally Posted by murx

I agree that you can link the momentum equations to the continuity equations of course. However, you are implying that du/dx is not a function of y because du/dx(y=0)= 0. And that is a false conclusion. You cannot derive the dependence of du/dx on y by saying it is zero at y=0 and the derivative of 0 is 0. du/dx will definitely change with y unless you assume a developed flow in the given example, but that's obviously not the case we are discussing here.

Nope, in my very first post about this topic I considered a steady state flow between two flat plates, whose distance between each other h(x) is constant. I argued that (u,v)=f(y) because the geometry does not change moving along the x axis. Therefore du/dx = 0 because u=u(y). But obviously this was achieved considering a simplified case, e.g. a fully developed channel flow, very far from inlet or outlet section. I've always written about simplified cases (steady state, fully developed flow, fluid at rest, etc.) in my posts...

Originally Posted by murx

The momentum equations I cited were simplified, that means I already left out the terms that can be omitted due to the no-slip condition.

You can drop all convective terms and all derivates along the wall because of the no-slip condition. If we stick to the example of a flat wall along the x-direction, the momentum equation in y-direction can be written:

dp/dy = my*d2v/dy2

My comment was related to the equation in x-direction, which is:

v*du/dy+dp/dx=ny*d2u/dy2

and not

0= -dp/dx + ny (d2u/dy2) (x-direction)

because du/dy is NOT zero inside the flow...-> u=u(y)

Bye

[Blanco]

Originally Posted by odellar

Hi,

Since starting this thread I've come across Rempfer's 2006 paper 'On Boundary Conditions For Incompressible Navier-Stokes Problems' (http://appliedmechanicsreviews.asmed...icleid=1398501) which provides some interesting and helpful insights on using the dp/dn=0 (where n is the boundary normal unit vector) pressure boundary condition.

Section 3.1 is particularly useful, and essentially explains that dp/dn=0 CAN BE CORRECT in the setting of a projection method numerical procedure (where the 'pressure' is in fact not the physical, thermodynamic quantity, but instead an 'artificial' numerical parameter), however it is in general not true for the physical, continuous (in time and space) Navier-Stokes equations.

Thanks for the useful reference, I will try to get that paper.

I completely agree with the statement "the 'pressure' is in fact not the physical, thermodynamic quantity, but instead an 'artificial' numerical parameter". We know, indeed, that in incompressible N-S equations the pressure is NOT a physical quantity but it's just a so-called Lagrange multiplier. Therefore is lose all its physical background and it is just a "number" to be set in some way.
If I remember correctly, that's also the reason why we could have an infinite number of solution for a particular N-S incompressible problem, if we don't set the pressure. But the specified pressure simply "shift" the solution, without affecting the other quantities.

[murx]

Originally Posted by Blanco

Nope, in my very first post about this topic I considered a steady state flow between two flat plates, whose distance between each other h(x) is constant. I argued that (u,v)=f(y) because the geometry does not change moving along the x axis. Therefore du/dx = 0 because u=u(y). But obviously this was achieved considering a simplified case, e.g. a fully developed channel flow, very far from inlet or outlet section. I've always written about simplified cases (steady state, fully developed flow, fluid at rest, etc.) in my posts...

Hi Blanco, I did not mean to offend you and I appreciate your participation in this discussion. I mentioned in an earlier post that I agree with you on that for this simplified case. I just thought we were back to a more general CFD approach. However, you were of course right for the case you mentioned.

Originally Posted by Blanco

My comment was related to the equation in x-direction, which is:

v*du/dy+dp/dx=ny*d2u/dy2

and not

0= -dp/dx + ny (d2u/dy2) (x-direction)

because du/dy is NOT zero inside the flow...-> u=u(y)

Bye

Yes, du/dy is NOT zero inside the flow. I was stating the momentum equations for the wall, where we are looking for a pressure condition. Here du/dy is still not zero, but v is. And that's why you can drop the convective terms.

On another note, while looking for the article by Rempfer, I found this paper:
https://www.ljll.math.upmc.fr/pironn...s/GreshoOP.pdf
which is also interesting. This might be useful for somebody who is deeply involved in this topic, since the authors seem to disagree with Rempfer on one point.

[Blanco]

Originally Posted by murx

Hi Blanco, I did not mean to offend you and I appreciate your participation in this discussion. I mentioned in an earlier post that I agree with you on that for this simplified case. I just thought we were back to a more general CFD approach. However, you were of course right for the case you mentioned.

Hi Murx, don't worry, I'm not offended or hurt and I appreciate your comments too!
I just wanted to point out that I was still referring to simplified cases, for the sake of clarity, and that I don't have (unfortunately) any useful reference concerning more complicated cases (such as developing flow).

Originally Posted by murx

Yes, du/dy is NOT zero inside the flow. I was stating the momentum equations for the wall, where we are looking for a pressure condition. Here du/dy is still not zero, but v is. And that's why you can drop the convective terms.

On another note, while looking for the article by Rempfer, I found this paper:
https://www.ljll.math.upmc.fr/pironn...s/GreshoOP.pdf
which is also interesting. This might be useful for somebody who is deeply involved in this topic, since the authors seem to disagree with Rempfer on one point.

Ok, understood, I agree on that equation as long as we move "on the wall". Thanks for the reference on the pressure BC's for incompressible N-S equation.

[Munki]

Recently, i found a lecture in which the original question of this thread is discussed. This video (starting at 2:30min) might be helpful for future discussions:
https://www.youtube.com/watch?v=yWUc2D_WTMY