The method on dealing with velocity in static pressure outlet boundary condition

mona.li · September 29, 2017, 12:44

Dear everyone,
I am using CFX to do a transient simulation for a 3D incompressible flow.The outlet boundary condition I have chosen is to specify the static pressure.Now, what confuses me most is that:
From my point of view, a total of three scalar boundary conditions should be prescribed for each boundary in 3D incompressible problems to ensure the well-posedness of these ellipse equations (like specifying the values of three velocity components or the static pressure plus the tangential component of the velocity, etc).
Based on this understanding, just specifying the static pressure for the outlet boundary seems can cause an ill-posed problem, which, however, is what we do in cfx-pre for pressure outlet boundary condition. So I think there must be some special treatments for velocity at the outlet boundary in CFX codes (maybe some default exploration methods) playing as the other boundary conditions. But so far I have not found anything on it.
So, here I hope to know if there is something wrong with my above understanding and how exactly CFX deals with the velocity when using the static pressure outlet condition for incompressible flow?
Looking forward to your help! Thank you very much!!!

Opaque · September 29, 2017, 14:30

Boundary conditions at outlets are not independent of boundary conditions at inlets for incompressible flows, i.e. there is compatibility boundary conditions requirement.

Let's say the mode is a pipe, one inlet and one outlet. Inlet boundary condition is specified mass flow normal to the inlet. The mass flow is fixed at the inlet and for the outlet as well; therefore, the outlet condition cannot support a velocity condition by any means unless it exactly satisfies continuity within round off of the discretization being used. Otherwise, the system is ill-posed and it would never converge to round off.

Just more food for thought.

mona.li · September 30, 2017, 01:33

Thank you for your help! But I still have some confusion on this issue:

First, here for my simulation of the boundary layer flow, which is on a rectangle computational domain, all the boundary conditions I have chosen are: velocity for the inlet and upper boundary condition, no-slipping for the wall, static pressure for the outlet while periodic boundary condition for the others. For this setup, I think, since the velocity for the outlet is not specified, it will not cause that kind of ill-posed issues as you have said.

Yet despite all that, can this setup, i.e. just specifying static pressure for the outlet, be well-posed or just "enough" to gain a unique solution?

In terms of this, a paper I recently read shows that, for 3D simulation, the boundary conditions that the static pressure together with velocity components v and w are all specified at the outlet while the other boundarys are specifed with all the velocity components u,v,w can lead to a well-posed system and a unique solution. Here, although the v and w is specified at the outlet, it will not cause problems for the continuity for they are the tangential components which do not contribute to the mass flow.

Then, compared to this setup, it seems obvious that without the specified v amd w for the outlet, the resultant system will lack of constraints and cannot give a unique solution.

Therefore, I infer that there must be some default treatments in CFX for the velocity at the outlet boundary to make the system a well-posed one, but I cannot find what they exactly are?

September 29, 2017, 12:44	The method on dealing with velocity in static pressure outlet boundary condition	#1
mona.li New Member mona Li Join Date: Sep 2017 Posts: 8 Rep Power: 8	Dear everyone, I am using CFX to do a transient simulation for a 3D incompressible flow.The outlet boundary condition I have chosen is to specify the static pressure.Now, what confuses me most is that: From my point of view, a total of three scalar boundary conditions should be prescribed for each boundary in 3D incompressible problems to ensure the well-posedness of these ellipse equations (like specifying the values of three velocity components or the static pressure plus the tangential component of the velocity, etc). Based on this understanding, just specifying the static pressure for the outlet boundary seems can cause an ill-posed problem, which, however, is what we do in cfx-pre for pressure outlet boundary condition. So I think there must be some special treatments for velocity at the outlet boundary in CFX codes (maybe some default exploration methods) playing as the other boundary conditions. But so far I have not found anything on it. So, here I hope to know if there is something wrong with my above understanding and how exactly CFX deals with the velocity when using the static pressure outlet condition for incompressible flow? Looking forward to your help! Thank you very much!!!

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September 29, 2017, 14:30		#2
Opaque Senior Member Join Date: Jun 2009 Posts: 1,803 Rep Power: 32	Boundary conditions at outlets are not independent of boundary conditions at inlets for incompressible flows, i.e. there is compatibility boundary conditions requirement. Let's say the mode is a pipe, one inlet and one outlet. Inlet boundary condition is specified mass flow normal to the inlet. The mass flow is fixed at the inlet and for the outlet as well; therefore, the outlet condition cannot support a velocity condition by any means unless it exactly satisfies continuity within round off of the discretization being used. Otherwise, the system is ill-posed and it would never converge to round off. Just more food for thought.

September 30, 2017, 01:33		#3
mona.li New Member mona Li Join Date: Sep 2017 Posts: 8 Rep Power: 8	Thank you for your help! But I still have some confusion on this issue: First, here for my simulation of the boundary layer flow, which is on a rectangle computational domain, all the boundary conditions I have chosen are: velocity for the inlet and upper boundary condition, no-slipping for the wall, static pressure for the outlet while periodic boundary condition for the others. For this setup, I think, since the velocity for the outlet is not specified, it will not cause that kind of ill-posed issues as you have said. Yet despite all that, can this setup, i.e. just specifying static pressure for the outlet, be well-posed or just "enough" to gain a unique solution? In terms of this, a paper I recently read shows that, for 3D simulation, the boundary conditions that the static pressure together with velocity components v and w are all specified at the outlet while the other boundarys are specifed with all the velocity components u,v,w can lead to a well-posed system and a unique solution. Here, although the v and w is specified at the outlet, it will not cause problems for the continuity for they are the tangential components which do not contribute to the mass flow. Then, compared to this setup, it seems obvious that without the specified v amd w for the outlet, the resultant system will lack of constraints and cannot give a unique solution. Therefore, I infer that there must be some default treatments in CFX for the velocity at the outlet boundary to make the system a well-posed one, but I cannot find what they exactly are?