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March 22, 2015, 13:34 
Periodic Boundary Condition Implementation

#1 
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John
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I am trying to implement a periodic boundary condition for unsteady flow over a wing. I am attempting to model the wing as being infinite by applying periodic boundary conditions.
If I understand things correctly, the condition should be that the pointwise flux on the two periodic surfaces should be the same. However, I am having trouble realizing how to implement this on an unstructured mesh where the two periodic surfaces do not have identical meshes. Would the proper approach be to interpolate the pointwise flux on the periodic surfaces? Thanks, John 

March 24, 2015, 10:42 

#2 
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Matt
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Can you explain your thought process of how a periodic boundary condition would approximate an infiite wing using periodic boundary conditions?
Is your wing circular? Periodic boundary conditions are usually used for rotating devices (like a wind turbine blade) so that you only have to model a slice of the pie. It sounds to me like you want to apply a symmetry boundary condition not periodic. The unsteady aspect would come into play through explicit (rather than implicit) analysis and (perhaps) unsteady freestream conditions. The implementation of that will depened greatly on your software. 

March 24, 2015, 11:03 

#3 
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John
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The particular case that I am interested in now is transitional flow over an airfoil specifically predicting transition with implicit LES. This needs to be done in 3D, since 2D CFD simulations do not model the 3D nature of the flow (vortex structures will behave entirely differently).
My mesh is essentially a 2D airfoil mesh extruded into the extra dimension for a certain distance, which I will call D. Currently, I have D=chord. I was thinking that a symmetry boundary condition would be incorrect to apply at the two end planes since this would force the flow to be parallel to the plane, which seems physically unrealistic. It seems like the flow would be better modeled by a periodic boundary at the end planes, which would permit the flow to have some flux through the end planes. That's my logic, although it may be entirely faulty. Am I thinking about this the wrong way? Thanks 

March 24, 2015, 11:16 

#4 
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Matt
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I think your logic is flawed. First of all, if you have an infinite wing your flow would be parallel at every spanwise station (minus local effects caused by turbulence). That is the nature of an infinite wing. Second, an infinite wing is an airfoil. That is the definition of an airfoil (at least in my aero text book). The only thing that differentiates a finite wing from infinite wing is that an infinte wing has constant circulation distribution. Is that the situation you are trying to model? If so, symmetry is definitely the way to go.
Probably should give it a span larger than the chord though, at least I would. Probably around 3c or 4c. Then you can ignore what is happening at the tips and focus on the middle 1c portion or so. That should capture whatever it is you are looking for in the flow. 

March 24, 2015, 11:23 

#5 
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John
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That's not entirely the case that I'm thinking about. I am interested in solving the unsteady LES flow, and the lengthscale of the vortical structures is not negligible compared to the extrusion distance, D.
I've attached a link picture of someone else's results for the case I am trying to run. In literature, it appears that this case was modeled with periodic boundary conditions. 

March 24, 2015, 12:40 

#6 
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Matt
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Got it, 'infinite wing' kind of implies a specific class of problem which sent me off on a tangent. Most likely you will need a translational periodic boundary, not just a periodic boundary. Usually when you hear 'periodic boundary' people are implying rotation. So that being said... you are probably on the right track.
However, from my experience with StarCCM+ you cannot have nonconformal mesh bewteen the two translational faces. What software are you using? You might have better luck taking this quesiton to one of the software user forums. 

March 24, 2015, 12:47 

#7 
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John
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Yeah, I haven't seen it done with a nonconformal mesh, either. However, I think you could do it if you interpolated the fluxes between the faces correctly.
I'm using my own code. It's an arbitrarily high order accurate DG solver in space and time with implicit timestepping and support for unstructured meshes. 

March 24, 2015, 12:52 

#8 
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Matt
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Oh. Well, I would say that your approach of point wise flux would probably work. It's a little beyond anything I have ever tried, especially in my own code. Good luck.
Maybe I am wrong about this, but I would think the point wise approach would still require conformal matching would it not? You might be able to map one side over, then use a nearest neighbor approach to interpolate from one set of points to the other (and viseversa). Maybe I am way off base on that, just a thought... 

March 24, 2015, 13:09 

#9 
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John
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Yeah, I'm not sure if it would work either. It would be easy if the faces were conformal.


March 24, 2015, 13:13 

#10 
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Matt
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If it's your own code, why not create a structured mesh? That would solve your problem woudn't it? Or is that more work than you want to take on?


March 24, 2015, 13:47 

#11 
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John
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I probably will just create an extruded mesh. I'm trying to keep the code as general as possible, but some things like this probably aren't worth the time and effort.


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