Boundary Condition: Antisymmetric periodicity
Has anyone come across boundary conditions in OpenFoam that impose antisymmetric periodicity …
An antisymmetric periodic boundary condition is just like periodic boundary conditions only swapped or mirrored … i.e. u(x, y)=u(x+L, ymaxy) v(x, y)=v(x+L, ymaxy) p(x, y)=p(x+L, ymaxy) rather then (pure periodicity): u(x, y)=u(x+L, y) v(x, y)=v(x+L, y) p(x, y)=p(x+L, y) here u =velocity in x, v = velocity in y, p=pressure, x and y coordinates where y[0, ymax]. The boundary condition is described in “ON THE IMPLEMENTATION OF SYMMETRIC AND ANTISYMMETRIC PERIODIC BOUNDARY CONDITIONS FOR INCOMPRESSIBLE FLOW” by GUUS SEGAL, KEES VUIK AND KEES KASSELS. 
Cyclic boundary conditions can be used in this case.

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yes they can, but then you need a cyclic geometry. Let me explain my case : I have a cubic domain which describe a porous media (liquid and solid). Only the liquid phase is meshed. Since the media is pretty random, the faces of my cube do not have the same mesh. To apply a cyclic boundary conditions (because that's what I want), I mirror the mesh in the x, y and finally z directions. I have then a cube 8 times bigger than my initial cube with all the same faces. I can then use cyclic boundary. But, I compute 7 times something I am not really interessted in. If I could apply antisymmetric periodicity, that would save a lot a time. Do you have any suggestions ? Fred. 
Hi Fredo,
What I do in this case: I had a thin layer of cells surrounding my domain. Like that I can impose cyclic boundary conditions. The two main problems when mirroring the domain: 1) it significantly increases the number of cells, 2) it biases the anisotropy (primordial for permeability estimation!). 
Hi Cyp,
thank you for this quick reply. Your solution seems very relevant ! Did you quantify the errors induced by this thin layer. My media is not very percolating so I fear that all the fluid goes through this thin layer. I will try and keep you updated. Fred. 
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