What is empty boundary condition?
What on earth does "empty" mean in OpenFOAM?

Daniel,
OpenFOAM does not have special machinery do deal with 2D domains. Therefore, a 2D mesh has twice as many faces on the front and back as it has cells. Therefore it is a good idea to do nothing for those faces and that is what "empty" does. Henrik 
Daniel,
the internal workings are not easy to explain in this context and by far offtopic for this thread. I suggest you have a look into Hrvoje's thesis. Physically there is no zcomponent in the equations of your 2D problem which brings us intuitively back to "nothing" and "empty". If it runs, cyclics will probably give you the right answer. Note that the above applies to 2D domain, not wedges (2.5D domain). Henrik 
Okay, I have found if cyclic bc is used, nonuniform values come out in that patch, how did they come if no zcomponent in the equations, no interfaces in zdirection. But it seems these values are very small.
Another concern is about mapFields, if I have a 2D result in hand with empty patch for frontAndBack, and I want to map it to a finer grid with gridding in zdirection, cyclic bc for frontAndBack, can I directly change the empty to cyclic and then do mapFields? Anyway, I tried this, and everything is okay so far. 
Daniel,
I understand you want to map the results obtained on a coarse 2D grid onto a finer 2D grid. mapFields will map the cell values from one grid to another. The empty patches remain empty  There are just more empty faces in the fine grid. So what exactly concerns you? Henrik 
No, I mean map from a coarse 2D grid result onto a finer 3D grid, from 2DRANS to 3DRANS to LES. Is the procedure okay??

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