If we use unstructured grids to do Large Eddy Simulation, how can we impose the periodic boundary conditions for certain flow field boundaries? Any suggestion?

(1). It is easier if you define the boundary mesh of the periodic condition by either a linear translation or a rotation. (2). In this way, the boundary itself will be identical to each other. (3). Then the condition itself simply says that the flow variable will be identical. That is PHI(translated, or rotated location)=PHI(corresponding original location). (4). So, the mesh distribution along the periodic boundary (or on the periodic boundary surface) must wait until the corresponding original boundary mesh is completed. In 2-D, you can only specify mesh distribution along the three edges (say inlet, exit, one of the periodic boundary). In 3-D , you can only specify 5 out of 6 boundary surfaces. The second periodic boundary mesh must be identical to the first one by translation of rotation.(5). You can also write your interpolation routines along the periodic boundary, if the meshes along the boundary are not identical to each other.

International Journal for Numerical Methods in Fluids Volume 18, Issue 12 30 June 1994 Pages 1153-1165

On the implementation of symmetric and antisymmetric periodic boundary conditions for incompressible flow

Segal, Guus; Vuik, Kees; Kassels, Kees