can anybody suggest a logic for implementing periodic boundary conditions on Unstructured meshes for a turbine cascade flow. unstructured mesh has random numbering of cells.so how we can implement periodic boundary conditions ? thank you

The random numbering of cells makes implementation of BC a problem. You will have to define more variables to handle this. What I suggest is this: in the face data structure (or the edge data structure in case of 2D), define a TAG variable which will have values like BCupper, BClower or BCwall depending on the type of boundary the face lies on. While updating the values during the scheme keep a check if the current face is on boundary using TAG variable.

After each iteration you need to update values on the bdrys in accordance to periodic condition. You can traverse through all the faces, checking the TAG value and update BC accordingly.

On the matter of how to know if the face lies on boundary or not, it depends on the data structure implemented to store the mesh. In case of half face data structure, we check if the twinface of the face is NULL. Hope this helps...