The boundaries of a periodic interface are physically separated in space but can be mapped from one to the other through some constant rotation and/or translation. Thus, upon completion of the intersection of the boundaries, there should be no remaining surface area. In other words, the perimeter of one boundary should be coincident with the transformed perimeter of the periodic matching boundary. Furthermore, the periodic interface represents a cyclic repeat of information across the boundaries. Fluxes that cross one boundary are transformed and applied to the other.
The figures below shows examples of a periodic interfaces as applied to translational and rotational geometries. Only a repeating mesh segment is used in this case, usually belonging to the same region. The dotted black line in each case represents the location of the periodic interface boundaries, which enable the entire repeating geometry to be replicated for the simulation.