A streamfunction-vorticity formulation of spatially periodic flows

In this paper we implement the spatially periodic boundary conditions in finite element solutions of the Navier-Stokes equations based on the streamfunction-vorticity formulation. Periodic boundary conditions are enforced at both inflow/outflow and lower/upper boundaries. As an example of application we consider the fluid flow, at two different Reynolds numbers, through an array of pin fins. The limiting assumption of symmetry conditions at the boundaries parallel to the main flow is shown to yield unphysical-looking configurations.