A central-difference scheme for a pure stream function formulation of incompressible viscous flow

We present a numerical scheme for incompressible viscous flow, formulated as an equation for the stream function. The pure stream function formulation obviates the difficulty associated with vorticity boundary conditions. The resulting biharmonic equation is discretized with a compact scheme and solved with an algebraic multigrid solver. The advection of vorticity is implemented with a high-resolution central scheme that remains stable and accurate in the presence of large gradients. The accuracy and robustness of the method are demonstrated for high Reynolds number flows in a lid-driven cavity.