Convergence of a Finite Difference Scheme for the Navier–Stokes Equations Using Vorticity Boundary Conditions

A rigorous convergence result is presented for a finite difference scheme for the Navier-Stokes equations which uses vorticity boundary conditions. The approximating scheme is based on the vorticity-stream function formulation of the Navier-Stokes equations. The no-slip boundary condition is satisfied approximately by using a boundary condition of vorticity creation type. Convergence with second-order accuracy in vorticity and velocity is established for general domains in two space dimensions. Generalization to three space dimensions is also considered.