Iterative solution of the stream function-vorticity formulation of the stokes problem, applications to the numerical simulation of incompressible viscous flow

We discuss in this article the numerical solution of the Stokes problem in its stream function-vorticity formulation by a preconditioned conjugate gradient algorithm. The preconditioning operator is constructed via Fourier analysis and leads to an algorithm which is naturally suited to finite element implementations. In the article we also discuss the application of this new Stokes/biharmonic solver to the numerical solution of the Navier-Stokes equations modelling unsteady incompressible viscous flow.