A block preconditioning technique for the streamfunction-vorticity formulation of the Navier-Stokes equations

Iterative methods of Krylov-subspace type can be very effective solvers for matrix systems resulting from partial differential equations if appropriate preconditioning is employed. We describe and test block preconditioners based on a Schur complement approximation which uses a multigrid method for finite element approximations of the linearized incompressible Navier-Stokes equations in streamfunction and vorticity formulation. By using a Picard iteration, we use this technology to solve fully nonlinear Navier-Stokes problems. The solvers which result scale very well with problem parameters.