AN EFFICIENT ITERATIVE METHOD FOR THE GENERALIZED STOKES PROBLEM

The generalized Stokes problem, which arises frequently in the simulat ion of time-dependent Navier-Stokes equations for incompressible fluid flow, gives rise to symmetric linear systems of equations. These syst ems are indefinite due to a set of linear constraints on the velocity, causing difficulty for most preconditioners and iterative methods. Th is paper presents a novel method to obtain a preconditioned linear sys tem from the original one which is then solved by an iterative method. This new method generates a basis for the velocity space and solves a reduced system which is symmetric and positive definite. Numerical ex periments indicating superior convergence compared to existing methods are presented. A natural extension of this method to elliptic problem s is also proposed, along with theoretical bounds on the rate of conve rgence, and results of experiments demonstrating robust and effective preconditioning.