Fast Iterative Solution of Models of Incompressible Flow

We discuss new efficient algorithms for computing the numerical solution of the incompressible Navier-Stokes equations. We show that preconditioning algorithms that take advantage of the structure of the linearized equations can be combined with Krylov subspace methods to produce algorithms that are optimal with respect to discretization mesh size, largely insensitive to Reynolds numbers, and easily adapted to handle both steady and evolutionary problems. We also show the relation between these approaches and traditional methods derived from operator splittings, and we demonstrate the performance of the new methods in some practical settings.