A nearly optimal preconditioner for the Navier-Stokes equations

We present a preconditioner for the linearised Navier-Stokes equations which is based on the combination of a fast transform approximation of an advection diiusion problem together with the recently introduced`BF B T ' resulting preconditioner when combined with an appropriate Krylov subspace iteration method yields the solution in a number of iterations which appears to be independent of the Reynolds number provided a mesh P eclet number restriction holds, and depends only mildly on the mesh size. The preconditioner is particularly appropriate for problems involving a primary ow direction.