A nearly optimal preconditioner for the Navier-Stokes equations

We present a preconditioner for the linearized Navier-Stokes equations which is based on the combination of a fast transform approximation of an advection diffusion problem together with the recently introduced 'BFBT' preconditioner of Elman (SIAM Journal of Scientific Computing, 1999; 20:1299-1316). The 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 Peclet number restriction holds, and depends only mildly on the mesh size. The preconditioner is particularly appropriate for problems involving a primary flow direction. Copyright (C) 2001 John Wiley & Sons, Ltd.