A nearly optimal preconditioner for the Navier-Stokes equations

We present a preconditioner for the linearized Navier-Stokes equations whic h is based on the combination of a fast transform approximation of an advec tion diffusion problem together with the recently introduced 'BFBT' precond itioner of Elman (SIAM Journal of Scientific Computing, 1999; 20:1299-1316) . The resulting preconditioner when combined with an appropriate Krylov sub space iteration method yields the solution in a number of iterations which appears to be independent of the Reynolds number provided a mesh Peclet num ber restriction holds, and depends only mildly on the mesh size. The precon ditioner is particularly appropriate for problems involving a primary flow direction. Copyright (C) 2001 John Wiley & Sons, Ltd.