We present a preconditioner for the linearized Navier-Stokes equations which is based on the combination of a fast transform approximation of an advection di usion problem together with the recently introduced 'BFB T ' preconditioner of Elman (SIAM Journal of Scientiÿc 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 PÃ eclet number restriction holds, and depends only mildly on the mesh size. The preconditioner is particularly appropriate for problems involving a primary ow direction.
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