A nearly optimal preconditioner for the Navier–Stokes equations

Abstract 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 T ’ 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 Péclet number restriction holds, and depends only mildly on the mesh size. The preconditioner is particularly appropriate for problems involving a primary flow direction. Copyright © 2001 John Wiley & Sons, Ltd.