A nearly optimal preconditioner for the Navier-Stokes equations

Abstract

We present a preconditioner for the linearised Navier-Stokes equations which is based on the combination of fast transform approximation of an advection diffusion problem together with the recently introduced '' preconditioner of Elman (SIAM J. Sci. Comput. 20 pp. 1299-1316, 1999). 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.