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 '$BFB^{T}$' 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