Efficient solution of the steady-state Navier-Stokes equations using a multigrid preconditioned Newton-Krylov method

An inexact Newton's method is used to solve the steady-state incompressible Navier-Stokes equations. The equations are discretized using a mixed finite element approximation. A new efficient preconditioning methodology introduced by Kay et al. (SIAM J. Sci. Comput., 2002; 24:237-256) is applied and its effectiveness in the context of a Newton linearization is investigated. The original strategy was introduced as a preconditioning methodology for discrete Oseen equations that arise from Picard linearization. Our new variant of the preconditioning strategy is constructed from building blocks consisting of two component multigrid cycles; a multigrid V-cycle for a scalar convection-diffusion operator; and a multigrid V-cycle for a pressure Poisson operator. We present numerical experiments showing that the convergence rate of the preconditioned GMRES is independent of the grid size and relatively insensitive to the Reynolds number. Copyright (C) 2003 John Wiley Sons, Ltd.