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

• Published in: International journal for numerical methods in fluids 2003-12, Vol.43 (12), p.1407-1427
• Main Authors: Syamsudhuha, Silvester, David J.
• Format: Article
• Language: English
• Subjects: Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Krylov; Laminar flows; Laminar flows in cavities; multigrid; Navier-Stokes; Newton; non-linear; Physics
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.627

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 © 2003 John Wiley & Sons, Ltd.