Block preconditioners for the discrete incompressible Navier-Stokes equations

Howard C. Elman, David J. Silvester, Andrew J. Wathen

    Research output: Contribution to journalArticlepeer-review


    We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. For steady-state problems, we show that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. These characteristics are directly correlated with the convergence properties of iterative solvers, with convergence rates independent of mesh size and only mildly dependent on viscosity. For evolutionary problems, we show that implicit treatment of the time derivatives leads to systems for which convergence is essentially independent of viscosity. Copyright © 2002 John Wiley and Sons, Ltd.
    Original languageEnglish
    Pages (from-to)333-344
    Number of pages11
    JournalInternational Journal for Numerical Methods in Fluids
    Issue number3-4
    Publication statusPublished - 30 Sept 2002


    • Iterative algorithms
    • Navier-stokes equations
    • Preconditioning


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