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Thursday, Sep 12, 9:30 am in MTH 3206, University of Maryland, College Park

Preconditioning for the steady-state Navier-Stokes equations with low viscosity

Prof. Howard Elman

Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park

We introduce a preconditioning for the linearized Navier-Stokes equations with finite difference discretization that is effective when either the discretization mesh size or the viscosity approaches zero. We present a Fourier analysis for periodic boundary conditions showing that an idealized version of this method yields a system whose eigenvalues do not depend on the Reynolds number or the mesh size. Thus, Krylov subspace methods display convergence rates that are independent of these quantities. For other boundary conditions, experimental results indicate that convergence is still independent of the Reynolds number and depends only mildly on the mesh size.