Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations

Michael Griebel () and Frank Koster ()
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Michael Griebel: Universität Bonn, Institut für Angewandte Mathematik
Frank Koster: Universität Bonn, Institut für Angewandte Mathematik

A chapter in Advances in Mathematical Fluid Mechanics, 2000, pp 67-118 from Springer

Abstract: Abstract In this paper we describe adaptive wavelet-based solvers for the Navier-Stokes equations. Our approach employs a Petrov-Galerkin scheme with tensor products of Interpolet wavelets as ansatz functions. We present the fundamental algorithms for the adaptive evaluation of differential operators and non-linear terms. Furthermore, a simple but efficient preconditioning technique for the resulting linear systems is introduced. For the Navier-Stokes equations a Chorin-type projection method with a stabilized pressure discretization is used. Numerical examples demonstrate the efficiency of our approach.

Keywords: Wavelet Transform; Sparse Grid; Lift Scheme; Adaptive Wavelet; Time Step Method (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57308-8_3

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DOI: 10.1007/978-3-642-57308-8_3

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