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Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations

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Advances in Mathematical Fluid Mechanics

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.

Research supported by the Deutsche Forschungsgemeinschaft, GR 1144/7-2.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115, Bonn, Germany

    Michael Griebel & Frank Koster

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  1. Michael Griebel
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  2. Frank Koster
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Editors and Affiliations

  1. Mathematical Institute, Charles University, Sokolovská 83, 18675, Prague 8, Czech Republic

    Josef Málek , Jindřich Nečas  & Mirko Rokyta ,  & 

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115-2888, USA

    Jindřich Nečas

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Griebel, M., Koster, F. (2000). Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations. In: Málek, J., Nečas, J., Rokyta, M. (eds) Advances in Mathematical Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57308-8_3

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  • DOI: https://doi.org/10.1007/978-3-642-57308-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67786-4

  • Online ISBN: 978-3-642-57308-8

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