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Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations

In: Advances in Mathematical Fluid Mechanics

Author

Listed:
  • Michael Griebel

    (Universität Bonn, Institut für Angewandte Mathematik)

  • Frank Koster

    (Universität Bonn, Institut für Angewandte Mathematik)

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.

Suggested Citation

  • Michael Griebel & Frank Koster, 2000. "Adaptive Wavelet Solvers for the Unsteady Incompressible Navier-Stokes Equations," Springer Books, in: Josef Málek & Jindřich Nečas & Mirko Rokyta (ed.), Advances in Mathematical Fluid Mechanics, pages 67-118, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-57308-8_3
    DOI: 10.1007/978-3-642-57308-8_3
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