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Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations

  • Textbook
  • © 1997

Overview

Authors:
  1. Andreas Prohl

    1. University of Minnesota, USA

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Part of the book series: Advances in Numerical Mathematics (ANUM)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Introduction

    • Andreas Prohl
    Pages 1-16

  3. Preliminaries

    • Andreas Prohl
    Pages 17-23

  4. Stationary Quasi-Compressibility Methods: The Penalty Method and the Pressure Stabilization Method

    • Andreas Prohl
    Pages 25-47

  5. Nonstationary Quasi-Compressibility Methods

    • Andreas Prohl
    Pages 49-90

  6. Mixed Quasi-Compressibility Methods

    • Andreas Prohl
    Pages 91-103

  7. The Projection Scheme of Chorin

    • Andreas Prohl
    Pages 105-140

  8. The Projection Scheme of Van Kan

    • Andreas Prohl
    Pages 141-177

  9. Two Modified Chorin Schemes

    • Andreas Prohl
    Pages 179-205

  10. Multi-Component Schemes

    • Andreas Prohl
    Pages 207-232

  11. Time Discretization on Time-Grids with Structure — from Euler and Trapezoidal Method to Revised Projection Schemes

    • Andreas Prohl
    Pages 233-282

  12. Summary and Outlook

    • Andreas Prohl
    Pages 283-288

  13. Back Matter

    Pages 289-294
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Keywords

About this book

Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor

Authors and Affiliations

  • University of Minnesota, USA

    Andreas Prohl

Bibliographic Information

  • Book Title: Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations

  • Authors: Andreas Prohl

  • Series Title: Advances in Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-663-11171-9

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Fachmedien Wiesbaden 1997

  • Softcover ISBN: 978-3-519-02723-2Published: 01 January 1997

  • eBook ISBN: 978-3-663-11171-9Published: 11 November 2013

  • Series ISSN: 1616-2994

  • Edition Number: 1

  • Number of Pages: XIV, 294

  • Number of Illustrations: 29 b/w illustrations

  • Topics: Engineering, general

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