Advances in Numerical Mathematics

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

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About this Textbook

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

Table of contents (11 chapters)

  • Introduction

    Prohl, Andreas

    Pages 1-16

  • Preliminaries

    Prohl, Andreas

    Pages 17-23

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

    Prohl, Andreas

    Pages 25-47

  • Nonstationary Quasi-Compressibility Methods

    Prohl, Andreas

    Pages 49-90

  • Mixed Quasi-Compressibility Methods

    Prohl, Andreas

    Pages 91-103

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-663-11171-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-519-02723-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations
Series Title
Advances in Numerical Mathematics
Copyright
1997
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Springer Fachmedien Wiesbaden
eBook ISBN
978-3-663-11171-9
DOI
10.1007/978-3-663-11171-9
Softcover ISBN
978-3-519-02723-2
Series ISSN
1616-2994
Edition Number
1
Number of Pages
XIV, 294
Number of Illustrations and Tables
29 b/w illustrations
Topics