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

  • Andreas Prohl

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

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Andreas Prohl
    Pages 1-16
  3. Andreas Prohl
    Pages 17-23
  4. Andreas Prohl
    Pages 91-103
  5. Andreas Prohl
    Pages 105-140
  6. Andreas Prohl
    Pages 141-177
  7. Andreas Prohl
    Pages 179-205
  8. Andreas Prohl
    Pages 207-232
  9. Andreas Prohl
    Pages 283-288
  10. Back Matter
    Pages 289-294

About this book

Introduction

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

Keywords

Introduction Navier-Stokes equation Penalty Method Preliminareis Pressure Stabilization Method stabilization structure

Authors and affiliations

  • Andreas Prohl
    • 1
  1. 1.University of MinnesotaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-663-11171-9
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 1997
  • Publisher Name Vieweg+Teubner Verlag, Wiesbaden
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-519-02723-2
  • Online ISBN 978-3-663-11171-9
  • Series Print ISSN 1616-2994
  • About this book