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Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations

Author: Andreas Prohl
Publisher: Stuttgart : B.G. Teubner, 1997.
Series: Wiley-Teubner series, advances in numerical mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Prohl, Andreas, 1968-
Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
(DLC) 98128478
(OCoLC)38164803
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andreas Prohl
ISBN: 9783663111719 3663111717
OCLC Number: 883381989
Description: 1 online resource (xii, 293 pages) : illustrations.
Contents: Preliminaries --
Stationary Quasi-Compressibility Methods: The Penalty Method and the Pressure Stabilization Method --
Nonstationary Quasi-Compressibility Methods --
Mixed Quasi-Compressibility Methods --
The Projection Scheme of Chorin --
The Projection Scheme of Van Kan --
Two Modified Chorin Schemes --
Multi-Component Schemes --
Time Discretization on Time-Grids with Structure --
from Euler and Trapezoidal Method to Revised Projection Schemes --
Summary and Outlook.
Series Title: Wiley-Teubner series, advances in numerical mathematics.
Responsibility: von Andreas Prohl.
More information:

Abstract:

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.

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