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

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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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

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

• University of Minnesota, USA

  Andreas Prohl

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