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

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, thei...

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Detalles Bibliográficos
Autor principal: Prohl, Andreas
Lenguaje:eng
Publicado: Springer 1997
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-663-11171-9
http://cds.cern.ch/record/1667168
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author Prohl, Andreas
author_facet Prohl, Andreas
author_sort Prohl, Andreas
collection CERN
description 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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spelling cern-16671682021-04-21T21:15:11Zdoi:10.1007/978-3-663-11171-9http://cds.cern.ch/record/1667168engProhl, AndreasProjection and quasi-compressibility methods for solving the incompressible Navier-Stokes equationsMathematical Physics and MathematicsProjection 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 ArborSpringeroai:cds.cern.ch:16671681997
spellingShingle Mathematical Physics and Mathematics
Prohl, Andreas
Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
title Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
title_full Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
title_fullStr Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
title_full_unstemmed Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
title_short Projection and quasi-compressibility methods for solving the incompressible Navier-Stokes equations
title_sort projection and quasi-compressibility methods for solving the incompressible navier-stokes equations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-663-11171-9
http://cds.cern.ch/record/1667168
work_keys_str_mv AT prohlandreas projectionandquasicompressibilitymethodsforsolvingtheincompressiblenavierstokesequations