Volume 27, Issue 2-3
A Note on Pressure Approximation of First and Higher Order Projection Schemes for the Nonstationary Incompressible Navier-Stokes Equations

Erich Carelli & Andreas Prohl

DOI:

J. Comp. Math., 27 (2009), pp. 338-347.

Published online: 2009-04

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  • Abstract

Projection methods are efficient operator-splitting schemes toapproximatesolutions of the incompressible Navier-Stokes equations.As a major drawback, they introduce spurious layers, both in space and time.In this work, we survey convergence results forhigher order projection methods, in the presence ofonly strong solutions of the limiting problem; in particular, wehighlight concomitantdifficulties in the construction process of accurate higher orderschemes, suchas limitedregularities of the limiting solution, and a lack of accurate initialdata for thepressure.Computational experiments are includedto compare the presented schemes, and illustrate the difficulties mentioned.

  • Keywords

Incompressible Navier-Stokes equation Time discretization Projection method

  • AMS Subject Headings

65N22 65F05 65M15 35K55 35Q30.

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COPYRIGHT: © Global Science Press

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@Article{JCM-27-338, author = {}, title = {A Note on Pressure Approximation of First and Higher Order Projection Schemes for the Nonstationary Incompressible Navier-Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {338--347}, abstract = {

Projection methods are efficient operator-splitting schemes toapproximatesolutions of the incompressible Navier-Stokes equations.As a major drawback, they introduce spurious layers, both in space and time.In this work, we survey convergence results forhigher order projection methods, in the presence ofonly strong solutions of the limiting problem; in particular, wehighlight concomitantdifficulties in the construction process of accurate higher orderschemes, suchas limitedregularities of the limiting solution, and a lack of accurate initialdata for thepressure.Computational experiments are includedto compare the presented schemes, and illustrate the difficulties mentioned.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8576.html} }
TY - JOUR T1 - A Note on Pressure Approximation of First and Higher Order Projection Schemes for the Nonstationary Incompressible Navier-Stokes Equations JO - Journal of Computational Mathematics VL - 2-3 SP - 338 EP - 347 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8576.html KW - Incompressible Navier-Stokes equation KW - Time discretization KW - Projection method AB -

Projection methods are efficient operator-splitting schemes toapproximatesolutions of the incompressible Navier-Stokes equations.As a major drawback, they introduce spurious layers, both in space and time.In this work, we survey convergence results forhigher order projection methods, in the presence ofonly strong solutions of the limiting problem; in particular, wehighlight concomitantdifficulties in the construction process of accurate higher orderschemes, suchas limitedregularities of the limiting solution, and a lack of accurate initialdata for thepressure.Computational experiments are includedto compare the presented schemes, and illustrate the difficulties mentioned.

Erich Carelli & Andreas Prohl. (2019). A Note on Pressure Approximation of First and Higher Order Projection Schemes for the Nonstationary Incompressible Navier-Stokes Equations. Journal of Computational Mathematics. 27 (2-3). 338-347. doi:
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