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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

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

Published online: 2009-04

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  • Abstract

Projection methods are efficient operator-splitting schemes to approximate solutions 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 for higher order projection methods, in the presence of only strong solutions of the limiting problem; in particular, we highlight concomitant difficulties in the construction process of accurate higher order schemes, such as limited regularities of the limiting solution, and a lack of accurate initial data for the pressure. Computational experiments are included to 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.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-338, author = {Erich Carelli and Andreas Prohl}, 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 to approximate solutions 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 for higher order projection methods, in the presence of only strong solutions of the limiting problem; in particular, we highlight concomitant difficulties in the construction process of accurate higher order schemes, such as limited regularities of the limiting solution, and a lack of accurate initial data for the pressure. Computational experiments are included to 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 AU - Erich Carelli & Andreas Prohl 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, Time discretization, Projection method. AB -

Projection methods are efficient operator-splitting schemes to approximate solutions 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 for higher order projection methods, in the presence of only strong solutions of the limiting problem; in particular, we highlight concomitant difficulties in the construction process of accurate higher order schemes, such as limited regularities of the limiting solution, and a lack of accurate initial data for the pressure. Computational experiments are included to compare the presented schemes, and illustrate the difficulties mentioned.

Erich Carelli and Andreas Prohl. (2009). 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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