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Volume 20, Issue 2
Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation

Sean Ingimarson, Monika Neda, Leo G. Rebholz, Jorge Reyes & An Vu

DOI: 10.4208/ijnam2023-1008

Int. J. Numer. Anal. Mod., 20 (2023), pp. 176-198.

Published online: 2023-01

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  • Abstract

We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular that the Gronwall constant’s exponential dependence on the Reynolds number is removed (for sufficiently smooth true solutions) or at least significantly reduced compared to the commonly used skew-symmetric formulation. We also show the method preserves momentum and angular momentum, and while it does not preserve energy it does admit an energy inequality. Several numerical tests show the advantages EMAC can have over other commonly used formulations of the nonlinearity. Additionally, we discuss extensions of the results to the usual Crank-Nicolson temporal discretization.

  • Keywords

Navier-Stokes equations, EMAC formulation, projection methods.

  • AMS Subject Headings

65M60, 76D05, 35Q30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-176, author = {Ingimarson , SeanNeda , MonikaRebholz , Leo G.Reyes , Jorge and Vu , An}, title = {Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {2}, pages = {176--198}, abstract = {

We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular that the Gronwall constant’s exponential dependence on the Reynolds number is removed (for sufficiently smooth true solutions) or at least significantly reduced compared to the commonly used skew-symmetric formulation. We also show the method preserves momentum and angular momentum, and while it does not preserve energy it does admit an energy inequality. Several numerical tests show the advantages EMAC can have over other commonly used formulations of the nonlinearity. Additionally, we discuss extensions of the results to the usual Crank-Nicolson temporal discretization.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1008}, url = {http://global-sci.org/intro/article_detail/ijnam/21353.html} }
TY - JOUR T1 - Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation AU - Ingimarson , Sean AU - Neda , Monika AU - Rebholz , Leo G. AU - Reyes , Jorge AU - Vu , An JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 176 EP - 198 PY - 2023 DA - 2023/01 SN - 20 DO - http://doi.org/10.4208/ijnam2023-1008 UR - https://global-sci.org/intro/article_detail/ijnam/21353.html KW - Navier-Stokes equations, EMAC formulation, projection methods. AB -

We consider a pressure correction temporal discretization for the incompressible Navier-Stokes equations in EMAC form. We prove stability and error estimates for the case of mixed finite element spatial discretization, and in particular that the Gronwall constant’s exponential dependence on the Reynolds number is removed (for sufficiently smooth true solutions) or at least significantly reduced compared to the commonly used skew-symmetric formulation. We also show the method preserves momentum and angular momentum, and while it does not preserve energy it does admit an energy inequality. Several numerical tests show the advantages EMAC can have over other commonly used formulations of the nonlinearity. Additionally, we discuss extensions of the results to the usual Crank-Nicolson temporal discretization.

Ingimarson , SeanNeda , MonikaRebholz , Leo G.Reyes , Jorge and Vu , An. (2023). Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation. International Journal of Numerical Analysis and Modeling. 20 (2). 176-198. doi:10.4208/ijnam2023-1008
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