Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation

Improved Long Time Accuracy for Projection Methods for Navier-Stokes Equations Using EMAC Formulation

Year:    2023

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

International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam2023-1008

International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 2 : pp. 176–198

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Navier-Stokes equations EMAC formulation projection methods.

Author Details

Sean Ingimarson

Monika Neda

Leo G. Rebholz

Jorge Reyes

An Vu