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.