A note on the long-time stability of pressure solutions to the 2D Navier Stokes equations

Sean Breckling, Joseph Fiordilino, Jorge Reyes and Sidney Shields

Applied Mathematics and Computation, 2024, vol. 478, issue C

Abstract: Herein we investigate the long-time behavior of pressure solutions to the incompressible 2D Navier Stokes equations (NSE) when discretized by finite element methods (FEM) in space, and using the linearly-extrapolated backward differentiation formula (BDF2LE) in time. We consider two linearizations of the advective term in the momentum equations; the usual skew-symmetric formulation, as well as the velocity-vorticity (Lamb vector) formulation. We provide two brief analyses that demonstrate that these schemes permit uniform (in time) estimates of pressure solutions under the L2 norm, as well as a long-time numerical demonstration of the 2D lid-driven cavity.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:478:y:2024:i:c:s009630032400300x

DOI: 10.1016/j.amc.2024.128839

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