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

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  • Breckling, Sean
  • Fiordilino, Joseph
  • Reyes, Jorge
  • Shields, Sidney

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.

Suggested Citation

  • Breckling, Sean & Fiordilino, Joseph & Reyes, Jorge & Shields, Sidney, 2024. "A note on the long-time stability of pressure solutions to the 2D Navier Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    • Handle: RePEc:eee:apmaco:v:478:y:2024:i:c:s009630032400300x
    DOI: 10.1016/j.amc.2024.128839
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    1. Breckling, Sean & Shields, Sidney, 2019. "The long-time L2 and H1 stability of linearly extrapolated second-order time-stepping schemes for the 2D incompressible Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 263-279.
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