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Mathematics > Numerical Analysis

arXiv:2006.07295 (math)
[Submitted on 12 Jun 2020]

Title:Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations

Authors:Matthew Gardner, Adam Larios, Leo G. Rebholz, Duygu Vargun, Camille Zerfas
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Abstract:We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove that under a typical finite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is applied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its effectiveness on an application problem of channel flow past a flat plate.
Comments: 28 pages, 8 figures, 2 tables
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2006.07295 [math.NA]
  (or arXiv:2006.07295v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2006.07295

Submission history

From: Duygu Vargun [view email]
[v1] Fri, 12 Jun 2020 16:24:04 UTC (4,690 KB)
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