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arXiv · 2006.07295

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

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.

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Matthew Gardner, Adam Larios, Leo G. Rebholz, Duygu Vargun, Camille Zerfas. 2020-06-12. Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations. https://arxiv.org/abs/2006.07295

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