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arXiv · 2210.11282

Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations

Animikh Biswas·Zachary Bradshaw·Michael Jolly
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Abstract

We introduce a localized version of the nudging data assimilation algorithm for the periodic 2D Navier-Stokes equations in which observations are confined (i.e., localized) to a window that moves across the entire domain along a predetermined path at a given speed. We prove that, if the movement is fast enough, then the algorithm perfectly synchronizes with a reference solution. The analysis suggests an informed scheme in which the subdomain moves according to a region where the error is dominant is optimal. Numerical simulations are presented that compare the efficacy of movement that follows a regular pattern, one guided by the dominant error, and one that is random.

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Animikh Biswas, Zachary Bradshaw, Michael Jolly. 2022-10-20. Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations. https://arxiv.org/abs/2210.11282

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