Continuous data assimilation for the 3D primitive equations of the ocean

Pei, Yuan

doi:10.3934/cpaa.2019032

Cited by 31 publications

(22 citation statements)

References 49 publications

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“…Since its inception in [3,4], the AOT algorithm has been the subject of much recent study in both analytical studies [1,5,6,8,9,10,11,13,15,16,21,22,23,24,25,26,27,28,29,31,30,32,34,35,36,37,39,41,44,45,48,49,50,53] and computational studies [2,12,14,18,20,33,38,40,42,43].…”

Section: Introductionmentioning

confidence: 99%

The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations

Franz,

Larios,

Victor

2021

Preprint

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We adapt a continuous data assimilation scheme, known as the Azouani-Olson-Titi (AOT) algorithm, to the case of moving observers for the 2D incompressible Navier-Stokes equations. We propose and test computationally several movement patterns (which we refer to as "the bleeps, the sweeps and the creeps"), as well as Lagrangian motion and combinations of these patterns, in comparison with static (i.e. non-moving) observers. In several cases, order-of-magnitude improvements in terms of the time-to-convergence are observed. We end with a discussion of possible applications to real-world data collection strategies that may lead to substantial improvements in predictive capabilities. "I'm having trouble with the radar, sir. [...] I've lost the bleeps, I've lost the sweeps, and I've lost the creeps." -Michael Winslow as Radar Technician in Spaceballs [51].

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Section: Introductionmentioning

confidence: 99%

The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations

Franz,

Larios,

Victor

2021

Preprint

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“…This algorithm works in tandem with a data assimilation method proposed in [4,5]. This algorithm, commonly referred to as the Azouani-Olson-Titi (AOT) or Continuous Data Assimilation (CDA) algorithm, has seen much recent work (see, e.g., [1,2,6,7,8,9,13,14,15,19,20,21,22,23,24,25,26,27,30,31,32,33,34,36,39,40,41,42,45,46,47,48,49,50,51,52,57,59,65] and the references therein.) Specifically, [4] considers the 2D Navier-Stokes system, written abstractly in the form The difficulty is that the initial data is unknown; however, it is assumed that the solution can be measured at certain points.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation

Larios¹,

Carlson²

2020

Preprint

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We rigorously prove the well-posedness of the formal sensitivity equations with respect to the Reynolds number corresponding to the 2D incompressible Navier-Stokes equations. Moreover, we do so by showing a sequence of difference quotients converges to the unique solution of the sensitivity equations for both the 2D Navier-Stokes equations and the related data assimilation equations, which utilize the continuous data assimilation algorithm proposed by Azouani, Olson, and Titi. As a result, this method of proof provides uniform bounds on difference quotients, demonstrating parameter recovery algorithms that change parameters as the system evolves will not blow-up. We also note that this appears to be the first such rigorous proof of global existence and uniqueness to strong or weak solutions to the sensitivity equations for the 2D Navier-Stokes equations (in the natural case of zero initial data), and that they can be obtained as a limit of difference quotients with respect to the Reynolds number. du dt = F Re (u).

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“…This seemingly minor change had profound impacts, and the authors of [5] were able to prove that using only sparse observations, the CDA algorithm applied to the 2D Navier-Stokes equations converges to the correct solution exponentially fast in time, independent of the choice initial data. This stimulated a large amount of recent research on the CDA algorithm; see, e.g., [3,6,7,10,11,13,17,18,19,20,21,22,27,31,30,35,40,41] and the references therein. The recent paper [15] showed that CDA can be effectively used for weather prediction, showing that it can indeed be a powerful tool on practical large scale problems.…”

mentioning

confidence: 99%

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

Gardner

Larios

Rebholz

et al. 2021

era

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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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Continuous data assimilation for the 3D primitive equations of the ocean

Cited by 31 publications

References 49 publications

The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations

The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations

Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation

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

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