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

2022/10/20 by Biswas, Animikh, Bradshaw, Zachary, Jolly, Michael
#35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.11282

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.

Related

• A discrete data assimilation scheme for the solutions of the 2D Navier-Stokes equations and their statistics
• Data assimilation for the Navier-Stokes equations using local observables
• On the nudging approach to continuous data assimilation in the limit of infinite error feedback gain
• The second-best way to do sparse-in-time continuous data assimilation: Improving convergence rates for the 2D and 3D Navier-Stokes equations
• Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: The 2D Navier-Stokes equations paradigm