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

Abstract

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.

References in corpus (6)

• Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone
• Continuous Data Assimilation with Stochastically Noisy Data
• Concurrent multi-parameter learning demonstrated on the Kuramoto-Sivashinsky equation
• Nonlinear Continuous Data Assimilation
• Continuous data assimilation and long-time accuracy in a $C^0$ interior penalty method for the Cahn-Hilliard equation
• An Efficient Continuous Data Assimilation Algorithm for the Sabra Shell Model of Turbulence

Cited by in corpus (1)

• Variational assimilation of sparse time-averaged data for efficient adjoint-based optimization of unsteady RANS simulations