The bleeps, the sweeps, and the creeps: Convergence rates for dynamic observer patterns via data assimilation for the 2D Navier-Stokes equations

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. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, we adapt the Azouani-Olson-Titi (AOT) algorithm, a continuous data assimilation scheme, to the case of moving observers for the 2D incompressible Navier-Stokes equations. We test different movement patterns and combinations, such as bleeps, sweeps, creeps, and Lagrangian motion, against static observers, and observe significant improvements in terms of the time-to-convergence in several cases. The article concludes with a discussion of the potential applications to real-world data collection strategies that may enhance predictive capabilities.