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Using Data to Accurately and Efficiently Model Turbulent Flows: Data Assimilation & Parameter Recovery

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FKT - Frontiers in kinetic theory: connecting microscopic to macroscopic scales - KineCon 2022

One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. An emerging approach to data assimilation known as the Azouani-Olson-Titi (AOT) algorithm introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. The solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data. In this talk, we present our tests on the robustness, improvements, and implementation of the AOT algorithm, as well as generate new ideas based off these investigations. First, we discuss the application of the AOT algorithm to the 2D NSE with an incorrect parameter and prove it still converges to the correct solution up to an error determined by the error in the parameters. This led to the development of a simple parameter recovery algorithm, whose convergence we recently proved in the setting of the Lorenz equations. It has now been proven by a co-author for the full 2D NSE , presenting new insights into the equation itself.  We may also discuss applications to climate models.      

This talk is part of the Isaac Newton Institute Seminar Series series.

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