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Recovery of Turbulent Fluids With Continuous Data Assimilation: Enhancing Results Through Effective Observation and Assimilation
In this thesis, I investigate a computationally efficient algorithm for data assimilation in recovering solutions to turbulent fluids, specifically the Azouani-Olson-Titi continuous data assimilation algorithm. I present modifications aimed at enhancing the algorithm’s performance while maintaining its relevance to physically realistic use cases. I apply the algorithm to a range of dissipative partial differential equations, from the 1D Allen-Cahn equation to the 2D and 3D Navier-Stokes equations, and a high-resolution realistic ocean model. A key focus of my research is the role of observational data in convergence rates, examining optimal strategies for gathering observations and effectively assimilating sparse observational data. Through my analysis, I provide insights into improving turbulent fluid recovery by leveraging the algorithm’s potential in various scenarios and identifying the crucial factors that contribute to its success.
Victor, Collin, "Recovery of Turbulent Fluids With Continuous Data Assimilation: Enhancing Results Through Effective Observation and Assimilation" (2023). ETD collection for University of Nebraska - Lincoln. AAI30575047.