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Recovery of Turbulent Fluids With Continuous Data Assimilation: Enhancing Results Through Effective Observation and Assimilation
Abstract
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.
Subject Area
Applied Mathematics|Mathematics
Recommended Citation
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.
https://digitalcommons.unl.edu/dissertations/AAI30575047