Date of Award
Doctor of Philosophy (PhD)
Leo Rebholz, Committee Chair
Modeling fluid flow arises in many applications of science and engineering, including the design of aircrafts, prediction of weather, and oceanography. It is vital that these models are both computationally efficient and accurate. In order to obtain good results from these models, one must have accurate and complete initial and boundary conditions. In many real-world applications, these conditions may be unknown, only partially known, or contain error. In order to overcome the issue of unknown or incomplete initial conditions, mathematicians and scientists have been studying different ways to incorporate data into fluid flow models to improve accuracy and/or speed up convergence to the true solution.
In this thesis, we are studying one specific data assimilation technique to apply to finite element discretizations of fluid flow models, known as continuous data assimilation. Continuous data assimilation adds a penalty term to the differential equation to nudge coarse spatial scales of the algorithm solution to coarse spatial scales of the true solution (the data). We apply continuous data assimilation to different algorithms of fluid flow, and perform numerical analysis and tests of the algorithms.
Zerfas, Camille, "Numerical methods and analysis for continuous data assimilation in fluid models" (2019). All Dissertations. 2428.