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dc.contributor.advisorVenkataramani, Shankar C.
dc.contributor.authorTao, Yuan
dc.creatorTao, Yuan
dc.date.accessioned2019-03-21T01:12:35Z
dc.date.available2019-03-21T01:12:35Z
dc.date.issued2019
dc.identifier.urihttp://hdl.handle.net/10150/631895
dc.description.abstractThere are many two-dimensional physical systems governed by potentials that satisfy the Laplace’s equation and Dirichlet boundary condition. An elegant approach is to set up the problem in the complex plane and use the freedom of conformal mappings to map the region and equation to different domains. In this paper, I focus on the problem of a uniform flow past two close-to-touching discs and the goal is to determine the potential and velocity field. The problem becomes very singular if the separation of the two discs gets smaller and it poses a challenge to both numerical and analytical solutions. Numerically, we come up with a new method that combines the method of images with conformal mappings and it performs better than all existing numerical methods in terms of efficiency and robustness. Analytically, we have a “limit solution” that matches the true solution uniformly and the “limit solution” is more accurate when the discs are closer. This solution also gives explicit relations between the behavior of the flow and the separation of the two discs.
dc.language.isoen
dc.publisherThe University of Arizona.
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
dc.titleThe Potential Exterior to Close-To-Touching Discs
dc.typetext
dc.typeElectronic Dissertation
thesis.degree.grantorUniversity of Arizona
thesis.degree.leveldoctoral
dc.contributor.committeememberGlickenstein, David C.
dc.contributor.committeememberKennedy, Tom
dc.contributor.committeememberSethuraman, Sunder
thesis.degree.disciplineGraduate College
thesis.degree.disciplineMathematics
thesis.degree.namePh.D.
refterms.dateFOA2019-03-21T01:12:35Z


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