Identifier

etd-06182010-150903

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

This dissertation is concerned with the applications of the Riemann-Hilbert problem on a hyperelliptic Riemann surface to problems on supercavitating flows of a liquid around objects. For a two-dimensional steady irrotational flow of liquid it is possible to introduce a complex potential w(z) which allows to apply the powerful methods of complex analysis to the solution of fluid mechanics problems. In this work problems on supercavitating flows of a liquid around one or two wedges have been stated. The Tulin single-spiral-vortex model is employed as a cavity closure condition. The flow domain is transformed into an auxiliary domain with known boundaries using the conformal mapping method. After that the problems have been reduced to the solution of Riemann-Hilbert problems on elliptic or hyperelliptic Riemann surfaces. The final step is to solve a system of transcendental equations which is accomplished numerically. The numerical results are presented. To the best of the author’s knowledge no numerical results were available for non-linear problems on supercavitating flows in multiply connected domains before.

Date

2010

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Antipov, Yuri

DOI

10.31390/gradschool_dissertations.3166

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