Title page for ETD etd-06182010-150903


Type of Document Dissertation
Author Zemlyanova, Anna
URN etd-06182010-150903
Title Method of Riemann Surfaces in Modelling of Cavitating Flow
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Antipov, Yuri Committee Chair
Baldridge, Scott Committee Member
Hoffman, Jerome Committee Member
Lipton, Robert Committee Member
Tom, Michael Committee Member
Adrian, Donald Dean's Representative
Keywords
  • cavitation
  • Riemann surface
  • Riemann-Hilbert problem
  • conformal mapping
Date of Defense 2010-04-16
Availability unrestricted
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 authorís knowledge no numerical results were available for non-linear problems on supercavitating flows in multiply connected domains before.

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