Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.733119
Title: A new transform approach to biharmonic boundary value problems in circular domains with applications to Stokes flows
Author: Louca, Elena
ISNI:       0000 0004 6496 1062
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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Abstract:
In this thesis, we present a new transform approach for solving biharmonic boundary value problems in two-dimensional polygonal and circular domains. Our approach provides a unified general approach to finding quasi-analytical solutions to a wide range of problems in Stokes flows and plane elasticity. We have chosen to analyze various Stokes flow problems in different geometries which have been solved using other techniques and present our transform approach to solve them. Our approach adapts mathematical ideas underlying the Unified transform method, also known as the Fokas method, due to Fokas and collaborators in recent years. We first consider Stokes flow problems in polygonal domains whose boundaries consist of straight line edges. We show how to solve problems in the half-plane subject to different boundary conditions along the real axis and we are able to retrieve analytical results found using other techniques. Next, we present our transform approach to solve for a flow past a periodic array of semi-infinite plates and for a periodic array of point singularities in a channel, followed by a brief discussion on how to systematically solve problems in more complex channel geometries. Next, we show how to solve problems in circular domains whose boundaries consist of a combination of straight line and circular edges. We analyze the problems of a flow past a semicircular ridge in the half-plane, a translating and rotating cylinder above a wall and a translating and rotating cylinder in a channel.
Supervisor: Crowdy, Darren Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.733119  DOI:
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