Free surface problem with variable bottom and its solution using conformal mapping technique

A thesis accepted by Tallinn University of Technology for the Degree of Master of Science

Päivo Simson

Tallinn University of Technology, Estonia

Pearu Peterson, PhD

Institute of Cybernetics at Tallinn Technical University, Estonia

Jaan Kalda, PhD.

Institute of Cybernetics at Tallinn Technical University, Estonia


The aim of this thesis was to develop a free surface problem solver for a layer of water over an uneven and time variable bottom profile. The mathematical theory of the free surface problem is formulated from the general equations of hydrody- namics using the assumption of potential flow in two dimensions. The method of solving the free surface problem uses the conformal mapping technique that allowed for the development of a numerical algorithm without introducing ad- ditional assumptions. As a result, a very efficient and accurate numerical method was developed that generalised a recently developed method from an even bot- tom to any arbitrary bottom profile. The conformal mapping technique was then generalised to a non-periodic boundary condition case. Mathematical aspects of the resulting theory are studied along with numerical examples.


The presentation of the thesis took place on June, 2011, at Tallinn University of Technology, Tallinn, Estonia.

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