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

Author:
Päivo Simson

Tallinn University of Technology, Estonia

Promoters:
Pearu Peterson, PhD

Institute of Cybernetics at Tallinn Technical University, Estonia

Opponents:
Jaan Kalda, PhD.

Institute of Cybernetics at Tallinn Technical University, Estonia

Abstract:

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.

Place/venue:

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

Softcopy:

http://cens.ioc.ee/~pearu/theses/paivo_msc_2011.pdf (6.1MB).