Document Type


Date of Degree


Degree Name

PhD (Doctor of Philosophy)

Degree In

Civil and Environmental Engineering

First Advisor

Lin, Ching-Long

Second Advisor

Weber, Larry J

First Committee Member

Lin, Ching-Long

Second Committee Member

Weber, Larry J

Third Committee Member

Carrica, Pablo M

Fourth Committee Member

Ettema, Robert

Fifth Committee Member

Xiao, Shaoping


This dissertation presents a study on the development of a numerical model aimed at simulating free surface flow, which still remains an active research area. Modeling these processes is very challenging since the interface between air and water is characterized by sharp discontinuities in fluid properties and flow characteristics due to different densities, viscosities, surface tension and consequent discontinuities in spatial gradients of velocity and pressure. The constraint of incompressibility poses another difficulty on the efficient design of algorithms. Recently, the level set method has emerged as a powerful tool for evolving interfaces in computational science and engineering for a wide range of applications while the finite element method has been long known for its geometrical flexibility. An effort to combine these two methods is made in this study. Several benchmark problems are used for the test of the developed code in view of temporal and spatial accuracy. Then, the capability and efficiency of the model are extended with advanced turbulence models and parallel algorithm. The model is applied to problems of practical importance in hydraulics, including hydraulic jump under a sluice gate and the design of spillways for fish migration. The main focus is on the capturing of free surface and identifying and understanding of the vortical structures and nonhydrostatic pressure distribution. The model has proved to be very effective for these purpose. The new technique dealing with air-water interface in a more physically accurate way is introduced for future development and the new method is applied to the problems of static equilibrium for validation.


level set method, finite element method, free surface, spillway, dam break


x, 162 pages


Includes bibliographical references (pages 153-162).


Copyright 2007 Haegyun Lee