Level-set finite element simulation of free-surface flow

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.