Electronic Theses and Dissertations

Date of Award


Document Type


Degree Name

Ph.D. in Engineering Science


Mechanical Engineering

First Advisor

Yafei Jia

Second Advisor

Cristiane Q. Surbeck

Third Advisor

Yan Ding

Relational Format



This dissertation develops a series of non-hydrostatic pressure wave models based on the finite element free surface flow model, CCHE2D, for simulating propagation, breaking, and run-up of coastal wave processes. The first non-hydrostatic formulation presented in this dissertation directly introduces a non-hydrostatic pressure module into CCHE2D. An edge-based pressure allocation method is implemented, and a depth-integrated vertical momentum equation is introduced. The depth-integrated horizontal momentum equations are solved for a provisional velocity field, and then the non-hydrostatic pressure is obtained by satisfying the divergence-free velocity field condition, subsequently the velocity field is corrected by the non-hydrostatic pressure. Finally the free surface elevation is computed by the depth-integrated continuity equation. Next, a depth-integrated non-hydrostatic model for simulating nearshore wave processes is developed by solving a depth-integrated vertical momentum equation and the conservation form of the shallow water equations including extra non-hydrostatic pressure terms. A pressure projection method and the divergence-free velocity field condition are used together to solve the non-hydrostatic pressure. To resolve discontinuous flows, involving breaking waves and hydraulic jumps, a momentum conservation advection scheme is developed. In addition, the model is implemented with a simple but efficient wetting and drying algorithm to deal with the moving shoreline. The depth-integrated non-hydrostatic pressure models, which assume a linear distribution of the vertical pressure, have limitations in certain applications (e.g., propagation of highly dispersive waves). A multi-layer non-hydrostatic model is developed by adding more layers to the aforementioned second depth-integrated non-hydrostatic model. The multi-layer model is capable of resolving more realistic vertical flow structures and better representing the wave dynamics. Finally, a well validated depth-integrated non-hydrostatic model is applied to simulate a wide range of coastal wave processes. These numerical tests further evaluate the non-hydrostatic model from different aspects of engineering practice. In particular, they demonstrate the efficiency of non-hydrostatic models for coastal wave modeling, and they also reveal the great potential of non-hydrostatic models to simulate real-life coastal wave processes.


Emphasis: Computational Hydroscience



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