Non-hydrostatic models for wave propagation, breaking, and run-up

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.