In this study a numerical model was developed to simulate the wave run-up and overtopping as a solitary wave attacks a seawall near the beach. The hybrid particle level set method (Enright et al., 2002) was applied to capture the evolution of complex free surface, such as wave run-up or overtopping near a seawall. The traditional level set method (Osher and Sethian, 1988) and the innovative immersed boundary method (Lin et al., 2010) were combined to mimic the arbitrary solid boundary and its corresponding boundary conditions on a fixed Cartesian grid system. To verify the accuracy of the presented numerical model, run-up of a solitary wave on a slope bed was simulated, and the numerical results were compared with the experimental data. After having demonstrated the accuracy of the numerical scheme, the developed computer code was applied to study the run-up and overtopping of a solitary wave near a seawall located at the east coast of Taiwan.
In recent years, the rising sea levels due to global warming has caused widespread concern about the coastal flooding problem. To economically determine the crest elevation of the coastal structure, such as a seawall, coastal engineers need to know the maximum wave run-up height or the water amount resulted from the wave overtopping around a seawall. In coastal engineering, the solitary wave is often used to represent certain characteristics of tsunamis, storm surges, and other long waves. Hence, it becomes very important to understand the characteristics of run-up and overtopping of a solitary wave near a seawall. Synolakis (1987) developed both linear and nonlinear wave theories to predict the maximum run-up height of non-breaking solitary waves on a plane beach with a slope of 1:19.85 and the asymptotic results were compared with experimental data.