Consistent Particle Method simulation of solitary wave impinging on and overtopping a seawall

Tsunamis are among the most destructive natural hazards and can cause massive damage to the coastal communities. This paper presents a first numerical study on the tsunami-like solitary wave impinging and overtopping based on the mesh-free Consistent Particle Method (CPM). The distinct feature of CPM is that it computes the spatial derivatives in a way consistent with the Taylor series expansion and hence achieves good numerical consistency and accuracy. This largely alleviates the spurious pressure fluctuation that is a key issue for the particle method. Validated by the benchmark example of solitary wave impact on a seawall, the CPM model is shown to be able to capture the highly deformed breaking wave and the impact pressure associated with wave impinging and overtopping. Using the numerical model, a parametric study of the effect of seawall cross-sectional geometry on the characteristics of wave overtopping is conducted. It is found that a higher water level can lead to much more intensive overtopping volume and kinetic energy of the overtopping flow, which implies that the coastal areas are at higher risk as the sea level rises. For the purpose of engineering interest, a simple and practical way to estimate the intensity of a real tsunami is presented in terms of the volume and energy of the bulge part of the incident wave.