Study of a solitary wave interacting with a surface piercing square cylinder using a three-dimensional fully nonlinear model with grid-refinement technique on surface layers

This study introduces a three-dimensional fully nonlinear wave model, which solves the Laplace equation of the velocity potentials. A base-grid system is adopted in view of a transient curvilinear coordinate transformation along the vertical direction, while the horizontal coordinates remain uniformly distributed. To capture the variations of the free surface more accurately and effectively, the necessary denser grids can be specified within the vertically divided multi-plane layers near the free surface. In addition, fine grids can be arranged around the structures included in the flow domain. The model is first validated for the case of a solitary wave propagating along a narrow uniform-depth channel to investigate the level of solution improvement by the grid-refining technique. Smoothing is applied to remove the weak-fluctuation waves produced by the interpolation. In addition, the initial condition of the solitary wave is adjusted from the long-wave analytical solution to fit the presented fully nonlinear wave model. The results indicate that both efficiency and accuracy increase greatly by applying the fully nonlinear wave model as compared with a model using a uniformly non-refined grid system. Second, this model is applied to study a coastal problem related to a solitary wave diffracted by a surface-piercing square cylinder with or without a separating distance between the seabed and the bottom of the structure.