This article presents an optimized numerical model based on the interaction between shallow water waves and solid bodies, employing the finite element method to develop an enhanced propagation model governed by the Boussinesq equations. Through this refined approach, we achieve accurate simulations of elliptical cosine waves and subsequently investigate the phenomenon of nonlinear shallow water waves climbing over Homma-type artificial islands. Previous research on the climbing behavior of waves over Homma-type islands predominantly relied on linear wave theory. In contrast, this study utilizes the established nonlinear wave model to conduct a comparative analysis of the climbing behavior of elliptical cosine waves over Homma-type islands against outcomes derived from linear theory. Furthermore, we explore the influence of nonlinear wave intensity on the climbing behavior of shallow water waves over identical curved Homma-type islands, providing insights into the complexities of wave interactions in this context.
Sun et al. (Sun,) studied this question.