Reconstruction of Finite Element Method Based on Spherical Hankel Shape Functions for Wave Propagation

This study examines the advantages of finite element methods for simulating the shallow water equations using spherical Hankel (SH) shape functions. To this end, the run-up and run-down of a solitary wave over a vegetated bed is simulated, representing tsunami wave propagation over wet and dry beds. A momentumconserving Taylor–Galerkin algorithm is developed, and the Hansen filter is implemented to eliminate numerical instabilities and spurious oscillations. The model is verified by comparing its results with experimental measurements, demonstrating that the finite element model can accurately capture wave propagation. Furthermore, the performance of the model employing SH shape functions is compared with that of the model using classical Lagrange shape functions through error metrics such as the Root Mean Square Error (RMSE). The results show that adopting SH shape functions can improve model accuracy while reducing the required number of elements, indicating their suitability as an alternative to classical Lagrange shape functions for solving shallow water problems.