Finite element method for non-linear dispersive wave analysis

This report presents the finite element method for the analysis of the short wave problem expressed by the Boussinesq equation. The Boussinesq equation considers the effect of wave crest curvature. The standard Galerkin finite element method is employed for the spatial discretization using the triangular finite element based on the linear interpolation function. The combination of the explicit and the quasi-explicit schemes-- i.e., the explicit scheme for the continuum equation and the quasi-explicit scheme for the momentum equation--is employed for the discretization in time. To show the applicability of the present method to the practical problem, the simulation of wave propagation in one-dimensional and two-dimensional channel flows is carried out. The numerical results are in good agreement with the experimental results being. The practical example for Miyako Bay is presented.