Finite Element Solution of Linear Waves on a Sloping Bottom Boundary

Abstract

A new, finite-element solution of linear water waves, which can be applied to a nonvertical bottom boundary, is introduced in this study. The present solution can be applied to regions in which the water depth gradually approaches zero, such as coastlines. To obtain this solution, the entire domain is divided into three subregions. In the up-wave and down-wave subregions, analytical solutions are used. In the middle region, which occupies most computational domain, the standard Galerkin finite-element method is applied. The introduced numerical method is compared with an analytical solution to show its validity.