Finite-element model for modified Boussinesq equations. I: Model development

This paper and its companion paper describe the development of a finite-element model based on modified Boussinesq equations and the applications of the model to harbor resonance problems. This first of the two papers reports the model development and validations. A Galerkin finite-element method with linear elements is employed in the model. Auxiliary variables are introduced to remove the spatial third derivative terms in the governing equations, and an implicit predictor-corrector iterative scheme is used in the time integration. The treatments of various boundary conditions, including the perfect reflecting boundary with an irregular geometry, the absorbing (sponge layer) boundary, and the incident wave boundary, are described. Numerical results are obtained for several examples, and their accuracy is checked by comparing numerical results with either experimental data or analytical solutions.