A Novel Finite Element Scheme of Nwogu Extended Boussinesq Equations to Predict Free Surface Elevation over Different Bathymetry of Beaches

摘要

In this study, free surface elevation is predicted by using a new finite element scheme. This numerical method solves a Nwogu Boussinesq equation system to simulate wave propagation in the complicated bathymetry of coastal regions. The numerical approach is based on a Galerkin finite element approach for spatial discretization and Adam-Bashforth-Moulton predictor-corrector strategy for time integration. Governing equations are rewritten in lower-order forms by introducing a novel form of auxiliary variable in order to make the application of the linear finite element method possible. Then, the stability of the suggested finite element schemes is studied using a theoretical analysis. For the validation of the present numerical method, five test cases are considered to show the capability of the numerical model for simulating the free surface elevation of wave propagation over different beach profiles where the nonlinear and dispersive effects are so important. The simulated results agree well with experimental observations.