Numerical investigation of free surface elevation and celerity of solitary waves passing over submerged trapezoidal breakwaters

摘要

In this paper, evolution of both free surface elevation and celerity of solitary wave interacting with submerged breakwater is numerically investigated by solving one-dimensional extended Boussinesq equations derived by Madsen and Sorensen. Spatial discretization is done by Galerkin finite element method (FEM) and for time integration, predictor-corrector method of Adams-Bashforth-Moulton is used. Propagation of solitary waves has been simulated over four different seabed slopes and computed results, compared against published work of Grilll et al. [17], indicate favorable agreement. Furthermore, a solitary wave with two different amplitudes is propagated over trapezoidal breakwater and evolution of free surface elevation is studied and validated. Finally, effects of side slopes of trapezoidal breakwater on wave characteristics has been investigated for 6 different slopes. It is clearly indicated that damping of the free surface elevation and celerity of the wave are strongly affected by the steepness of the breakwaters.