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

Parviz Ghadimi,Mohammad Chekab,Amin Rahimzadeh

doi:10.1260/1750-9548.9.1.61

Parviz Ghadimi, Mohammad Chekab + Show 1 more

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https://doi.org/10.1260/1750-9548.9.1.61

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Abstract

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 Grilli 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.

Highlights

In most of the engineering problems, mathematical models cannot be solved analytically and require a numerical solution
4.2 PROPAGATION OF SOLITARY WAVE OVER A SUBMERGED BREAKWATER propagation of solitary waves over submerged trapezoidal breakwaters is considered using one dimensional Boussinesq equations derived by Madsen and Sorensen
By using linear Galerkin finite element method, spatial domain has been discretized by subdivision of the continuum into non-overlapping elements

Summary

Introduction

In most of the engineering problems, mathematical models cannot be solved analytically and require a numerical solution. With an increase in computational technologies and because of the advantages of numerical methods over analytical solutions, many numerical models and software programs have been developed for various engineering practices. This is in addition to the fact that, more realistic models of greater complexity, can be investigated using numerical techniques. This makes it possible to predict the course of an event before it occurs, or to study various aspects of an event mathematically without running expensive and time-consuming experiments.

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