Finite Element Modeling of Regular Waves by 1-D Madsen and Sorensen Extended Boussineq Equations

Parviz Ghadimi^1, , Amin Rahimzadeh¹, Mohammad H. Jabbari¹ and Rahim Zamanian²

¹Department of Marine Technology, Amirkabir University of Technology, Tehran, Iran

²International Campus – Mechanical Engineering Group, Amirkabir University of Technology, Tehran, Iran

Cite this paper:
Parviz Ghadimi, Amin Rahimzadeh, Mohammad H. Jabbari and Rahim Zamanian. Finite Element Modeling of Regular Waves by 1-D Madsen and Sorensen Extended Boussineq Equations. American Journal of Marine Science. 2013; 1(1):1-6. doi: 10.12691/marine-1-1-1

Abstract

In this paper, finite element modeling of one-dimensional extended Boussinesq equations derived by Madsen and Sorensen is presented for simulation of propagating regular waves. In order to spatially discretize the finite element equations, method of weighted residual Galerkin approach is used. Discretization of third-order derivative in momentum equation is performed by introducing of an auxiliary equation, which makes it possible to use linear finite element method. Adams-Bashforth-Moulton predictor-corrector method is used for time integration. Regular wave trains are simulated using the proposed numerical scheme. For validation of the developed code, the model is applied to several examples of wave propagation over the computational domain and the obtained results of the current computations are compared against the experimental measurements. In all cases, the proposed model has proved very suitable for simulating the propagation of wave indicating favorable agreements with experimental data.

Keywords:
Enhanced Boussinesq equations Galerkin finite element method Auxiliary equation

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