Numerical Modeling of Solitary Wave Propagation Based on Boussinesq Wave Equations

Solitary wave is a two-dimensional and nonlinear gravity wave that was observed for the first time by John Scott Russell in 1894 during researches in a channel and First was named translating Wave. Modeling of solitary wave propagation in a long channel with constant depth is a suitable test to assess the stability and accuracy rate of governing equation’s dispersion and nonlinear terms recruitment and provide dynamic equilibrium. In this study, a numerical model based on the extended boussinesq equations derived by Beji and Nadaoka as a suitable system of governing equations based on standard Galerkin finite element method is presented. The time integration is performed using the semi-implicit method. Flat triangular elements with linear Interpolation functions are employed for the two horizontal velocity components and the water surface elevation. In order to evaluate the ability of one and two-dimensional numerical model, solitary wave propagation is simulated in a channel. The model is capable of giving satisfactory predictions in all cases.