The numerical solution of Boussinesq equation for shallow water waves

Abstract

In the last many years for coastal regions the prediction of waves is still a big challenge for scientists. Many times, wave transformation harms the property and humans near coastal regions. To produce the exact numerical simulation of wave disturbances within bathymetry requires consideration of both dispersive and nonlinear waves in order to get physical effects. The current numerical model contains all these effects with variable bathymetry with Bossiness equation. Bossiness equation is used to determine the non-linear transformation of water surface waves in coastal region with the effects of shoaling, diffraction, reflection and refraction. Linear dispersion relations are determined in different form of the velocity variables. It improves the dispersion properties of the linear Boussinesq equations significantly, allowing them applicable to a larger water depth ranges. Nonlinear Boussinesq equations are used for describing the shallow water waves in intermediate water depth and dissemination of strong linear waves in surfing areas where breaking of the wave dominates. The Adams-Bashfourth (AB) predictor-corrector method is utilized to solve the non-linear Boussinesq equation. The validation of the numerical solution is compared with previous studies and experimental data. Further, the current numerical approach can be utilized for practical application in realistic situations.