Boussinesq-type Equation Formulated using the Weighted Taylor Series

Abstract

In this study, a Boussinesq equation was developed to model water waves. The equations were formulated using a weighted Taylor series, the Taylor series with weighted coefficients in the terms. The equation consists of the water surface elevation equation, the water particle velocity in the direction of the horizontal axis and vertical axis. The formulation of the continuity equation and the momentum equation is carried out on the same control volume with the same characteristics of particle velocity change. Thus, both equations have velocity variables with the same characteristics. The study obtained the Boussinesq equation that can be used with large wave amplitudes that are in line with those found in nature and can model shoaling and breaking well.