This study investigates wave transformation when a wave passes over circular cylinders. The numerical model is based on the Boussinesq equation developed by Nwogu (1993), expressed by velocity with arbitrary water depth. The numerical model utilizes the Fourth-Order Adams-Bashforth-Moulton Predictor-Corrector Scheme and is combined with a source function and absorbing boundary condition to enhance calculations stability and reduce the required processing time. The absorbing boundary condition is a sponge layer combined with a radiation boundary condition. Several numerical experiments are made to simulate wave transformations over circular cylinders. The interactions among incident wave, reflected wave and scattered waves due to cylinder are obvious in wave height distributions.
Recently, Boussinesq equation has become the most popular equation in the prediction of wave transformations. Boussinesq (1872) derived the original Boussinesq equations. Thereafter, numerous researchers improved and extended their applicability. Peregrine (1967) considered various water depth conditions to derive a shallow-water wave equation from small amplitude wave theory. He used a depth-averaged velocity as the dependent variable to derive the Boussinesq equation at a constant water depth. Witting (1984) included the free surface velocity as the dependent variable in a nonlinear depth-integrated momentum equation. Expanding velocity terms as Taylor series yields a onedimensional Boussinesq equation; however, the weakness of the equation is its limited applicability to constant-depth situations and the difficulty of applying it to two-dimensional cases. Conventional Boussinesq equations are limited to relatively shallow water. Hence, many studies have focused on extending them to deeper water. McCowan (1985, 1987) calculated nonlinear wave propagations in shallow water using the Boussinesq equation. The error between the derived phase velocity and the linear phase velocity was under 5%, and the relative depth of the water was extended to 0.2. improved the Boussinesq equation to enable it to be applied to relatively deeper water.
