Numerical model for shallow water waves using parabolic equation

One of the most influential in determining the characteristic of beach morphology is the information of the wave field in the area of consideration. The determination of beach morphology changeseither with hydraulic model or mathematical one are needed to overcome the problems of coastal processes. A mathematical model, which numerically solved was used to predict the water wave propagation in shallow water. One of the model is using parabolic equation proposed by Li (1997), which able to simulate the distribution of wave height in shallow water. The distribution of wave heights over parallel-contoured sloping beach with different given wave periods firstly was tested in comparison with experimental data by Sakai (1984), which was adopted from Diposaptono (2000) to observe the breaking wave, while the other cases were in comparison with data of laboratory of some existing experiments. The improvement by addition of energy dissipation term enhanced the capability of the existing model over some cases. The parallel-contoured sloping beach case revealed a good agreement in refraction phenomenon with the analytical solution by Snell\u27s Law, although the insertion of wave breaking did not perform very well for some wave periods, and the diftaction phenomenon did not yet included. The performance of elliptic shoal case proved the capability of the model over such complicated bathymetry. The circular shoal case proved that the parabolic model was satisfactory for wide angle situation. The entire combined phenomenon including wave breaking was covered up in a structural (jetty) case although a slightly discrepancy had occurred in the vicinity of the jetty. Keywords: refraction, dyfraction, finite-difference, parabolic equatio