Numerical modeling of wave attenuation at Uluwatu Beach Bali by submerged breakwaters using a new finite element...

This study develops a one-dimensional numerical scheme based on the finite element pair $P_1^{NC}-P_1$ for simulating wave attenuation over submerged breakwaters, with a case study at Uluwatu Beach, South Bali. The formulation extends our previous scheme by incorporating radiation boundary conditions (RBC) and employing a Crank-Nicolson time integration scheme, which is unconditionally stable, second-order accurate, and capable of conserving mass and energy. The model is validated against benchmark cases, including the well-known standing waves in a closed basin, a bottom step-up and an idealized submerged breakwater, showing excellent agreement with analytical and another numerical scheme. The effect of bottom step-up and submerged breakwater will produce a reflected and transmitted wave, whose both masses is closely related to the change in the bathymetry. Furthermore, the total mass between the reflected and the transmitted waves is always constant and equals to the mass of incident waves. Application to the site-specific bathymetry of Uluwatu Beach, derived from GEBCO data, indicates that an artificial submerged breakwater 10 m wide and 10 m high, positioned 0.5 km offshore, can reduce shoreline wave amplitudes by approximately 35% against no-breakwater scenario. The results demonstrate that the proposed method is both accurate and well suited for the design of coastal protection structures in wave-exposed environments. ● Developed a new finite element method for simulating wave propagation and attenuation under complex coastal bathymetry. ● Demonstrated accurate and physically consistent prediction of reflected and transmitted waves over submerged coastal structures. ● Applied the proposed model to Uluwatu Beach, Bali, showing that submerged breakwaters can significantly reduce shoreline wave amplitudes.