Numerical Model for Wave Attenuation by Breakwater and Trench

This study presents a numerical and analytical investigation of wave attenuation induced by coastal structures, specifically breakwaters and trenches, using the one-dimensional linearized Shallow Water Equations (SWE). An analytical expression for the wave transmission coefficient is derived using the method of separation of variables, providing insight into the influence of structural configurations on wave transformation. To complement this, a numerical solution is developed using the Lax–Wendroff finite difference scheme, offering a robust and efficient approach for simulating wave propagation across variable bathymetry. The model setup includes representations of submerged breakwaters and trenches as modifications to the bathymetric profile, enabling evaluation of their effectiveness in attenuating incident wave energy. The validation is performed by comparing the numerical results with the analytical solution for various wave and structural parameters, which demonstrates good agreement. Furthermore, a sensitivity analysis is conducted to examine the impact of trench depth, breakwater height, and structure spacing on the transmission coefficient. The findings highlight the importance of integrated structural design in optimizing wave attenuation and provide a useful framework for coastal engineers to evaluate coastal protection strategies.