Investigation of the U-shape submerged breakwater performance by the finite-different scheme

The submerged U-shape breakwater interaction with the solitary wave is simulated by the Boussinesq equations using the finite-difference scheme. The wave reflection, transmission, and dissipation (RTD) coefficients are used to investigate the U-shape breakwater's performance for different crest width, Lc1, and indent breakwater height, du. The results show that the submerged breakwater performance for a set of U-shape breakwater with the same cross-section area is related to the length of submerged breakwater crest, Lc1, and the distance between the crests, Lc2 (or the height of du). The breakwater has the maximum performance when the crest length is larger, and at the same time, the distance between them increases. Changing the Lc1 and du of the U-shape breakwaters result in a significant change in the RTD coefficients. Comparison of the U-shape breakwater, having the best performance, with the averaged RTD values shows that the transmission coefficients, K_t, has a better performance of up to 4% in comparison to other breakwaters. Also, the reflection coefficients K_R and the diffusion coefficients, K_d shows a better performance of about 30% and 55% on average, respectively. However, the model governing equations are non-dissipative. The non-energy conserving of the transmission and reflection coefficients due to wave and breakwater interaction results in dissipation type contribution. The U-shape breakwater with the best performance is compared with the rectangular breakwater with the same cross-section area to investigate the economic advantages of the U-shape breakwater. The transmission coefficients, K_t, of the U-shape breakwater shows a better performance of 5% higher than the rectangular one. The reflection coefficient, K_R, is 60% lower for U-shape in comparison to rectangular one; however, the diffusion coefficients, K_d, of U-shape breakwater is 35% higher than the rectangular breakwater. Therefore, we could say that the U-shape breakwater has a better performance than the rectangular one.