Numerical simulation of extended mild-slope equation including wave breaking effect

Abstract

Wave breaking often happens in the process of wave propagation to shallow water near the shore, which causes sharp attenuation of wave height and dissipation of wave energy. In this paper, an extended mild-slope equation (EMSE), including the effect of dissipation caused by wave breaking, is adopted to establish a numerical model. The current work develops a meshless technique, based on the local radial basis function-based method coupled with the differential quadrature method (local RBF-DQM) to solve the EMSE. Due to the influence of obstacles on wave propagation, the selection of the shape of the local support domain is improved to promote the accuracy of local RBF-DQM. For the numerical simulation, a modified iterative method based on previous research is suggested to estimate the energy dissipation term herein, which effectively solves the numerical oscillation problem. Two classical numerical cases are simulated to evaluate the validity and accuracy of local RBF-DQM in solving the EMSE. The results are in broad agreement with other numerical and experimental data. Finally, the numerical technique is used to study the influence of the factors of shore-parallel breakwater on wave breaking.