An enhanced spectral boundary integral method for modeling highly nonlinear water waves in variable depth

Abstract

This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived based on the boundary integral equation considering the water depth variability. A successive approximation scheme is also proposed in this study for calculating the surface vertical velocity. With the usage of Fast Fourier Transform, the model can be efficiently used for simulating highly nonlinear water waves on large spatiotemporal scale in a phase-resolving approach. The new model is comprehensively verified and validated through simulating a variety of nonlinear wave phenomenon including free propagating solitary wave, wave transformations over submerged bar, Bragg reflection over undulating bars, nonlinear evolution of Peregrine breather, obliquely propagating uniform waves and extreme waves in crossing random seas. Good agreements are achieved between the numerical simulations and laboratory measurements, indicating that the new model is sufficiently accurate. A discussion is presented on the accuracy and efficiency of the present model, which is compared with the Higher-Order Spectral method. The results show that the present model can be significantly more efficient at the same level of accuracy. It is suggested that the new model developed in the paper can be reliably used to simulate the nonlinear evolution of ocean waves in phase-resolving approach to shed light on the dynamics of nonlinear wave phenomenon taking place on a large spatiotemporal scale, which may be computationally expensive by using other existing methods.