  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.
