A general boundary-fitted 3D non-hydrostatic model for nonlinear focusing wave groups

Abstract

This paper employs a three-dimensional (3D) non-hydrostatic model to simulate nonlinear focusing wave groups. The non-hydrostatic model utilizes an explicit projection method to solve the Navier–Stokes equations. To accurately simulate the steep free surface involved in focusing waves, the model is built upon a general boundary-fitted coordinate system. This grid system allows for a great adaptability of the vertical discretization and meanwhile maintains the boundary-fitted properties of better fitting the bed and free surface. The advantage of the general boundary-fitted model is first validated by two test cases of nonlinear waves, including nonlinear standing waves and two-dimensional (2D) focusing freak wave. Then, the model is applied to simulate 2D focusing waves in deep and intermediate-water depths and 3D focusing waves in deep-water depth. By comparing with experimental data, the model results well reproduce the main characteristics of 2D deep-water focusing waves and 2D intermediate-water focusing waves as well as 3D deep-water focusing waves, demonstrating the model׳s capability to resolve 2D or 3D focusing wave groups. Furthermore, in the test of 2D intermediate-water focusing waves, the downstream shifting of the focusing position and time is also studied numerically, which is not presented in the experiments.