Time domain simulation of focused waves by High-Level Irrotational Green–Naghdi equations and Harmonic Polynomial Cell method

Abstract Wave focusing is one of the main mechanisms that can generate freak waves in deep water. The strongly nonlinear High-Level Irrotational Green–Naghdi (HLIGN) equations and the Harmonic Polynomial Cell (HPC) method are used here to simulate the focused waves. Numerical simulations are performed in intermediate water depth as well as in deep water. In intermediate water, the HLIGN free surface and wave kinematics are then compared with the well-accepted laboratory data and the results of the HPC method. The effect of water depth on focused waves is also carried out. It is demonstrated that both the HLIGN equations and the HPC method can accurately simulate the surface elevation and particle velocity of focused waves compared with the experiments. The velocity distribution is distinct for the focused waves with the same crest elevations but in different water depths. The HLIGN equations are considered to be an accurate and efficient wave model to investigate focused waves in the intermediate and deep water cases.