Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical simulation of irregular waves by HOS method
Congyi Huang1, Ping Xu2, Decheng Wan1*, Sergei Strijhak3
1Computational Marine Hydrodynamic Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University, Shanghai, China
2Marine Design and Research Institute of China, Shanghai, China
3
Ivannikov Institute for System Programming of the Russian Academy of Sciences, Moscow, Russia*Corresponding author

simulate nonlinear gravity waves. At that time, HOS method could only
be used to simulate deep water waves under two-dimensional periodic
boundary conditions. Subsequently, Liu and Dommermuth (1992)
further extended the HOS method on the basis of the previous work. The
diffraction interaction between three-dimensional nonlinear wave andsubmerged objects was simulated, and the calculated results agreed wellwith the experimental data. In order to avoid the calculation errors
caused by the direct nonlinear evolution of the initial wave surface,
Dommermuth (1999) adopted a relaxation scheme to make the linear
initial wave smoothly transferred to nonlinear in a specific period of time.
Tanaka (2000) introduced the wave spectrum function and theinitialization of HOS calculation directly based on the wave spectrum
was realized. Bonnefoy (2004) considered the aliasing error caused by
the time-domain and frequency-domain transformation. He introduced
an aliasing elimination method that allowed long-time evolution basedon wave spectrum. Ducrozet et al. (2007) simulated the wave field basedon JONSWAP spectrum in a large area (thousands of square kilometers)
for a long time (nearly three hours). The generation probability of
extreme waves and the change of characteristic morphology wereexplored under the influence of different wave directional parameters.
Ducrozet (2012) proposed a three-dimensional nonlinear numerical poolbased on HOS method. The model can be used for wave generation withpush plate and swing plate based on nonlinear wave generation boundary.
The wave generation results of the numerical pool were in good
agreement with the laboratory pool, which verified the accuracy andvalidity. Ducroze et al. (2016) developed HOS-ocean, an open source
solver for the evolution of nonlinear waves in the open sea. Song et al.
(2018) introduced ITTC two-parameter spectrum into the HOS-ocean
solver based on previous work. The two-parameter spectrum of ITTC
was analyzed, the focused wave was simulated, and the multi-directional
irregular wave was studied. Zhuang et al. (2018) coupled the HOS
method with the CFD method and conducted 2D and 3D simulation
verification of regular and irregular waves.

ABSTRACT
Ships and offshore structures often encounter irregular waves in theocean. Therefore, the simulation of irregular waves is very necessary andmeaningful. The potential flow method is often used to simulate theirregular waves because the evolution needs a long time and a large
amount of calculation. High order spectral (HOS) method is a kind of
potential flow method, which has the advantages of high efficiency. In
this paper, the HOS method is used to simulate the formation andevolution of irregular waves. Firstly, the governing equations, boundary
conditions and the solving procedure of the HOS-ocean model based on
the HOS method are introduced. Then the accuracy and stability of theHOS-ocean model are verified by a standard example. After that, theformation and evolution of two-dimensional and three-dimensional
irregular waves are simulated based on JONSWAP spectrum and ITTC
spectrum respectively. The frequency domain curves, time domain
curves, maximum wave height, maximum wave steepness, average wave
steepness and other parameters of the waves generated by the two wave
spectrums are compared, and the differences between the two wave
spectrums in generating irregular waves are analyzed.

KEY WORDS: Higher order spectral method; Potential flow
method; Irregular waves; JONSWAP spectrum; ITTC spectrum.
INTRODUCTION
High-order Spectrum (HOS) method is a kind of pseudo-spectral method(PSM), which is based on the potential flow theory. This method canefficiently simulate the generation and evolution of nonlinear waves bypseudo-spectral expansion and fast Fourier transform (FFT). Firstly, thevelocity potential perturbation is expanded into a series of characteristic
functions, and then the derivative term is solved by FFT. This method
has high computational accuracy and efficiency, so it is widely used in
the simulation of nonlinear waves.

In this paper, the basic theoretical equations and solving process of HOS
method are introduced. Then the boundary conditions and initialization
process of the HOS-ocean solver used in this paper are introduced. After
that, the wave evolution in open water is analyzed based on JONSWAPHOS method was first proposed by West (1987) and Dommermuth andYue (1987) respectively in the same year, and was initially used to2423