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

A Numerical Simulation of Irregular Waves Based on the Cartesian Grid Algorithm
Meng-Yuan Zhu, Shan Ma, Kang-Ping Liao*, Guo-Dong Zhang, Dou-Dou Liu
College of Shipbuilding Engineering, Harbin Engineering University.
Harbin, Heilongjiang Province, China

directional irregular wave implementation in the open-source CFD
model REEF3D. The non-directional frequency spectra Joint North Sea
Wave Observation Project (JONSWAP) together with a cos-squaredtype directional spreading function is used for the simulation.
Ramezanzadeh et al. (2019) proposed a numerical scheme to model
irregular wave systems through a Lagrangian, particle-based numericalmethod, namely, Smoothed Particle Hydrodynamics (SPH). Uniform
current effects on the characteristic of irregular waves along with its
uncertainty are presented considering wave-current interaction in theactual ocean environment by Yao et al. (2021). Based on the given orreal times series in certain space along the incident wave boundary,Luo et al. (2022) established the Inhomog-Bound-EEED and InhomogBound-PTPD methods for simulating the inhomogeneous incident
wave boundary of the multidirectional irregular waves. In thenumerical calculation domain, some scholars generated waves bymeans of source function method, such as Liu et al. (2005), Kim et al.
(2007) and Luo et al. (2019), some by model coupling approaches(Yang et al., 2013). At present, there are intensive studies on irregularwave with numerical methods. But the feasibility of irregular wave
numerical simulation by using the Cartesian grid CFD algorithm,
especially the numerical dissipation characteristics of long-term
simulation were not studied.
In this study, the Cartesian grid CFD algorithm (Liao et al.,2018)
based on the coupled potential-viscous flow method is applied tosimulate ITTC spectrum irregular wave. The coupled potential-viscous
flow method is introduced firstly. Then the influence of mesh size, time
step, number of linear wave superpositions and transition function typeon the simulation accuracy of irregular wave inversion spectrum areanalyzed respectively. Finally, the rule of the Cartesian grid CFD
method simulating irregular waves is summarized.

ABSTRACTAt present, computational fluid dynamics (CFD) is widely used in thefield of ships and the sea. The Cartesian grid CFD algorithm has theadvantages of simple mesh division, small numerical dissipation andfast calculation speed. The Cartesian grid CFD method is based on acartesian coordinate system and the finite difference method is used todiscretize the N-S equation in space. A compact CIP method(constrained interpolation method) with third-order accuracy is used tosolve the convective term, which can restrain the numerical dissipation
effectively. By introducing the CIP improvement method, namely
THINC/SW algorithm, it can effectively simulate wave propagation,
climbing, rolling, breaking and other violent free surface motion. In
this paper, the Cartesian grid algorithm is used to simulate irregularwaves. By changing the mesh size, time step, number of linear wave
superpositions and transition function type to study and compare withthe wave spectrum. The effects of various factors on the accuracy ofwave simulation are analyzed and the appropriate wave simulation
strategy is finally proposed. The results show that the simulated
irregular wave inversion results agree well with the theoretical wave
spectrum by using the Cartesian grid CFD algorithm and selecting
appropriate parameters. Therefore, the algorithm can provide the basis
for the accurate prediction of slamming load and ship structure design.

KEY WORDS: Cartesian grid algorithm; Irregular wave simulation;
CFD.

INTRODUCTION
At present, hydrodynamic research is very important in the field ofMarine structures. The accuracy of wave numerical simulation directly
affects the accuracy of load simulation. The wave simulation methods
mainly include potential flow simulation, viscous flow simulation andcoupled potential-viscous flow method. Because irregular waves withviscosity are closer to the real environment of Marine structures, CFD
numerical simulation of irregular waves has attracted much attention.
Gatinet et al. (2017) proposed a framework for efficient irregularwave simulations using higher order spectral method coupled withviscous two phase model. Based on this method, he conducted a
numerical simulation of three-dimensional extreme waves encounteredby a large container ship. Wang et al. (2019) presented a multi-NUMERICAL METHOD
The continuity equation and momentum conservation equation ofincompressible fluid are V = 0(1)

 ui
 ui
 p 1  ij+uj=−++ fit xj
 xi   x j(2)where, i =1,2,3, V represents the velocity of the fluid particle; u i is2124