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

Study on time-domain hydrodynamic analysis and second order forces
calculation based on nonlinear Multi-domain method
Wen-jun Zhoua, Xi Chena, Bao-qing Wanga and Ren-chuan Zhub
(aMarine Design & Research Institute of China, China
bState Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University)

S175 containership (Fujii and Takahashi, 1975) and the S60 models

ABSTRACT(Gerritsma and Beukelman, 1972). Recently, Kashiwagi et al. (2004)

A nonlinear multi-domain method is proposed to conduct time-domain

showed the experiment data of second order forces for 170kBC.

hydrodynamic analysis of ships in waves based on three-dimensional

Valanto and Hong (2015) presented the experimental results of HSVA

potential flow theory. The computation domain is divided into the innercruise ship. Stocker (2016) measured the second order forces of KCS

domain and the outer domain by control surfaces. In the inner domain,

ship in oblique waves.

the Rankine panel method incorporated with nonlinear boundary

Further study on second order force by numerical methods starts fromconditions is applied, where influence of both the steady ship wave and1960s, of which the far field and the near field methods are the two

the incident wave on wave-body interactions are considered. In themajor methods proposed based on potential flow theory. Maruo (1960,

outer domain, a fast free surface Green’s function method with linear1963) derived the far field formula of second order force based onboundary conditions is used. On the control surface, the velocity

energy and momentum conservation within the flow field enclosed bypotential and its derivatives are kept continuous. With marching on

the body surface, free surface and far field surface. Newman (1967)

time step, the framework of nonlinear time-domain analysis

refined the far field method in calculation of second order forces. Liu

hydrodynamic are established. Second order forces of ships in waves

et al. (2011) studied the added wave resistance using far field formula

are then calculated with near-field integral method and components

based on Green’s function method in frequency domain and hybrid

discussions are made with numerical simplification for engineering

Green’s function method in time domain. Joncquez (2009), Seo et al.

application.

(2013) applied the Rankine panel method in investigating motion ofMath model ship Wigley-III, container ship S175 and oil tanker

ships advancing in waves and calculated the integral of second order50500T are chosen for validation of motions and second order forces

forces on vertical control surfaces in far field. The far field method wascalculation. Effects of different components of added resistance are

well described in ITTC report (1981), and in recent years Hong et al.

summarized and classified according to different working conditions,(2016) applied the far field methods into solving added wave resistancewhich balances the accuracy and efficiency of calculation. Based onwith three-dimensional translating–pulsating source. Huang et al. (2020)

the theoretical analysis and numerical validation, present method

extend the method by panel integration and improved the efficiency.

shows significant potential in time domain hydrodynamic analysis andHowever, the far field method has limitations in oblique sea cases andsecond order forces calculation.

is hard to estimate second order forces of multi floating bodies and

KEY WORDS: multi-domain; nonlinearity; hydrodynamic analysis;

nonlinear problems. Alternatively, the near field method was proposed

second order force.

in studying second order forces with direct integration of the second
order pressure on the body surface. The formula expression of near

INTRODUCTION

field method is intuitional and the numerical components are tightly

Second order forces of waves acting on ships or offshore structures inlinked with physical features, which contributes to analysis andwaves are related with the speed, operation rate and economic index.

applications. Grue and Biberg (1993) applied the near field method

For ships with forward speed, the longitudinal component of thealong with frequency-domain Green’s function method to estimate thesecond order forces is the added wave resistance, which affects theresistance induced by waves on a floating body advancing in waves.

actual performance of ships in seaways. Experimental and numerical

Joncquez (2009) use the Rankine panel method to analyze to second

methods are two major approaches in studying second order forces.

order forces, of which the Neumann-Kelvin and double-bodyExperiment for the added resistance on standard ship models waslinearization boundary conditions are adopted. Kim and Kim (2011)

conducted by several researchers such as Wigley (Journee, 1992), thepredicted ship motions and second order forces by time-domain three-2524