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

Direct Integration of Green’s Function Method in Wave-Structure Interaction
Yuan Wang1, Yonghe Xie1*, Gangqiang Li1,2
1School of Naval Architecture and Maritime, Zhejiang Ocean University,

Zhoushan, Zhejiang Provence, China
2Department of Mechanical, Aerospace and Civil Engineering, University of Manchester,Manchester, United Kingdomelement method (BEM). Hess and Smith (1964) firstly created a method
to calculate the flow around a non-lifting, three-dimensional body in theinfinite fluid domain. This method is based on the simple source
distribution on a planar quadrilateral panel similar to the object surface,also known as the panel method, namely, BEM. Subsequently, many
researchers have made further research on the panel method. Hess andWilcox (1969) extended this theory to a small oscillating body with thepresence of a free surface. Wehausen (1971) described the theory ofwave diffraction and scattering to establish a potential flow method forsolving the motion of floating bodies. Sclavounos and Lee (1985) discussvarious topics on boundary element methods such as the removal ofirregular frequencies etc. Then, Newman (1986) optimized the program
based on the panel method to make it suitable for a large number ofpanels with controlled accuracy. Many researchers have studied theapplication of the panel method in deep water in the frequency domain(Faltinsen, 1990; Lee and Newman, 2005; Guha, 2012; Guha andFalzarano, 2013). In this paper, we will choose the boundary element
method to solve the wave-structure interaction problem. The flat
quadrilateral element is selected as the discrete element. Meanwhile, theelements and the coordinates of nodes are generated by the software
Ansys-AQWA, as the input of subsequent calculation.
For the BEM applying to the wave-structure interaction problem, the key
is solving the certain solution problem, consisting of the governing
equation and the linear boundary conditions. The numerical solution
methods developed so far can be categorized into two groups: Green’sFunction Methods (Chun-Djatmiko and McGregor, 1990; Guha, 2012;
Guha and Falzarano, 2013; Lee and Newman, 2005; Lin, 1997;
Viswanathan-Holden-Egeland and Gregor, 2021), and Rankine Source
Methods (Nakos, 1990; Nakos and Sclavounos, 1991; Nakos-Kring andSclavounos 1994; Yasuda-Iwashita and Kashiwagi 2016). The
expression of the rankling source method is simple and clear. However,discrete elements need to be arranged on the boundary of the wholecalculation basin, so the calculation quantity is huge. To reduce thenumber of elements, a new harmonic function expression is obtained byadding a correction term (obtained by solving the definite solution
problem other than the material surface condition) based on the ranklingsource method. This is the so-called Green's function method.
Green's function method is the most commonly used method for solving
certain solution problems in the three-dimensional frequency domain.
Green’s theorem and the distribution of singularities are discussed in
Newman (1977). Garrison (1984) gave a method of using Green'sfunction to represent the source potential when calculating the wave load
on a large floating body. And the numerical implementation of the panel

ABSTRACTIn this paper, the numerical simulation of wave-structure interaction
problem in infinite water depth without speed in the frequency domain
is studied. Green’s function method is used to solve the boundary-value
problem for the velocity potential based on the boundary element method.
The solution method of the free surface Green function is the focus of
this paper, and the direct integration method is compared with themethod proposed by Newman in 1985, and its impact on thehydrodynamic coefficient and force is studied. A slight difference
between the counterparts is observed in some areas, and its impact on thehydrodynamic results is void. The advantage of the direct numericalintegration method is straight forward and easy implementation for thecoding. In this paper, a program FLUHAN based on the constantboundary element method is developed for evaluating loads of a floating
structure in infinite water depth in waves. The results of the FLUHAN
and the commercial software WADAM are compared, and the results
show they match very well, which verifies the feasibility of the program.

KEY WORDS: Infinite water depth; The free surface Green function;
Direct numerical integration; Constant element method.

INTRODUCTION
With the development and utilization of marine oil and gas energy, as animportant means of transportation at sea, the research on a ship has been
continuous. The research on seakeeping of ships sailing in waves is oneof the major research focuses, and it is also an essential drawing data inthe ship design stage, which can ensure the navigation safety of the ship.
In the 1780s, Lagrange introduced the concept of velocity potential.
Lamb (1924) applied Green’s second identity to express the velocity
potential of a body as the effect of a distribution of simple and double
sources over the body boundary in a fluid domain with infinite space.
Then, John(1949) obtained the expression of the wave function for thewave function in the case of regular incident waves interacting withbodies satisfying geometric assumptions. The above studies give themathematical theoretical derivation of wave-structure interaction
problems, which provides a theoretical basis for the later research on
numerical solution methods. In the last decades, many efforts have been
devoted to developing numerical simulation methods for the wavestructure interaction problem. Among them, the following methods formodeling the body and fluid domain are mainly adopted: the boundary

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