Alternative approaches of evaluating Diffraction Transfer Matrix and Radiation Characteristics using the hybrid source-dipole formulation

Yingyi Liu,Hui Liang,Masashi Kashiwagi,Peiwen Cong

doi:10.1016/j.apor.2021.102769

Abstract

The interaction theory presented by Kagemoto and Yue (1986) significantly reduces the computational burden in the wave interaction problem of multiple surface-piercing bodies, particularly arrays of wave energy converters in recent years. Two essential operators of the theory are the so-called Diffraction Transfer Matrix and Radiation Characteristics. Many subsequent researchers (Goo and Yoshida, 1990; Flavià et al., 2018) have implemented the theory using the source distribution method in evaluating the two linear operators of a single unique geometry. However, nowadays, a great majority of boundary element method codes have been written by virtue of the hybrid source-dipole distribution method on account of its high accuracy. In this regard, the present work aims to introduce a full set of mathematical formulations, as well as a complete derivation process of evaluating the two operators based on the hybrid source-dipole distribution method. The proposed formulations are then applied to two benchmark geometries, as given by McNatt et al. (2015) and Flavià et al. (2018). Good agreement is found between the present results and those from the literature. Moreover, two alternative approaches to solve the diffraction problem have been compared to assess both their accuracy and efficiency. It is found that the two methods present similar levels of accuracy but very different computational burden.

Highlights

Wave loads are of primary concern during the lifetime of a marine structure in the real sea environment
In order to verify the present method based on the hybrid sourcedipole boundary integral equation, numerical computations are per formed against two benchmark problems given in Flaviaet al. (2016) and Flaviaet al. (2018)
An alternative method of evaluating the Diffraction Transfer Matrix (DTM) and the Radiation Characteristics (RC) encoun tered in wave interactions with multiple bodies is presented

Summary

Introduction

Wave loads are of primary concern during the lifetime of a marine structure in the real sea environment. Along with the development of computational technology, great progress has been witnessed in the prediction of wave loads on multiple bodies, such as the interconnected multi-moduled floating offshore structure (Chakrabarti, 2001), ice-floes in the marginal ice zone (Peter and Meylan, 2004b; Bennetts and Squire, 2009), and very-large floating structures (Kashiwagi, 2000; 2001; 2017), etc. A broad interest has been focused on arrays of wave energy converters or wave farms in recent years (Goteman et al, 2015; Sun et al, 2016; Goteman, 2017; Zhong and Yeung, 2019; Zheng et al, 2018; Zheng et al, 2020), in which analytical approaches or semi-analytical ap proaches applying the multiple-scattering interaction theory have been extensively used.

Methods

Results

Conclusion