Enhanced Endo's approach for evaluating free-surface Green's function with application to wave-structure interactions

Water wave scattering by impermeable and perforated plates

“…The evaluation of the free-surface term G F in Eq. (5c) has been extensively studied in the literature (Newman, 1985, Chen, 1993, Liu et al, 2020, Mackay, 2019. In the present study, the free-surface term is evaluated using the algorithm described by Newman (1985).…”

A Simplified Method for the Evaluation of Floating-Body Motion Responses over a Sloping Bottom

“…k sinh kh e − υ cosh kh e e −kh J 0 (kR)dk (25) where G denotes the velocity potential at the field point (x, y, z) due to a point source at (ξ, η, ζ), υ = ω 2 /g, r is the distance between the source and field points, and r 2 is the distance between the field point and the image of the source point with respect to the bottom: here, an equivalent constant depth h e is assumed to represent the contribution of the variable depth associated with the sloping seabed on the wave diffraction and radiation. Numerical methods for solving the finite-depth Green's function have been fully studied elsewhere [10][11][12]33,38,39] and, thus, are not discussed here.…”

Modelling and Optimisation of Wave Energy Converters

“…There have been numerous works on developing efficient and accurate algorithms for free-surface Green's functions, for the deepwater condition (e.g., [572,843]), and for the finite-depth water condition ( [572,120,458,473]). In general, the calculation strategies can be categorised into several types (in particular for finite-depth Green's function): (1) extracting slow-varying components from the Green function and using a Chebyshev or multi-dimensional polynomial method to approximate them (e.g., [572,120,473]); (2) applying asymptotic or power series expansions, such as eigenfunction expansions, rapid convergent series, or a combination with other numerical acceleration algorithms in different subregions (e.g., [634,448,456]); (3) decomposing the principal-value integral into two parts by subtracting a special term from the integrand and applying a direct Gauss-Laguerre quadrature to the numerical integration (e.g., [200,455]). In order to reduce the repeated effort in implementation of these algorithms, [761] and [447] released their open-source codes for the deepwater Green function, and [458] released an open-source code for the finite-depth Green function.…”