Straightforward integration for free surface Green function and body wave motions

TL;DR

This paper introduces a new direct integration method for the classical water wave problem involving floating bodies, improving numerical stability and accuracy in evaluating Green functions and their gradients.

Contribution

It presents an alternative approach that treats singular wave integrals as regular, enabling direct numerical integration and enhanced stability for wave motion calculations.

Findings

Method yields accurate results compared to benchmark data.

Numerical stability for Green function gradient matches that of the Green function.

Approach simplifies computation of wave integrals in fluid-structure interaction problems.

Abstract

An alternative manner is provided for solving the classical linearised problem of the radiation and diffraction of regular water waves caused by oscillation of a floating body in deep water. It is shown that the singular wave integrals of the three-dimensional free surface Green function $G$ and its gradient $\nabla G$ can be regarded as regular wave integrals and are integrated directly. The method is validated by comparing with benchmark data for a floating or submerged body undergoing oscillatory wave motions. The comparison shows that the evaluation is sufficiently accurate for practical purposes. As the significance of the method, the numerical approximation stability for the gradient $\nabla G$ is shown to be the same with that for $G$.