On the Theory of Potential Flow About a Ship Advancing in Waves

Abstract

This study considers the three-dimensional potential flow due to a ship advancing with constant average speed in a train of regular waves. A modified integro-differential equation for determining the velocity potential on the mean position of the hull surface is obtained, and a solid theoretical basis for obtaining a numerical solution of the equation via a panel method is developed following the approach used by Kochin more than 50 years ago. In short, the approach is essentially based on a Fourier representation of the solution of a modified integro-differential equation. This approach circumvents the fundamental difficulties associated with the numerical evaluation of the Green function and its gradient, and their subsequent integration over the panels used to approximate the hull surface of a ship.