Alternative flow models, vector Green functions and boundary integral flow representations in ship and offshore hydrodynamics

Abstract

Wave diffraction-radiation by large bodies such as offshore structures and ships advancing in regular waves or in calm water is widely analyzed via panel methods based on a boundary integral flow representation and a Green function that satisfies the relevant free-surface boundary condition. The boundary integral flow representations solved in existing panel methods express the flow potential in terms of distributions of sources and dipoles, related to a Green function and its gradient, over the body surface. Other notable features of existing boundary integral flow representations are that they can be ill-posed for a set of irregular frequencies, and that – for a ship advancing in calm water or in regular waves – they involve a troublesome line integral around the ship waterline. Several alternative boundary integral flow representations that are well suited for wave diffraction-radiation by offshore structures or by ships advancing in regular waves or in calm water are given in this study. These representations, based on an alternative linear flow model (given previously) and an alternative vector Green function (not previously considered), are weakly singular and do not involve a waterline integral. The influence coefficients related to these new flow representations consist of Rankine components associated with complementary types of weakly singular Rankine singularities, and Fourier components defined by a Fourier superposition of elementary waves. Both the Rankine and Fourier components of the influence coefficients can be evaluated simply and efficiently. In particular, the Fourier component can be evaluated via the Fourier–Kochin (FK) method, in which the dominant computational task is independent of the number of panels that approximate the body surface. Thus, the new boundary integral flow representations given in this study and the FK method expounded previously provide a practical new basis for the evaluation of three main classes of wave diffraction-radiation by ships and offshore structures via panel methods.