The 3D boundary integral method (or panel method) was pioneered by Hess and Smith (1964) in the context of infinite fluid flow In their method the body surface is replaced by plane quadrilateral panels and a constant source density is assumed on each panel In terms of Green's theorem, a Fredholm integral equation can be derived from the body surface boundary condition and then solved by the collocation technique for the velocity potential on each panel Based on their work, numerous others, such as Garrison (1974) and Faltinsen and Michelsen (1974), have extended this approach to the radiation and diffraction problem of linear surface waves by introducing the free surface potential or Green's function.
Nowadays, this approach which uses quadrilateral panels with constant source density and collocation technique for its solution (called ordinary panel method in the following), is already used m most 3D method programs, but there are two limitations which are worth noting here.
(1) The composite source surface is discontinuous For an arbitrary body it is not possible to arrange the trapezoids so that all four comers of each panel match the comers of adjacent panels. In other words, the source surface has leaks (Fig 1).
(2) The source distribution is discontinuous The source density is constant over each panel and therefore jumps stepwise at boundary of two panels.
To avoid these limitations, one can either increase the number of panels used to approximate the body surface or improve the accuracy of each panel (changing the shape of panels or using a higher order distribution of source density over each panel) In some cases, the latter approach is effective and it has already been used successfully in some panel programs, for example Breit et al (1985) and Breit (1985) In this study, an alternative way using triangular panels with linear source density distribution was employed in the 3D panel method. It is clear that this kind of panel can eliminate the two limitations mentioned above and improve the accuracy of panel description. Two alternative methods based on the triangular panel approach are used in this chapter One of them uses the "collocation" technique to solve the boundary integral equation (the TC method) and the other uses the "Galerkin" technique (the TG method) The comparisons were made among the three methods, TC, TG and ordinary panel(Fig. 1 is available in full paper) method wlth the collocabon solubon, for heave added mass and damping coefficients of a spheroid, and the heave added mass and damping coefficient distribution along the hull of a Series 60 model The results show that the TG method is computationally inefficient, but it can minimize the effect from the Irregular frequencies The TC method is shown to be more efficient than the ordinary panel method In the present numerical examples, for which only a few hundred or fewer panels were used, the improvement of computational efficiency of the TC method is not significant.
