Numerical Computations and Integrations of the Wave Resistance Green's Function

Abstract

In order to develop an efficient method, using Kelvin--Havelock singularities, to compute the steady lifting flow around a ship with forward speed, the accuracy of computations of Green's function and boundary integrations have been investigated. The computations have been done using interpolation from tables for the nonoscillatory term of Green's function and using series for the oscillatory one; it has been shown that a region exists, close to the free-surface, where this last term must be computed by complete integration to ensure a prescribed error. Three schemes of boundary integrations have been studied; first boundary integrations have been performed using a Gauss method. Then, to improve accuracy, Fourier and boundary integrations have been interchanged either only for the oscillatory term or for both terms. Numerical results are compared and discussed taking into account both precision and computational time, for a submerged ellipsoid and for a lifting surface-piercing body.