Influence of the Waterline Integral on the Solution of the Frequency-domain Forward-Speed Radiation-Diffraction Problem of a Ship Advancing in Waves

Abstract

The radiation-diffraction potential of a ship advancing in waves is studied using the three-dimensional frequency-domain forward-speed free-surface Green function (Brard 1948) and the forward-speed Green integral equation (Hong 2000). Numerical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.ical solutions are obtained by making use of a second-order inner collocation boundary element method which makes it possible to take account of the line integral along the waterline in a rigorous manner (Hong et al. 2008). The present forward-speed Green integral equation includes not only the usual free surface condition for the potential but also the adjoint free surface condition for the forward-speed free-surface Green function as indicated by Brard (1972). Comparison of the present numerical results of the heave-heave wave damping coefficients and the experimental results for the Wigley ship models I, II and III (Journee 1992) has been presented. These coefficients are compared with those calculated without taking into account of the line integral along the waterline in order to show the forward speed effect represented by the waterline integral when it is properly included in the free-surface Green integral equation. Comparison of the present numerical results and the equivalent time-domain results (Hong et al. 2013) has also been presented.