Computations of Hydrodynamic Forces on Vessels Advancing in Waves by Four-Node Higher-Order Boundary Element Method

A higher-order boundary element method (HOBEM) using three dimensional translating-pulsating (3DTP) Green’s function is developed and applied to calculate the hydrodynamic forces on vessels advancing in waves in the present study. In this HOBEM, geometrical and physical variables are expressed by the shape functions defined by four nodal values; and Green’s function in Havelock form is adopted in the numerical implementation. The Gauss-Legendre quadrature is first adopted for the integral of 3DTP Green’s function over panel. However, due to the highly oscillating characteristic of Green’s function near the free surface, numerical instability is observed in the final results. To avoid this unstable problem, an improved algorithm for the integral of Green’s function is proposed. We discretize the panel into a series of horizontal line segments and derive an integral expression of 3DTP Green’s function distributing on the line segment. By accumulating a series of 3DTP Green’s function distributing on various horizontal line segments, the panel integral of Green’s function is obtained. To validate the performance of the improved algorithm, hydrodynamic forces on a mathematical ship model Wigley III are first calculated. The results are compared with those of the former algorithm and experimental data, which shows that improved algorithm is more stable and accurate. The present HOBEM is then applied to analyse the radiation and diffraction problems for a Series 60 hull and a catamaran hull. The computed hydrodynamic coefficients and wave forces are found to be in good agreement with experimental data.