Numerical investigations on nonlinear motions of ships sailing in large-amplitude waves based on hybrid HOBEM

Abstract

This paper presents a nonlinear numerical approach based on hybrid higher-order boundary element method (HOBEM) to investigate the wave-induced motion responses of ships with forward speed. The radiation and diffraction forces in time domain are determined by convolution of the impulsive response functions computed from frequency-domain hydrodynamic data of the hybrid method using a combination of Rankine source and translating-pulsating Green's function. In its numerical implementation, steady flow effects are included in the inner domain encompassing the ship, 9-node bi-quadratic curvilinear elements are employed to discretize the boundaries and analytical quadrature formulas are derived to calculate the influence coefficients related to the Green's function over the control surface so as to improve the accuracy, efficiency and stability. Meanwhile, the nonlinear incident wave force and hydrostatic restoring force are calculated over the instantaneous wetted surface of the ship hull during the motion process to capture the nonlinear properties. Based on the method, a numerical program is developed to predict and analyze the motion response of a modified Wigley hull and a non-wall-sided S175 containership advancing in waves with different amplitudes and heading angles. By comparing the present computed results with experimental data and other numerical solutions, it is found that the nonlinear calculations can produce more accurate motion responses in large-amplitude waves with strong nonlinearity. And the present nonlinear method based on hybrid HOBEM is of higher accuracy and better stability than traditional nonlinear methods based on three-dimensional pulsating source (3DP) and translating-pulsating source (3DTP), especially for S175 with large flare near the waterline.