A frequency-domain hybrid HOBEM for motion responses and added resistance of ships sailing in head and oblique waves

Abstract

A hybrid higher-order boundary element method (HOBEM) within the framework of potential flow theory in frequency domain is developed for solving ship hydrodynamic problems with forward speed. The method introduces a wall-sided artificial control surface to decompose the fluid domain into two subdomains, one encompassing the ship and the other on the outside. To guarantee the radiation condition at infinite for any frequency, the translating-pulsating Green's function method with singularities distributed on the control surface is used in the outer domain. The panel integrals of the Green's function are evaluated by a robust and efficient semi-analytical scheme. In the inner domain, the Rankine panel method (RPM) is adopted, and the steady flow effects are considered in the free surface and body surface conditions. The integral equation imposed on the inner boundaries is discretized and solved by a numerical approach of HOBEM based on bi-quadratic isoparametric elements. By imposing the continuous conditions of velocity potential and its normal derivative on the control surface, the solutions in the two domains are matched and a coupled equation system is formulated for the velocity potential on boundaries. Through the calculations of radiation and diffraction forces on a mathematical ship model, the present method is proved to have good mesh convergence, and satisfactory results can be obtained in a relatively small computational domain.The present hybrid HOBEM is applied to evaluate the hydrodynamic responses of ships sailing in head and oblique waves. Numerical simulations are first conducted on the free motions of two slender ships (i.e., a modified Wigley hull and a non-wall-sided S175 containership) in head waves. By comparing the computed results with the corresponding experimental data and numerical solutions of the translating-pulsating Green's function method and RPM, it is found that the present method is of better stability and accuracy, especially for the non-wall-sided ship. Then further investigations are conducted on the wave-induced motions and added resistance of S175, a newer container ship KCS and a full formed bulk carrier S-Cb84 with different forward speeds and heading angles. In all cases, the numerical results obtained by the present method are satisfactory in comparison with the experimental data.