A time domain boundary element method for wave added resistance of ships taking into account viscous effects

Linear boundary element methods generally provide accurately enough predictions of ship motions in small amplitude waves. However, when the wave-induced added resistance is investigated, nonlinear effects are to be accounted for. Higher order effects, such as second order wave-induced drift forces, depend largely on ships forward speed. This article presents a nonlinear time-domain Rankine source method to calculate the wave-induced added resistance of ships advancing at constant forward speed in regular head waves. The fully nonlinear steady flow was computed. Nonlinear Froude-Krylov and hydrostatic forces were obtained by integrating pressures over the instantaneous wetted surface (undisturbed incident wave). Radiation forces were computed in time domain using convolution integrals (Cummins approach); diffraction forces, were computed using the complex force amplitude resulting from the linear seakeeping problem of incident wave diffraction. Radiation and diffraction effects caused by the changing wetted surface were accounted for. An empirical approach to account for the viscous wave added resistance was introduced. Numerical results for a 14,000TEU container ship and a very large tanker were compared to results from a frequency domain method, CFD calculations, and experimental towing tank measurements.