Time-domain modeling of heave and pitch motions of two vessels during lightering operations based on nonlinear Froude–Krylov forces

Accurate prediction of the coupled motions of two side-by-side vessels is important for ship-to-ship transfer operations. This study develops a partially nonlinear time-domain model for the coupled heave and pitch motions of two vessels at zero forward speed. Radiation and diffraction forces are computed using a linear hybrid Green function method, while incident-wave Froude–Krylov (F–K) and hydrostatic restoring forces are evaluated over the instantaneous wetted surfaces using a quadtree-based adaptive mesh. The model is validated against experimental data for a Wigley III hull and a modified Wigley–barge configuration. Results show that F–K nonlinearity is mainly governed by body-motion-induced modulation of the incident-wave pressure. The flat-bottomed barge exhibits a stronger second-harmonic heave F–K component than the modified Wigley hull; at λ / L = 1.25 and ζ a = 0.05 m, the corresponding ratios are approximately 14.7% and 4.5%. Fundamental motion RAOs differ from linear predictions by only a few percent over most conditions, whereas the steady heave mean shift is strongly sensitive to the incident-wave model. Overall, the fundamental and second-harmonic responses remain comparatively robust within the examined range.