A time-efficient approach for nonlinear hydrostatic and Froude-Krylov forces for parametric roll assessment in irregular seas

•A derivative model is proposed to assess nonlinear responses in irregular waves.•The model is capable of reproducing parametric roll and its non-ergodicity.•Heave and pitch responses evidenced weakly ergodic character.•Due to its inherent features, the derivative model is computationally efficient.•The proposed methodology may be applied in Monte Carlo simulations.

In the context of second generation stability criteria assessments, the present paper introduces a fast time domain algorithm for parametric roll assessment in irregular seas. Two features can be distinguished in the present proposal: a) it involves the essential heave-roll-pitch nonlinear coupling and b) it is a pre-calculated derivative model, convenient for the required systematic Monte Carlo simulations.The main features of the model are described. The proposed methodology is based on a 3D panel method in which hydrostatic and wave-induced forces are computed on the actual body surface considering a set of systematic pre-defined hull positions. This set of data is preprocessed through polynomial fitting and the coefficients of the derivative model, corresponding to a Taylor series expansion defined up to the third order, are obtained. The methodology is applied to a container ship in head seas. The model is capable of reflecting the non-ergodicity of the head seas parametric rolling. At the same time, heave and pitch motions display “weakly ergodic” responses.