Mathematical modelling of ship manoeuvring and ship–ship interaction in deep and shallow waters

This paper presents a suite of mathematical models for predicting ship manoeuvring in shallow water and during ship–ship interactions, to capture complex hydrodynamic effects under restricted water conditions and dynamic ship–ship interactions, with a focus on overtaking scenarios. A regression-based manoeuvring model is first introduced, in which hydrodynamic forces and moments are systematically extended to account for shallow water effects through dedicated correction functions. To address dynamic interaction phenomena, a Fourier-based model is developed for the prediction of time-dependent forces and moments during overtaking manoeuvres, explicitly incorporating the influence of vessel speed, lateral separation, and water depth. The required hydrodynamic coefficients are obtained from high-fidelity CFD simulations using OpenFOAM, supported by tailored numerical procedures for efficient zero-frequency force estimation. The proposed models are systematically validated against experimental model-scale data and available full-scale measurements. The results provide new insights into ship dynamics in confined environments and under interaction conditions.