Mathematical Modeling of Ship Maneuvering and Ship-Ship Interaction in Deep and Shallow Waters

The primary goal of this thesis was to develop mathematical models for predicting the maneuverability of ships under shallow water conditions and during ship-ship interactions. Four mathematical models were developed to achieve this goal. First, a baseline regression model was refined to calculate hydrodynamic forces and moments acting on ships at various water depths. This model was further enhanced by incorporating correction functions that account for the shallow water effects on the hydrodynamic forces and moments. Additionally, a Fourier-based model was developed to compute dynamic interaction forces and moments during overtaking maneuvers, considering factors such as ship speed, lateral distance, and water depth. Finally, a four-quadrant model was developed to analyze various ship maneuvers, including stop maneuvers and reverse motions. To obtain the hydrodynamic coefficients required for these models, extensive flow simulations were performed using the open-source CFD software OpenFOAM. Dedicated simulation procedures were developed to efficiently determine hydrodynamic coefficients at zero frequency. The CFD simulations and mathematical models were validated against existing model test data and full-scale measurements. Standard ship maneuvers, such as turning circle, zigzag, and spiral tests, were simulated at various water depths to assess the shallow water effects on ship maneuverability and course stability. The results of this work provide valuable insights into ship dynamics in shallow water and during ship-ship interactions. A substantial part of this research has been published in five articles in international journals.