Stability against capsizing is one of the most fundamental requirements to design a ship. In this research, for the first time, CFD is performed to predict main modes of capsizing. CFD first is conducted to predict parametric rolling for a naval ship. Then CFD study of parametric rolling is extended for prediction of broaching both by using CFD as input to NDA model of broaching in replacement of EFD inputs or by using CFD for complete simulation of broaching. The CFD resistance, static heel and drift in calm water and static heel in following wave simulations are conducted to estimate inputs for NDA and 6DOF simulation in following waves are conducted for complete modeling of broaching. CFD parametric rolling simulations show remarkably close agreement with EFD. The CFD stabilized roll angle is very close to those of EFD but CFD predicts larger instability zones. The CFD and EFD results are analyzed with consideration ship theory and compared with NDA. NDA predictions are in qualitative agreement with CFD and EFD. CFD and EFD full Fr curve resistance, static heel and drift in calm water, and static heel in following waves results show fairly close agreement. CFD shows reasonable agreement for static heel and drift linear maneuvering derivatives, whereas large errors are indicated for nonlinear derivatives. The CFD and EFD results are analyzed with consideration ship theory and compared with NDA models. The surge force in following wave is also estimated from Potential Theory and compared with CFD and EFD. It is shown that CFD reproduces the decrease of the surge force near the Fr of 0.2 whereas Potential Theory fails. The CFD broaching simulations are performed for series of heading and Fr and results are compared with the predictions of NDA based on CFD, EFD, and Potential Theory inputs. CFD free model simulations show promising results predicting the instability boundary accurately. CFD calculation of wave and rudders yaw moment explains the processes of surf-riding, broaching, and periodic motion. The NDA simulation using CFD and Potential Flow inputs suggests that CFD/ Potential Flow can be considered as replacement for EFD inputs.

In this dissertation, the extended Melnikov's method has been applied to several nonlinear ship dynamics models, which are related to the new generation of stability criteria in the International Maritime Organization (IMO). The advantage of this extended Melnikov's method is it overcomes the limitation of small damping that is intrinsic to the implementation of the standard Melnikov's method. The extended Melnikv's method is first applied to two published roll motion models. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is a model with a biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of the extended Melnikov's method is demonstrated. Then this method is used to predict more accurately the threshold of global surf-riding for a ship operating in steep following seas. A reference ITTC ship is used here by way of example and the result is compared to that obtained from previously published standard analysis as well as numerical simulations. Because the primary drawback of the extended Melnikov's method is the inability to arrive at a closed form equation, a 'best fit'approximation is given for the extended Melnikov numerically predicted result. The extended Melnikov's method for slowly varying system is applied to a roll-heave-sway coupled ship model. The Melnikov's functions are calculated based on a fishing boat model. And the results are compared with those from standard Melnikov's method. This work is a preliminary research on the application of Melnikov's method to multi-degree-of-freedom ship dynamics. In the last part of the dissertation, the method of manufactured solution is applied to systems with chaotic behavior. The purpose is to identify points with potential numerical discrepancies, and to improve computational efficiency. The numerical discrepancies may be due to the selection of error tolerances, precisions, etc. Two classical chaotic models and two ship capsize models are examined. The current approach overlaps entrainment in chaotic control theory. Here entrainment means two dynamical systems have the same period, phase and amplitude. The convergent region from control theory is used to give a rough guideline on identifying numerical discrepancies for the classical chaotic models. The effectiveness of this method in improving computational efficiency is demonstrated for the ship capsize models. / Ph. D.

A recently developed approach, in the area of nonlinear oscillations, is used to analyze the single degree of freedom equation of motion of a oating unit (such as a ship) about a critical axis (such as roll). This method makes use of a closed form analytic solution, exact upto the rst order, and takes into account the the complete unperturbed (no damping or forcing) dynamics. Using this method very-large-amplitude nonlinear vessel motion in a random seaway can be analysed with techniques similar to those used to analyse nonlinear vessel motions in a regular (periodic) or random seaway. The practical result being that dynamic capsizing studies can be undertaken considering the shortterm irregularity of the design seaway. The capsize risk associated with operation in a given sea state can be evaluated during the design stage or when an operating area change is being considered. Moreover, this technique can also be used to guide physical model tests or computer simulation studies to focus on critical vessel and environmental conditions which may result in dangerously large motion amplitudes. Extensive comparitive results are included to demonstrate the practical usefulness of this approach. The results are in the form of solution orbits which lie in the stable or unstable manifolds and are then projected onto the phase plane.