Ship-shaped hulls have often been found to be subject to excessive roll motions, which can inhibit their use as a stable production platform. To solve the problem, bilge keels have been widely adopted as an effective and economic way to mitigate roll motions, and their effectiveness lies in their ability to damp out roll options over a range of frequencies. In light of this, the present research focuses on roll motions of shipshaped hulls. A finite volume method based two-dimensional Navier-Stokes solver is developed and further extended into three dimensions. The present numerical scheme is implemented for modeling the flow around ship-shaped hulls in prescribed roll motion and for predicting the corresponding hydrodynamic loads. Studies on the hydrodynamic performance of ship-shaped hull in transient roll decay motions are also conducted. Systematic studies of grid resolution, the effects of free surface, hull geometries and amplitude of roll angle on the results are performed. Predictions from the present method compare well to those of other methods, as well as to measurements from experiments. Non-linear effects, due to the effect of viscosity, were observed in small as well as in large roll amplitudes, particularly in the cases of hulls with sharp corners. The results of the present method also suggest that it is inadequate to use a linear combination of added mass
and damping coefficients to represent the corresponding hydrodynamic loads. As a result, the calculation of the hull response is performed in the time domain. Finally, the capability of the present numerical scheme to apply in fully three-dimensional ship motion simulations is demonstrated.