Nonlinear shallow water flow on deck and its effect on ship motion

The main objective of this study is to examine the hydrodynamic characteristics of shallow water flow in the deck well of a boat or a ship and their effects on ship motion.; Euler's equations in fluid mechanics have been used for the nonlinear shallow water flow on deck. The equations are simplified under the shallow water assumption to obtain the governing equations. Then, the governing equations are expressed in the flux-vector form. A numerical method, called the Flux-Difference Splitting method is devised to solve this shallow water flow problem. This method was developed based on the similar idea in the flux-vector splitting method which was originally introduced to compute the shock wave in gasdynamics. The flux-difference in the governing equations is split based on characteristic directions. This method takes advantage of both the finite difference method and the characteristic method. The Superbee flux limiter has been employed in the algorithm to make the finite difference scheme of second-order with high resolution. Numerical results for shallow water flow on deck are presented with different parameters to reveal the characteristics of shallow water flow on deck.; Furthermore, the Flux-Difference Splitting method devised for the two-dimensional shallow water flow is extended to the shallow water flow in a three-dimensional deck space. The ship motion in six-degrees-of-freedom is taken into account in the governing equation of the nonlinear shallow water flow problem. The Fractional Step method is used so that solutions of the shallow water equation can be obtained by solving two sets of one-dimensional differential equations. Numerical results are presented to show the wave pattern due to different modes of motion excitation. Velocity vectors in the flow field are also given to help understand the flow properties.; The nonlinear equation of a rigid body moving in space is adopted for studying the time domain ship motions. The angular motions of the ship in space are measured by Euler angles. In this work, the time domain added mass, hydrodynamic damping and hydrodynamic restoring force coefficients are calculated using the impulse potential with the three-dimensional panel method. The radiated and diffracted wave forces are linearized. To formulate the equations of ship motion, the hydrodynamic forces caused by the shallow water flow on deck, the nonlinear Froude-Krylov forces, nonlinear restoring forces and nonlinear viscous roll damping, and other maneuvering forces are considered. The Extrapolation method is applied to solve the equations of ship motion numerically in the time domain. Finally, the developed method is applied to compute motions of two Nova Scotia inshore fishing vessels.