Calculations of three dimensional nonlinear ship waves and ship resistance in a shallow water channel

This dissertation is on the calculation of waves generated by a wall-sided ship steadily moving along the straight centerline of a shallow-water channel of rectangular cross section. The ship considered is of an arbitrary blockage coefficient and the generalized Boussinesq (gB) equations obtained by T. Y. Wu (1981) are used as the governing equations. The Green-Naghdi equations (1977) are also used when the ship is thin. The simple condition representing the ship boundary is obtained as a unified boundary condition which can easily be extended to a strut. A boundary-fitted curvilinear coordinate system is generated to transform the physical plane characterized by an irregular grid to a computational plane with a uniform grid. The Modified Euler Method is applied to the equations in the time domain and a second-order finite-difference method is used to solve the boundary-value problem at each time step. The cases of a thin strut and a thin ship, in which the numerical grid generation is not required, are also presented. In these calculations, the CPU time is reduced significantly. In addition, the GN equations (1977) are used for the cases of a thin strut and of a thin ship. The upstream solitons and ship wave resistance are obtained and compared with the experimental data of Ertekin (1984). The permanent forms of solitary and cnoidal waves are directly derived from the gB equations and then numerically solved. The steady-state results are compared with the upstream and downstream waves obtained by the unsteady solutions of the gB equations as well as with the experimental data.