Calculation of Two-Dimensional Nonlinear Fluid Flow Resulting from Large-Amplitude Forced Heave Motion of a U-Shaped Cylinder in a Free Surface.

Progress in developing a tool to compute large amplitude ship motions is reported. In particular, a method to calculate transient two-dimensional potential flow about a body moving in a free surface is described. The flow problem is formulated as an initial-boundary value problem in which the velocity potential along the free surface and the positions of the moving boundaries are sought as solutions of a coupled system of differential equations. An implicit finite-difference method is used to advance the solution of the coupled system of equations in time. The auxiliary problem of computing the velocity potential inside the fluid region is solved by a method which is based on boundary-fitted coordinates and is directly extensible to three-dimensional flows. Results from calculating the potential flow about a body in forced heave motion are presented. The hydrodynamic force on the body has been obtained and compared with the hydrodynamic force predicted from second-order perturbation theory. Keywords: Free Surface Effects; Heaving Cylinder; Perturbation Theory; Ship Motions; Ship Hydrodynamics; Water Waves.