A higher-order method for large-amplitude simulations of bodies in waves

Abstract

In this thesis, we simulate large-amplitude motion of three-dimensional bodies in waves using a higher-order boundary element method. A 'geometry-independent' approach is adopted in which the representation of the body surface is separated from the discretization of the hydrodynamic solution. Traditional formulations of the wave-body problem assume small-amplitude waves and body motions, and perturbation expansion about the mean position of the body and free surface leads to a completely linearized system. In the present thesis, the body boundary condition is imposed exactly, but disturbances at the free-surface are assumed to be small enough to justify linearization. Previous applications of this so-called body-exact problem have concentrated on the analysis of heave and pitch motion of ships with forward speed. This study focuses on marine applications where a large-amplitude response is induced by small-amplitude incident waves. The time-varying nature of the body-exact formulation makes its numerical solution computationally intensive. Therefore, a new 'higher-order' panel method has been developed to overcome inefficiencies associated with the conventional constant-strength planar-panel approach. Unlike most higher-order schemes, the present method separates the discretization of the hydrodynamic solution from the representation of the body surface by applying a 8-spline description of the potential over a generic parameterization of the geometry. This allows for accurate (or even analytic) representation of the surface while retaining the desirable characteristics of higher-order methods, most. notably improved efficiency and the ability to evaluate gradients of the potential needed for nonlinear analyses. Robustness and efficiency of the present method are demonstrated by its application to three problems in which the large-amplitude response of the body is important. In the first example, we examine the hydrodynamic loads on an underwater vehicle during a near surface maneuver. The vertical drift force is found by integrating the quadratic Bernoulli pressure, and its variation with respect to submergence is shown to complicate the control of the vessel. Next, multi-body interactions are examined in the cont.ext of the drift motion of a floating body in the vicinity of a fixed structure. Here, the presence of the structure is shown to repel the floating body against the direction of incident wave propagation for certain conditions. In the final application, we examine instabilities of floating bodies to illustrate the importance of accounting for finite-amplitude motions. Period doubling and exponentially large motions in the numerical simulations are related to parametric forcing captured by the body-exact formulation.