Author | van Daalen, E. |

Title | Numerical and Theoretical Studies of Water Waves and Floating Bodies |

Conference/Journal | PhD-Thesis, University of Twente |

Month | January |

Year | 1993 |

Abstract (EN)

In ocean engineering many problems involve the analysis of free surface waves interacting with large fixed or floating bodies either partially or totally submerged where surface tension, viscosity, and compressibility effects are of minor importance and may

be neglected. Under these assumptions the fluid flow is governed by a velocity potential which satisfies the time-independent Laplace equation throughout the fluid domain. The wave evolution is described by the dynamic and kinematic free surface conditions, which

are time-dependent partial differential equations. The motion of a floating body is described by the hydrodynamic equations of motion, involving pressure integrations over the wetted body surface. The first and second parts of this thesis are devoted to the development of a numerical model for the simulation of these water-wave and wave-body systems. The algorithm is based on a boundary integral equation method for the spatial discretization, and a fourth order Runge-Kutta method for the discrete time marching.

First, the formulations of both problems are considered, as well as the transition to the boundary integral equation formulation through Green's theorem. A brief literature survey of numerical solution procedures for the nonlinear wave-body problem is presented.

The most important feature of the approach followed here is that the dynamic equilibrium of the fluid and the body is preserved for all times, through the solution of integral equations for both the velocity potential and its partial time derivative.

Numerical results for various water-wave and wave-body problems show fair to excellent agreement with analytical predictions and experimental measurements. The present method appears to be quite able to reveal nonlinear effects.

In the third part we discuss the description of water-wave and wave-body problems in terms of variational principles and Hamiltonian equations of motion. Based on earlier results for water waves only, it is demonstrated that the equations of motion for free

surface waves interacting with freely flooating bodies constitute an infinite-dimensional Hamiltonian system. Explicit expressions for the canonical variables and equations are presented. The complete set of constants of the motion for the wave-body problem is given for

both the two-dimensional and the three-dimensional problem; explicit proofs are given, and this theory is supported with numerical results obtained with the panel method described above. Finally, the use of variational principles and conservation laws is demonstrated in

the development of absorbing boundary conditions for general wave-like problems, and applications to a nonlinear one-dimensional Klein-Gordon equation are discussed. This theory is also applied to the nonlinear water-wave problem.

In ocean engineering many problems involve the analysis of free surface waves interacting with large fixed or floating bodies either partially or totally submerged where surface tension, viscosity, and compressibility effects are of minor importance and may

be neglected. Under these assumptions the fluid flow is governed by a velocity potential which satisfies the time-independent Laplace equation throughout the fluid domain. The wave evolution is described by the dynamic and kinematic free surface conditions, which

are time-dependent partial differential equations. The motion of a floating body is described by the hydrodynamic equations of motion, involving pressure integrations over the wetted body surface. The first and second parts of this thesis are devoted to the development of a numerical model for the simulation of these water-wave and wave-body systems. The algorithm is based on a boundary integral equation method for the spatial discretization, and a fourth order Runge-Kutta method for the discrete time marching.

First, the formulations of both problems are considered, as well as the transition to the boundary integral equation formulation through Green's theorem. A brief literature survey of numerical solution procedures for the nonlinear wave-body problem is presented.

The most important feature of the approach followed here is that the dynamic equilibrium of the fluid and the body is preserved for all times, through the solution of integral equations for both the velocity potential and its partial time derivative.

Numerical results for various water-wave and wave-body problems show fair to excellent agreement with analytical predictions and experimental measurements. The present method appears to be quite able to reveal nonlinear effects.

In the third part we discuss the description of water-wave and wave-body problems in terms of variational principles and Hamiltonian equations of motion. Based on earlier results for water waves only, it is demonstrated that the equations of motion for free

surface waves interacting with freely flooating bodies constitute an infinite-dimensional Hamiltonian system. Explicit expressions for the canonical variables and equations are presented. The complete set of constants of the motion for the wave-body problem is given for

both the two-dimensional and the three-dimensional problem; explicit proofs are given, and this theory is supported with numerical results obtained with the panel method described above. Finally, the use of variational principles and conservation laws is demonstrated in

the development of absorbing boundary conditions for general wave-like problems, and applications to a nonlinear one-dimensional Klein-Gordon equation are discussed. This theory is also applied to the nonlinear water-wave problem.