J. Broeze

A three-dimensional panel method for nonlinear free surface waves on vector computers

A number of recent improvements in a higher-order three-dimensional (3D) panel method for highly nonlinear free surface wave simulations is discussed. Special attention is paid to grid evolution techniques, and stability of the time-dependent problem. Due to the improvements, stable and accurate results can be obtained for linear and highly nonlinear wave problems. Although no artificial smoothing is applied, even extreme problems like the development of breaking waves in a 3D configuration can be simulated. The computer code has been specially developed for implementation on a vector computer. The program is highly vectorized, and use is made of mathematical libraries for acceptable CPU-times.

Radiation boundary conditions for the two-dimensional wave equation from a variational principle

A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon.

A Panel Method for the Simulation of Nonlinear Gravity Waves and Ship Motions

We present a higher order panel method for the numerical simulation of nonlinear gravity waves and ship motions in two and three dimensions. The method is based on a Green’s formulation for the velocity potential, which is introduced under the usual assumptions of an ideal fluid and an irrotational flow. Stable and accurate results for both linear and highly nonlinear waves are obtained. We discuss some essential feattires of our panel method, such as the time stepping mechanism and the approximation of the geometry. A variational formulation for the nonlinear free surface wave problem is presented, with direct implications for the numerical solution techniques which have been applied. Test results are shown for steady waves, overturning waves and wave-structure interactions. The numerical algorithm and preliminary results for surface piercing floating bodies are presented.

Variational principles and conservation laws in the derivation of radiation boundary conditions for wave equations

Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noethers theorem from the requirement that they transmit some appropriate density--such as the energy density--as well as possible. The theory is applied to a nonlinear version of the Klein-Gordon equation. For this application numerical test results are presented. In an accompanying paper the theory is applied to a two-dimensional wave equation.

The computation of highly nonlinear free surface waves wtiti a three-dimensional panel method

In this paper we discuss a higher order three dimensional panel method for nonlinear free surface wave simulations. A high degree of accuracy is obtained by a higher order resolution of the spatial problem and an efficient fourth order time integration method. Due to the accuracy, the algorithms provide stable results in the computation of linear and (highly) nonlinear wave problems.

A Higher Order Panel Method for Nonlinear Gravity Wave Simulation

We present an efficient higher order panel method for the numerical simulation of nonlinear gravity waves. The method is based on a Green’s formulation for the velocity potential that is introduced under the assumptions of an ideal fluid and an irrotational flow. This panel method gives accurate results for both linear and highly nonlinear waves. Test results are shown for a highly nonlinear Stokes wave and an overturning sinusoidal wave.