Pohang Institute of Science and Technology, Korea
In the present morning session, we hear that the nonlinear ship motion theory cannot prescribe the radiation condition in the far field, and hence the numerical methods developed so far are based on the so-called “open boundary condition in the far field.” For the 3-D potential theory, the physical condition dictates that the diffracted and radiated waves should decay in the far field. We unfortunately do not know how far the far field should be in the numerical solutions. I would like to see somebody perform a careful experiment to provide as a guideline how we should impose the far-field conditions in our numerical solutions for the nonlinear water waves.
In wave radiation and diffraction problems where the fluid domain is infinite, a radiation boundary condition is required in the computational domain in order to make the problem well-posed. No one has yet been able to find exact radiation boundary condition for fully nonlinear wave problems. This necessitates the use of approximate radiation boundary conditions. In our problem we have steady flow in a box which is perturbed by the presence of a body or by the generation of incident waves. The box is unbounded below, bounded above the free surface and on the centerline by symmetry. The remaining boundaries upstream, downstream and side all require appropriate boundary conditions. The examples we have published here have all been for τ>1/4 so the upstream condition is defined by the steady flow or by incident waves. The side boundary is truncated with a vertical wall made with source and collocation points that extend down to a depth of one wavelength (defined by the incident wave or the boat speed). We have also tried absorbing beaches along the side boundary but they interfere with the propagation of the incident waves. Only the downstream boundary has the “open” boundary condition. In this case we justify its use because the waves are carried out of the problem domain by the natural downstream convection of the free surface nodes. This is an implied radiation boundary condition, not a rigidly defined boundary condition, and we provide no proof of its legitimacy. Our results indicate that the “open” boundary has little effect on the wave pattern of forces on the body relative to previously published experimental results. We agree with Dr. Lee that an experiment might be contrived to provide insight into this problem. We are still searching for the perfect far-field boundary.