Ken-ichiro Hamanaka

Open, partial reflection and incident-absorbing boundary conditions in wave analysis with a boundary integral method

Abstract A wave field with constant depth and a linearized water surface condition is governed by the Helmholtz equation. This equation can be solved numerically with a boundary integral method implemented by Greens integral equation. In this method, suitable boundary conditions should be established corresponding to the type of boundary. The present paper proposes new boundary conditions for open boundary, partial reflection boundary and incident-absorbing boundary. These conditions do not depend on the incident angle, the number of wave components and the type of wave (plane and cylindrical). Numerical results show the complete validity of these conditions.

WAVE CONTROL BY A FLOATING STRUCTURE WITH ELASTIC DEFORMATION

In marinas, a type of floating structure composed by joined floating units is used for a breakwater or pier. Kato et al (2001) discussed the wave control effects by such a structure in the case of normalincident waves.But generally, the incident waves propagate obliquely toward the structure. In this case, the wave force is notuniform along the structure. Therefore the structure elastically vibrate with this un-uniform force. In thepresent paper, we analyze the wave field and the elastic vibration of the floating structure, and discuss thewave control effects and the interaction between the wave field and the motion of structure.

Boundary integral using The Legendre-Gauss quadrature in BEM

The Boundary element method (BEM) implemented by the Greens integral equation is used to solve wave field governed by the Laplace or Helmholts equation. When the boundary is divided into small segments and the integral on each segment is performed by a numerical method, the boundary integral equation is approximated by a liner algebraic equation. Locating the singular point on each segment, a simultaneous equation is obtained and can be solved by use of standard matrix method. Usually a simple trapezoidal rule is used on the numerical integration on the segments, and it has suitable accuracy at least in the linear analysis. But when the method is extended to nonlinear analysis, much higher accuracy is needed in the integral of multiplication of the linear potential and its derivatives in the forcing terms of surface condition.In the present paper, we investigate the accuracy of boundary integral with the Legendre-Gauss quadrature.

NUMERICAL ANALYSIS FOR FLOW STRUCTURE AROUND A CIRCULAR CYLINDER IN WATER WAVES

In this paper, flow structure around a circular cylinder was calculated in each cases of waves of small amplitude in long waves, in shallow water and in deep water. The Boundary Element Method with the Greens integral equation was used for numerical analysis of the potential flow in field of wave motion. Also, in case of analysis of flow structure around the circular cylinder, vorticity equation and Poissons equation for stream function ware employed for governing equation, and flow structure with separation and fluid force acting upon the circular cylinder ware calculated numerically, using the finite differential method and spectrum method. In the result of study, it was confirmed that flow structure or fluid force was evidently different in each cases of water waves. Further, fluid force by numerical analysis was compared with Morisons equation and was discussed.

Characteristics of Flexible Sheet for Wave Control

In this paper, the characteristics Of the flexible sheet with many springs on both sides for wave control on offshore were investigated using two-dimensional wave flame. Many experiments for 8 kinds of initial tension were carried out and coefficients of passing wave and reflected wave were measured. In this experiments, when the initial tension added to the sheet increases, coefficient of passing wave becomes small or of reflected wave large. But in the case of rigidiron plate, opposite result was obtained. Accordingly, it is expected that the best initial tension added to flexible sheet exists. In the experimental results, firstly, the best initial tension was found experimentally and secondly, it was discussed that the difference of phase between oscillation of the incident wave and the sheet regarded with wave control.