非線性波與固定浮式結構物的交互作用

Abstract

本文以邊界元素法發展一直推式非線性波數值水槽，且於水槽末端加入一假想海綿邊界來吸收入射波。模式中以Euler-Largrangian數值技巧描述自由水面的非線性運動，使用曲線近似法(Cubic Spline)求得水面點的各種物理量之切線方向一、二階微分值，利用Taylor級數展開法求得下一時刻的水位資料。模式中並使用了合適條件(Compatibility Conditions)及平滑技巧(Smoothing Technique)來增加模式的穩定性，更進一步地於水槽中置入一固定浮式結構物，藉以瞭解非線性波與固定浮式結構物間的交互作用問題。 在本研究中，首先將數值結果與實驗值比較後相當吻合，證明本數值模式的妥適性；考慮固定浮式結構物寬度：得知透射率隨著結構物寬度的增加而降低；考慮固定浮式結構物的沒水深度：透射率亦隨著沒水深度的增加而降低；此結果與線性波分析結果趨勢一致，惟線性波之分析無法探討波浪尖銳度對波浪變形的影響，而利用本文之非線性分析，發現尖銳度愈高則透射率愈小，且此現象在較淺水處(kh=0.9~1.2)較為明顯，在較深水處(kh>1.2)則較不明顯，研究中並對波浪通過固定浮式結構物時，其各頻波高的變化加以探討瞭解。

Based on the boundary element method, a numerical model for the simulation of nonlinear wavefields generated by a piston-type wavemaker has been developed. The free surface flow is assumed to be irrotational. In the numerical wave tank, a spongy layer is set in front of the wall at the end of the tank to absorb the incoming wave energy by frictional damping. In the present model, a time-steping lagrangian technique is employed to track the free surface movement. The free surface location and the associated velocity potential are computed by the second order numerical integration in time. The cubic spline interpolation scheme is used to compute the tangential derivatives of physical variables. To remove the sawtooth numerical instability and continue stably the numerical performance for a sufficiently long time, two effective solution techniques are introduced. The compatibility conditions are introduced to treat the corner points on the interface of solid boundaries and free surface. The smoothing technique is applied to the all node points on free surface. The numerical model is applied to study the interation of nonlinear waves with fixed floating bodies. The accuracy of the present nonlinear numerical model is proved by comparing results of present nonlinear numerical model, other numerical model and laboratory experiment. FFT is applied to detect the wave height and wave energy of different harmonic componente. Numerical results also show that the fully nonlinear analysis is different to the linear analysis, which proves the important of fully nonlinear analysis, In addition, the present study shows that the transmission coefficient is affected by many factors, such as the submerged depth and width of the floating bodies, the relative length and the steepness of incident wave. Both the increased width of the floating bodies and the increased steepness of incident wave denote a reduction in wave transmission.