本論文主軸在於研究船舶穩定前進、週期性振盪於波浪中航行所產生之非穩態流場問題。此流場邊界值問題(Boundary Value Problem)係建構於滿足理想流體之拉普拉斯方程式(the Laplace’s Equation)作為統御方程式，並採疊體流(Double-body Flow)為基礎流場附加相關波浪狀流場的作法，以及線性化邊界條件，藉以簡化本邊界值問題，推導出線性方程在頻域中求解。
在邊界積分方程式(Boundary Integral Equation)之建立上，乃基於在船體及自由液面等計算域邊界廣佈倫琴源點(Rankine Source)做為擾動點，以及運用雙重二次B木條(Biquadratic B-spline) 函數來呈現勢流流場及其連續性變化等數值作法，以求解不同條件下的流場；其中， 定義為ωU⁄g，U 及 ω 分別代表船舶前進速度及遭遇頻率。為能妥善地處理自由液面上波浪輻射現象，結合簡化後瀨戶輻射邊界條件(Seto’s Radiation Boundary Condition)，以及隨距離函數變化之雷利人工阻尼(Rayleigh artificial damping)等數值機制，使用於自由液面邊緣終端條件，以引導波浪行進以及減少波浪反射。
本文首先以潛行於水下的前進-振盪型單獨擾動點所誘導非穩態流場為例進行求解與比較，證明本文所建議之數值理論具有可行性；進一步關於散裝輪航行於波浪中所承受流體動力、波浪激盪力以及運動反應進行計算，並與實驗量測值與公開數值結果，在不同τ條件下進行比較，顯示本文所建立三維頻域倫琴小板法在船舶耐海性(Seakeeping)分析處理上具備有效性。

The unsteady wavy flow problem induced by a vessel at the steady forward translation and the periodical oscillation in waves is studied in this thesis. Additional to the Laplace’s Equation as the govern equation, assuming the double-body as the basis flow for superimposing the related wavy flow components and employing the appropriate linearized boundary conditions are taken to derive the linearized formulations of underlying Boundary Value Problem for frequency-domain solution.
The numerical scheme, which distributes the Rankine source as singularity over the boundary surfaces of the computation domain and utilize the biquadratic B-spline to approximate the flow potential field and its continuous variation, is considered to construct the involved Boundary Integral Equation for solving the flow field at various  condition, where τ=ωU⁄g, and U and ω are the forward speed and the frequency of encounter, respectively. To appropriately model radiation of generated free surface waves, the improved numerical mechanism, in which the spatially varying Rayleigh artificial damping is introduced in addition to employing the simplified Seto’s radiation boundary conditions, is implemented in the end conditions in free surface extent for guiding wave propagation and significantly reducing wave reflection.
In evaluations, the proposed scheme is demonstrated in the unsteady flow patterns produced by an translating-oscillating singularity under water at first. The further investigation is carried out for the bulker ship translating in waves. The predicted hydrodynamic coefficients, wave exciting force and resulting motions are found in good agreement in comparison with the related experimental measurement and the public well-known numerical results at a wide τ region. Finally, it illustrates the effectiveness of the established three-dimensional frequency-domain Rankine source method in handling the seakeeping analysis.

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