應用Boussinesq方程式在一維波浪場上之數值計算

Numerical Calculations of one-dimensional Wave Fields Using Improved Boussinesq Equations

林銘崇(Ming-Chung Lin) ； 丁肇隆(Chao-Lung Ting) ； 張國緯(Kou-Wei Chang)

《海洋工程學刊》 2卷1期 (2002/07) Pp. 15-31

https://doi.org/10.6266/JCOE.2002.0201.02

摘要

本研究旨在應用Boussinesq方程式發展一套數值模式，期能預測波浪傳遞之現象。文中以[2,2]Padé近似推導以任意水深位置形式表示之Boussinesq方程式，控制相位速度誤差在5%的條件下時，其相對水深限制h/L0可延伸至0.5。數值計算方法則利用四階Adams-Bashforth-Moulton預測修正技巧以及消波邊界條件求解Boussinesq方程式，以增加數值計算之穩定性。最後以消波邊界條件測試不同之計算例，並將Boussinesq方程式通過潛堤之數值計算結果與實驗數據及理論解作一比較，結果顯示本數值模式可以準確預估實驗結果。

關鍵字

Boussinesq方程式 ； 消波邊界 ； 潛堤

並列摘要

The improved Boussinesq equations were developed to predict wave transformations. By [2, 2] Padé approximation, different types of Boussinesq equations were derived. The limitation of h/L0 on the applications of Boussinesq equations can be extended to 0.5 with suitable choice of the velocity parameter and under the requirement of the difference of the phase velocities from calculation and from linear dispersion relation less than 5%. The fourth-order Adams-Bashforth-Moulton predictor-corrector scheme with proper absorbing boundary conditions was imposed as the basic numerical scheme. Finally, numerical results for wave evolutions during passage over a submerge breakwater show good agreements with past experimental and theoretical results.

並列關鍵字

Boussinesq equation ； absorbing boundary condition ； submerged break-water