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題名 | 淺水波模式與布氏模式應用於封閉水槽內駐波模擬之比較=Comparison of Numerical Solution of Shallow-Water Equations and Boussinesq Equations for Standing Wave in a Closed Basin |
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作者 | 梁興杰; 陳盈智; 藍烱揚; | 書刊名 | 海洋工程學刊 |
卷期 | 11:2 2011.12[民100.12] |
頁次 | 頁137-148 |
分類號 | 443.1 |
關鍵詞 | 淺水波方程式; 布氏方程式; 非線性; 頻散; 駐波; 孤立波; Shallow-water equations; Boussinesq equations; Nonlinearity; Dispersion; Standing wave; Solitary wav; |
語文 | 中文(Chinese) |
中文摘要 | 本文以時間空間最小平方有限元素法建立淺水波模式(Shallow Water Equations, SWE)與布斯尼斯克模式(Boussinesq Equations, BE),模擬封閉平坦水槽內不同水深之駐波運動。在淺水(長波)情況下,兩模式計算結果與微小振幅波理論值相當吻合;在深水(短波)之模擬,BE模式計算之振福與波速皆優於SWE模式。兩模式並應用於等水深渠道孤立波傳遞之模擬BE模式較SWE模式更準確預測孤立波之波幅、波速與守恆性質,尤其當頻散效應(波長與水深之關係)顯著時。 |
英文摘要 | Numerical solution of shallow-water equations (SWE) and Boussinesq equations (BE) using space-time least-squares finite element method is developed. Both models are applied to standing wave, ranging from shallow-water (long waves) to deep water (short waves), in a flat closed basin. Computed results of both models for shallow water waves agree well with solution of the small amplitude wave theory. However, for deep water waves prediction of BE model outperforms SWE model in terms of wave amplitude and wave speed. Both models are then applied to solitary wave propagation over a constant depth channel. Dispersive BE model gives better prediction of wave amplitude, frequency, and conservation property than non-dispersive SWE model does, especially when the dispersion effect, i.e., ration of water depth to wave length, is significant. |
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