(3.235.236.13) 您好!臺灣時間:2021/05/15 02:41
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

: 
twitterline
研究生:江文平
研究生(外文):Wen-Ping Chiang
論文名稱:利用淺水方程式與布氏方程式模擬不同水深駐波之比較
論文名稱(外文):Comparison of Numerical Solution of Shallow-Water Equations and Boussinesq Equations for Standing Wave in a Flat Closed Basin
指導教授:梁興杰
指導教授(外文):Shin-Jye Liang
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:海洋環境資訊學系
學門:自然科學學門
學類:海洋科學學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:47
中文關鍵詞:淺水波模式布氏模式駐波空間時間最小有限元素法
外文關鍵詞:Shallow-Water EquationsBoussinesq EquationsStanding WaveSpace-Time Least-squares Finite-element Method
相關次數:
  • 被引用被引用:1
  • 點閱點閱:149
  • 評分評分:
  • 下載下載:19
  • 收藏至我的研究室書目清單書目收藏:0
本論文利用空間時間最小有限元素法(Space-Time Least-Squares Finite Element Method, STLSFEM)建立淺水波模式(Shallow-Water Equations, SWE)與布氏模式(Boussinesq Equations, BE),模擬封閉平坦水槽內不同水深之駐波運動,並利用Matlab®之 psd函數,分析計算所得之水位與流速時間序列,以探討 SWE與BE 模式之適用範圍,及其對數值精度之影響,並將所得之模擬波速與理論值(淺水波速√gh以及Airy理論值)比較。研究結果發現在淺水情況下,SWE與BE模式均與理論值相當吻合,在中間水深及深水範圍,BE模式計算結果優於SWE模式結果。
Both shallow-water equations (SWE) and Boussinesq equations (BE) are used to simulate standing waves in a flat closed basin with various water depths, ranging from shallow waters to deep waters, where h is the water depth and is the wave length, respectively. Numerical model is based on the space-time least-squares finite-element method (STLSFEM). It is found that computed wave velocity of shallow water waves of both SWE and BE model agrees well with solution of the Airy theory. Computed wave velocity of intermediate water waves and deep water waves of SWE model does not agree with value of Airy theory due to neglecting of vertical acceleration and dispersion. Dispersive BE model gives better prediction of wave amplitude, frequency and conservation property than non-dispersive SWE model does for intermediate and deep water waves.
謝辭 I
摘要 II
Abstract III
目錄 IV
圖目錄 VI
表目錄 VIII
第一章 前言 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 文章組織 3
第二章 駐波 5
2.1 淺水波與深水波 5
2.2 波的疊加與干涉 7
2.3 駐波性質 8
2.4 港池振盪 10
第三章 理論介紹 12
3.1 淺水方程式與布氏方程式 12
3.2 空間時間最小平方有限元素法 13

第四章 結果與討論 14
4.1水深與波長比為2:20之駐波運動模擬結果 17
4.2水深與波長比為5:20之駐波運動模擬結果 18
4.3 結果比較與討論 19
第五章 結論與建議 23
5.1 結論 23
5.2 建議 24
參考文獻 25
附錄一 頻譜分析Matlab 程式原始碼 25
附錄二 時間序列資料頻譜分析範例 25
附錄三 Airy理論波速與布氏方程式Padé近似解之比較 25
附錄四 利用Matlab製作不同水深之駐波動畫 25

1. Ambrosi, D. and Quartapelle, L. (1998), A Taylor–Galerkin Method for Simulating Nonlinear Dispersive Water Waves, Journal of Computational Physics, vol. 146, pp. 546-569.
2. Beji, S. and Battjes, J. A. (1994), Numerical simulation of nonlinear wave propagation over a bar, Coastal Engineering, vol. 23, pp 1-16..
3. Brocchini, M. and Dodd, N. (2008), Nonlinear shallow water equations modeling for coastal engineering, Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 134, pp. 104-120.
4. Chaudhry, M.H. (1993), Open-Channel Flow,Prentice Hall.
5. Gunzburger, M. (1989), Finite Element Methods for Viscous Incompressible Flows, Academic Press.
6. Jiang, B.N. (1988), The Least-Squares Finite Element Method, Theory and Applications in Computatyional Fluid Dynamics and Electromagnetics, Springer.
7. Jiang, B.N. and Carey, G.F. (1987), Adaptive Refinement for Least-Squares Finite Elements with Element-by-element Conjugate Gradient Solution, International Journal for Numerical Methods in Engineering, vol. 24, pp. 569-580.
8. Johnson, R.S. (1997), A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge.
9. Lepelletier, T.G. and Raichlen, F. (1987), Harbor oscillations induced by nonlinear transient long waves, Journal of Waterway, Ports, Coastal and Ocean Engineering, vol. 113(4), pp. 381-400.
10. Li, Y.S. and Zhan, J.M. (2006), Chebyshev finite-spectral method for 1D Boussinesq-type equations, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 132, pp. 212-223.
11. Liang, S.-J. and Jan, Y.J. (2006), Numerical analysis of mass conservation property of the L2 least-squares finite-element methods for Navier-Stokes equations, Journal of Aeronautics Astronautics and Aviation, 2006,pp.199-205.
12. Liang, S.-J. and Chen, Y.C. (2010), Comparison of Numerical Solution of Shallow-Water Equations and Boussinesq Equations for Standing Wave in a Closed Basin, Proceedings of the 32nd Ocean Engineering Conference in Taiwan(第三十二屆海洋工程研討會),National Taiwan Ocean University, Taiwan, R.O.C., November.
13. Liang, S.-J. and Hsu, T.W. (2009), Least-squares finite-element method for shallow-water equations with source terms, Acta Mechanica Sinica, vol.25, pp. 597-610.
14. Liang, S.-J. and Wu, W.C. (2009), Numerical study of wave-bathymetry interactions using shallow-water equations, CSHydro 2009 conference,( 第二屆海峽兩岸船舶、海洋工程與環境工程水動力學研討會), Keelung, Taiwan.
15. Liang, S.-J., Wu, W.C. and Lan, C.Y. (2009), A space-time least-squares finite-element method for equal width equations, Proceedings of the 31st Ocean Engineering Conference in Taiwan(第三十一屆海洋工程研討會), pp. 31-37, Taichung, Taiwan, R.O.C., November 26-27.
16. Lin, P. (2008), Numerical Modeling of Water Waves, Taylor & Francis.
17. Liu, P. L.-F. (1994), Model Equations for Wave Propagation from Deep to Shallow Water, Advances in Coastal Engineering, World Scientific, Singapore, vol. 1, pp. 125-157.
18. Liu, P. L.-F. and Chen, Y. (1995), Modified Boussinesq Equations and Associated Parabolic Models for Water Wave Propagation, Journal of Fluid Mechanics, vol. 288, pp. 351-381.
19. Madsen, P.A. and Sorensen, O.R. (1992), A New Form of the Boussinesq Equations with Improved Linear Dispersion Characteristics. Part 2. A Slowly-Varying Bathymetry, Coastal Engineering, vol. 18, pp. 183-204.
20. Masud, A. and Hughes, T.J.R.(1997), A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems, Computer Methods in Applied Mechanics and Engineering, vol. 146, pp. 91-126.
21. Molls, T. and Chaudhry, M.H. (1995), Depth-averaged open-channel model, Journal of Hydraulic Engineering, vol. 121,pp. 453-465.
22. Nwogu, O. (1993), Alternative for Form of Boussinesq Equations for Near shore Wave Propagation, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 119, pp. 618-638.
23. Paulo, A.–V. and Fernando, J. S.-S. (2009), A High-order Petrov-Galerkin Finite Element Method for the Classical Boussinesq Wave Model, International Journal for Numerical Methods in Fluids, vol. 59, pp. 969-1010.
24. Peregrine, D.H. (1967), Long Wave on a Beach, Journal of Fluid Mechanics, vol. 27, pp. 815-827.
25. Rogers, S.R. and Mei C.C. (1978), Nonlinear Resonant excitation of a long narrow bay, Journal of Fluid Mechanics, vol. 88, pp. 161-180.
26. Thompson, E.G.(2004), An Introduction to the Finite Element Method, John Wiley & Sons.
27. Tsay, T.K. and Liu, P. L.-F. (1983), A finite element model for wave refraction and diffraction, Applied Ocean Research, vol. 5, No. 1, pp. 30-37.
28. Wei, G. and Kirby, J.T. (1995), Time-dependent Numerical Code for Extended Boussinesq Equations, Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 121, pp. 251-261.
29. Woo, S.B. and Liu, P. L.-F. (2004), Finite-Element Model for Modified Boussinesq Equations, II : Applications to Nonlinear Harbor Oscillations, Journal of Waterway, Port, Coastal and Ocean Engineering, vol. 130, pp. 17-28.
30. 吳威均 (2010),利用淺水方程式研究地形對波浪變形之影響,國立台灣海洋大學海洋環境資訊系研究所碩士論文。
31. 岳景雲、曹登皓 (2005),不透水半圓形離岸堤對矩形港池水面波高分佈之研究,海洋工程學刊,第5卷,第1期,第31-50頁。
32. 林鼎傑 (2005),高階Boussinesq模式於港池振盪之數值模擬,國立成功大學水利暨海洋工程研究所碩士論文。
33. 許泰文 (2003),近岸水動力學,科技圖書。
34. 張憲國 (2006),基礎波浪理論,http://ocean.cv.nctu.edu.tw/。
35. 陳盈智 (2012),利用淺水波方程式與布氏方程式模擬波浪通過潛堤之比較,國立臺灣海洋大學海洋環境資訊系研究所碩士論文。
36. 蔡立宏 (2000),花蓮港港池共振機制及改善對策之研究,交通部運輸研究所。
37. 藍烱揚 (2012),二元樹調適網格結合空間時間最小平方有限元素法之應用,國立臺灣海洋大學海洋環境資訊系研究所碩士論文
38. 傅崇徳 (2006),利用布氏模式模擬非水性水波通過規則底床之研究,國立成功大學水利暨海洋工程研究所碩士論文。

連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top