跳到主要內容

臺灣博碩士論文加值系統

(18.206.76.226) 您好!臺灣時間:2021/07/30 23:27
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

我願授權國圖
: 
twitterline
研究生:陳誠宗
研究生(外文):Cheng-TsungChen
論文名稱:時間領域三維非線性波浪場邊界元素法模擬
論文名稱(外文):Boundary Element Simulation of Three-Dimensional Nonlinear Waves in the Time Domain
指導教授:李兆芳李兆芳引用關係
指導教授(外文):Jaw-Fang Lee
學位類別:博士
校院名稱:國立成功大學
系所名稱:水利及海洋工程學系碩博士班
學門:工程學門
學類:河海工程學類
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:113
中文關鍵詞:三維邊界元素模式非線性方向波繞射矩形潛堤
外文關鍵詞:three-dimensional boundary element modellinear directional wavewave diffractionsubmerged rectangular cuboids
相關次數:
  • 被引用被引用:0
  • 點閱點閱:118
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本論文主要在探討三維邊界元素模式模擬造出非線性波的問題。本模式係延伸陳(1990)二維非線性模式和黃(1988)穩定週期性的三維模式,所建立的時間領域三維模式。為確認三維邊界元素法的正確性,求解海洋結構物受波浪作用的問題,結果與MacCamy and Fuchs (1954)繞射理論解比較,比較之結果顯示相當接近,因此可以證明所建立三維邊界元素法是正確的。接著,計算波浪通過潛式圓形淺灘算例,結果與Williams et al. (1980)試驗結果作比較,結果顯示相當的一致性。同時,也探討波浪通過矩形潛堤繞射問題,研究設定矩形立方體寬長比為3:1,結果顯示潛堤前方堤寬中間點的反射波可以用二維模擬的結果表示,但是堤後方繞射聚焦現象,則無法以二維呈現。
再者,以二維非線性正向波的數值模式為基礎,即係以Galerkin加權殘差之觀念為出發點,將流體運動方程式以及邊界上的運動邊界條件轉換成邊界積分式,並配合常數元素之概念而得到邊界元素方程式,另外再聯合由自由水面動力邊界條件導得之元素方程式,共同組成求解非線性波浪之數值模式。對於此一非線性動力問題之分析則使用對時間的增量表示式並配合Hirt and Harlow (1967)提出之誤差修正法處理。
接著,利用確認的三維邊界元素法架構,將問題的維度延伸至三維進一步計算。此數值模式的計算例中,將模擬造出時間領域線性正向波中央線結果與二維線性解析解和二維邊界元素結果比較,結果顯示三者的波高和相位的頗為一致,但是因計算時間漸增所累積的誤差漸增,因此波峰、波谷的誤差稍有增加,而相位也開始有些偏移。
再者,將模擬造出非線性正向波中央線結果與二維線性解析解和二維非線性有黏性之有限差分結果做比較。結果顯示三者的趨勢相當一致,但本論文的波峰和波谷大部分較二維結果小,而且當計算時間漸增則相位逐漸偏移。然而非線性正向波結果之累積誤差較大,其波峰、波谷及相位偏移的差異比線性正向波結果大。最後,進一步模擬造出時間領域線性方向波,由於波浪往造波平面水槽兩側衰減,結果其水位變化比時間領域線性正向波的結果小。因此可以證明本論文發展之三維時間領域的邊界元素法能夠合理的模擬造出三維線性方向波。

In this thesis, a boundary element numerical model for the simulation of generating three-dimensional nonlinear waves was developed.
The model is an extension of two-dimensional nonlinear model in the time domain developed by Chen (1990) and a seady periodic three-dimensional model developed by Huang (1988). To verify the present numerical model, the problem of wave acting on marine structures is solved. The present results then were compared with the diffraction theory of MacCamy and Fuchs (1954). The comparisons show favorable agreements indicating the accuracy of the present model. Then, the results from the calculation of wave passing submerged circular shoal were compared with experimental results of circular shoal conducted by Williams et al. (1980). It shows considerable consistency. Meanwhile, the wave diffraction passing a submerged rectangular cuboid with the ratio of width to length of the rectangular cuboid being 3:1 was computed. Results demonstrate that wave reflection at the centerline in front of the structure can be duplicated by the two-dimensional results. However, wave diffraction and focusing behind the structure cannot be calculated by the two-dimensional model.
Furthermore, based on the numerical model of the two-dimensional nonlinear wave, wherein the free surface boundary was nonlinear and the wave generation boundary was moving with time. A combined initial and boundary value problem was posed to solve the corresponding unsteady flow problems. A boundary element method with constant element was used to model the problems of time varying, moving boundaries, i.e., the free surface and the structural boundaries. The dynamic free surface boundary condition was considered by applying the Galerkin weighted residual method and then incorporated into the boundary element model. In the dynamic analysis, an incremental expression and Hirt and Harlow’s (1967) error correction procedures were used to solve the nonlinear dynamic problem.
Then, with the confirmed framework of three-dimensional boundary element method, the dimension of the problem extends to three dimension model. For the deep-water wave example, the central results of the linear-normal wave profile generated by piston-type and flap-type wave-maker in the time domain were compared to those of two-dimensional linear analytical solution and two-dimensional boundary element method. It shows that the wave heights and phases are consistent. But due to the increasing error cumulated by lengthening time, the error of the peak and the trough increased slightly and the phase started to shift.
Moreover, the central results of non-linear normal wave profile generated by piston-type wave-maker were compared to those of two dimensional linear analytical solution and two-dimensional non-linear viscous finite difference method. It shows that the trends were consistent, but the wave peak and trough from the present study were smaller than that from two dimension modeling. When computing time increased the wave phases gradually shifted. However, compared to linear-normal wave, the cumulative error of non-linear normal wave was larger and therefore the differences of the peak, the trough and the offset of the phase were greater. Finally, we further simulated the linear directional waves in the time domain. Since the wave decays to both sides of the plane tank, its water level was smaller than that of the linear normal waves in the time-domain. In conclusion, the present boundary element model in simulating three-dimensional linear directional wave can provide reasonable good results.

中文摘要 i
英文摘要 ii
誌謝 iv
圖目錄 vii
符號說明 xiii
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究目的 5
1.4 本論文組織架構 5
第二章 基本理論 7
2.1 問題的描述 7
2.2控制方程式與邊界條件 9
第三章 問題求解方法 11
3.1邊界元素法模式 11
3.2程式計算的流程 18
3.3自由水面的疊代技術 24
第四章 三維線性入射波通過潛堤問題之結果與討論 25
4.1 波浪通過不透水突出水面直立圓柱 25
4.2 波浪通過潛式圓形淺灘 30
4.3 入射波通過潛式矩形立方體 36
第五章 三維非線性波之結果與討論 40
5.1直推式時間領域的三維線性正向波之深水波算例 40
5.2直擺式時間領域的三維線性正向波之深水波算例 49
5.3直推式三維非線性正向波之淺水波算例 55
5.4 直推式三維線性方向波之深水波算例 59
第六章 結論與建議 67
6.1 結論 67
6.1.1關於「三維入射波通過潛堤的問題」之結論 67
6.1.2關於「三維非線性波的問題」之結論 68
6.2 研究建議 69
6.2.1關於「三維入射波通過潛堤的問題」之建議 69
6.2.2關於「三維非線性造波的問題」之建議 69
參考文獻 70
附錄A控制方程式和邊界條件的推導 75
附錄B三維線性入射波通過潛堤的問題 79
附錄C係數矩陣[G]和[H]的正規積分 84
附錄D係數矩陣[G]和[H]的奇異積分 95
附錄E 二維自由水面的疊代技術 100

1.Brandini, C. and Grilli, S. (2001), Modeling of Freak Wave Generation in a 3D-NWT, Proceedings of the International Offshore and Polar Engineering Conference, Vol. 3, pp. 124-131.
2.Boo, S.Y., Kim, C.H. and Kim, M.H. (1994), A Numerical Wave Tank for Nonlinear Irregular Waves by 3-D Higher Order Boundary Element Method, International Journal of Offshore and Polar Engineering, Vol. 4, No. 4, pp. 265~272.
3.Dean, R. G. and Dalrymple, R. A. (1984), Water Wave Mechanics for Engineers and Scientists, Prentice-Hall Inc, Englewood Cliffs, New Jersey.
4.Doo, Y. C., Wu, C. H. and Young, C. C. (2011). An Efficient Curvilinear Non-Hydrostatic Model for Simulating Surface Water Waves, International Journal for Numerical Methods in Fluids, Vol. 66, pp. 1093–1115.
5.Finkelstein, A. (1953), The Initial Boundary Value Problem for Transient Water Waves, Dissertation, New York University.
6.Hirt, C.W. and Harlow, F.H. (1967), A General Corrective Procedure for The Numerical Solution of Initial-Value Problems, Journal of Computational Physics, Vol. 2, pp. 114-119.
7.Hoffmann, K. A. (1989), Computational Fluid Dynamics for Engineers, Engineering Education System, Austin, Texas.
8.Huang, C. C. (1988), Experimental Study and Boundary Element Method Prediction of Wave Forces on Large Fixed Submerged Structures, PhD Thesis, Texas, A&M University.
9.Huang, C. J., Zhang, E. C. and Lee, J. F. (1998), Numerical Simulation of Nonlinear Viscous Wavefields Generated by Piston-Type Wavemaker, Journal of Engineering Mechanics, ASCE, Vol. 124, No. 10, pp. 1110-1120.
10.Jagannathan, S. (1986), Simulation of Two-Dimensional Nonlinear Free Surface Flows, OSDS’86, pp. 130-141.
11.Kennard, E. H. (1949), Generation of Surface Waves By a Moving Partition, Quarterly of Applied Mathematics, Vol. 7, No. 3.
12.Kim, S. K., Liu, P. L. F. and liggett, J. A. (1983), Boundary Integral Equation Solutions for Solitary Wave Generation, Propagation and Run-Up, Coastal Engineering, Vol. 7, pp. 299-317.
13.Kim, M. H. and Celebi, M. S. Kim, D. J. (1998), Fully Nonlinear Interactions of Waves with a Three-Dimensional Body in Uniform Currents, Applied Ocean Research, Vol. 20, pp. 309-321.
14.Lai, C. P. (1986), Wave Interaction with Structures: Hydro-dynamic Loadings on Platforms and Docks, Ph.D. Thesis, University of Southern California, May 1986.
15.Lee, J. F. (1986), Finite Element Analysis of Wave-Structure Interactions in the Time Domain, Ph.D. Thesis, Oregon State University, Oregon, U.S.A.
16.Lee, J. F., Kuo, J. R. and Lee, C. P. (1989), Transient Wavemaker Theory, Journal of Hydraulic Research, Vol. 27, No. 5, pp. 651-663.
17.Liu, P. L. F. and Liggett, J. A. (1982), Applications of Boundary Element Methods to Problems of Water Waves, Chapter 3, in Developments in Boundary Element Methods, Ed. by Banerjee, P. K. And Shaw, R. P., Applied Science Publishers, England, pp. 36-67.
18.MacCamy, R. C. and Fuchs, R. A. (1954), Wave Forces on Piles: A Diffraction Theory, Technical Memorandum No. 69, US Army Beach Erosion Board, Washington DC, USA.
19.Maskell, S. J. and Ursell, F. (1970), The Transient Motion of a Floating Body, Journal of Fluid Mechanics, Vol.pt. 2, pp. 303-313.
20.Multer, R. H. (1973), Exact Nonlinear Model of Wave Generator, J. Hydraulic Div., ASCE, Vol. 1, pp. 31-47.
21.Nakayama, T. and Washizu, K. (1981), The Boundary Eleent Method Applied to The Analysis of Two-Dimensional Nonlinear Sloshing Problems, Int. J. for Num Meth In Engrg., Vol. 19, pp. 953-970.
22.O’Brien, P. J. (1983) A Nonlinear Finite Element Model for The Generation Of Waves in a Laboratory Wave Flume, M.S. Thesis, University College, Galway.
23.Park, J. C., Uno, Y., Sato, T., Miyata, H. and Chun, H. H. (2004), Numerical Reproduction of Fully Nonlinear Multi-Directional Waves by a Viscous 3D Numerical Wave Tank, Ocean Engineering, Vol. 31, pp. 1549-1565.
24.Schäffer, H. A. and Steenberg, C. M. (2003), Second-Order Wavemaker Theory for Multidirectional Waves, Ocean Engineering, Vol. 30, pp.1203-1231.
25.Sulisz, W. and Hudspeth, R. T. (1993a), Complete Second-Order Solution for Water Waves Generated in Wave Flumes, Journal of Fluids and Structures, Vol. 7, pp. 253-268.
26.Sulisz, W. and Hudspeth, R. T. (1993b), Second-Order Wave Loads on Planar Wavemakers, Jourmal of Waterway, Port, Coastal and Ocean Engineering, Vol.119, pp. 521-536.
27.Takayama, T. (1984), Theory of Oblique Waves Generated by Serpent-Type Wave-Maker, Coastal Engineering in Japan, Vol. 27, pp.1-19.
28.Tu, L. F. (2002), The Second-Order Analysis of Wave Propagating over A Rectangular Impermeable Submerged Structure, Master dissertation, Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan.
29.Ursell, F. (1964), The Decay of The Free Motion Of a Floating Body, Journal of Fluid Mechanics, Vol. 19, pp. 305-319.
30.Washizu, K., Nakayama, T., Ikegawa, M. (1978), Application of the Finite Element Method to Some Free Surface Fluid Problems, Finite Element in Water Resources (W.G. Gray, G.F. Pinder, C.A. Brebbia), pp.247-266.
31.Williams, R. G., Darbyshire, J. and Holmes, P. (1980), Wave Refraction and Diffraction in A Caustic Region: A Numerical Solution and Experimental Validation, Proceedings - Institution of Civil Engineers, Vol. 69, No. 2, 635-649.
32.Wu, Y. C. and Dalrymple, R. A. (1987), Analysis of Wave Fields Generated by a Directional Wavemaker, Ocean Engineering, Vol. 11, pp.241-261.
33.Xu, H. and Yue, D.K.P. (1992), Computations of Fully-Nonlinear 3D Water Wave, Proc. 19th Symp. Naval Hydrodynamics, Seoul, Korea.
34.尹彰、周宗仁、林炤圭、黃偉柏(1998),平面造波水池之特性探討,第二十屆海洋工程研討會議論文集,95-102頁。
35.王豪偉、黃清哲和吳京(2004),三維數值黏性波浪水槽之模擬,第二十六屆海洋工程研討會議論文集,101-108頁。
36.李兆芳(1991), 直推式造波其瞬變波浪特性之理論分析,港灣技術第六期,第 23-40頁。
37.李兆芳,劉正祺,藍元志(1994),直擺式造波二階波浪特性,第十六屆海洋工程研討會議論文集,A60-A83頁。
38.周宗仁、尹彰、林炤圭、黃偉柏(1998),有關平面造波水槽內波場方向分佈函數的探討,第二十屆海洋工程研討會議論文集,80-86頁。
39.周宗仁、林騰威、翁文凱(2004),三維數值水槽之開發與研究(Ⅰ)—理論推導與平行計算運用,第二十六屆海洋工程研討會議論文集,109-115頁。
40.陳俠儒、 李自強、唐啟釗和丁舜臣(2007),非線性造波研究,中國土木水利工程學刊,第十九卷,第三期,第 379-387頁。
41.陳春錦(1990),邊界元素法模擬非線性造波,國立成功大學水利及海洋工程研究所,碩士論文。
42.劉正琪(2002),波浪通過潛堤之二階理論解析,國立成功大學水利及海洋工程研究所,博士論文。
43.劉宗龍、雷清宇和黃智偉(2004),數值波浪水槽之發展與應用,第二十六屆海洋工程研討會議專題研究計畫,25-32頁。

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