跳到主要內容

臺灣博碩士論文加值系統

(3.95.131.146) 您好!臺灣時間:2021/07/29 02:40
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:陳怡雯
研究生(外文):Chen, Yi-Wun
論文名稱:應用Trefftz配點法於滲流問題之研究
論文名稱(外文):Study on Solving Seepage Problems Using the Trefftz Collocation Method
指導教授:顧承宇顧承宇引用關係
指導教授(外文):Ku, Cheng-Yu,
口試委員:劉進賢蘇燕葉為忠顧承宇
口試委員(外文):Liu, Chein-Shan,Su, Yan,Yeih, Wei-Chung,Ku, Cheng-Yu,
口試日期:2016-06-29
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:河海工程學系
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:2016
畢業學年度:104
語文別:中文
論文頁數:107
中文關鍵詞:地下水滲流Trefftz配點法自由液面區域分解法
外文關鍵詞:SeepageTrefftz methodFree surfaceDomain decomposition method
相關次數:
  • 被引用被引用:2
  • 點閱點閱:90
  • 評分評分:
  • 下載下載:10
  • 收藏至我的研究室書目清單書目收藏:0
本研究利用Trefftz配點法求解飽和土層之地下水滲流問題,研究方法採用不須建置網格且不須對邊界進行積分的Trefftz配點法,該法利用近似解表示成線性函數組合使其滿足控制方程式之方式進而求解,與傳統數值方法相比Trefftz配點法求解精度高,且對於不規則邊界問題、不連續邊界問題與對角邊邊界問題的求解較傳統數值方法更具優勢。為解決Trefftz配點法僅應用於單連通問題之限制,本研究另採用多源點Trefftz配點法透過選用多個源點處理複雜之多連通問題,此外本研究利用區域分解法搭配Trefftz配點法進行互層土壤滲流問題之求解。為使本研究發展之模式更適切的模擬真實工程問題,本研究進一步利用Trefftz配點法求解土壩地下水滲流問題,考慮均質土壩、均質土壩含排水孔洞、互層土壩等問題進行分析。結果顯示,本研究以Trefftz配點法所開發之數值模式可分析均質與互層土層地下水滲流問題並獲得良好的應用成果。
This study presents the the numerical solutions for seepage flow in layered soil using the Trefftz collocation method. The Trefftz collocation method is a meshless numerical method with very high accuracy for solving boundary value problems where approximate solutions are expressed as a linear combination of functions automatically satisfy governing equations. To deal with complicated problems for multiply connected domain, the generalized multiple source point boundary collocation Trefftz method which allows many source points in the Trefftz formulation was adopted. In addition, the domain decomposition method which decomposes the problem domain into several simply connected subdomains and to use the Trefftz method in each one was also adopted to solve the seepage flow in layered soil. The validity of of the proposed method is established by conducting several numerical examples in a simply connected domain and a doubly connected domain. Application examples were also carried out using the proposed numerical model. Furthermore, the seepage problems of a vertically layered earth dam with the phreatic surface were also studied. The results revealed that the proposed method can not only obtain numerical solutions for seepage flow in layered soil but also can achieve very high accuracy result in numerical solutions to that of the conventional numerical method.
摘要 I
ABSTRACT II
圖目次 V
表目次 VII
一、緒論 1
1-1前言 1
1-2研究目的與動機 1
1-3研究內容 2
二、文獻回顧 4
2-1地下水滲流數值方法之發展與研究 4
2-2Trefftz配點法之發展與應用 8
三、飽和土層之地下水滲流理論介紹 10
3-1飽和土層地下水之定義與介紹 10
3-2達西定律 12
3-2.1白努利定律 12
3-2.2達西定律 13
3-3飽和土壤地下水滲流之控制方程式 14
四、飽和土層地下水滲流理論推導 20
4-1二維Trefftz配點法基底推導 20
4-2二維Trefftz配點法 27
4-2.1Trefftz配點法介紹 27
4-2.2特徵長度 33
4-2.3Trefftz法之收斂性分析 38
4-2.4Trefftz配點法求解滲流問題流程 39
4-3自由液面問題 45
4-3.1自由液面描述 45
4-3.2自由液面求解流程 46
4-4互層問題 53
4-4.1互層問題描述 53
4-4-2區域分解法 54
五、飽和土層滲流數值模式之驗證 59
5-1驗證案例一(規則型單連通問題) 59
5-2驗證案例二(規則型單連通問題) 63
5-3驗證案例三(規則型單連通問題) 66
5-4驗證案例四(不規則型單連通問題) 70
5-5驗證案例五(不規則型雙連通問題) 74
5-6驗證案例六(自由液面問題) 78
5-7驗證案例七(互層問題) 82
六、飽和土層滲流問題應用案例 86
6-1應用案例一 86
6-2應用案例二 90
6-3應用案例三 94
6-4應用案例四 98
七、結論與建議 102
7-1結論 102
7-2建議 103
參考文獻 104


1. E. Kita, N. Kamiya., T. Iio, Application of a direct Trefftz method with domain decomposition to 2D potential problems. Engineering Analysis with Boundary Elements, vol. 23, p. 539-548, 1999.
2. E. Kita, J. i. Katsuragawa, and N. Kamiya, Application of Trefftz-type boundary element method to simulation of two-dimensional sloshing phenomenon. Engineering Analysis with Boundary Elements, vol. 28, p. 677-683, 2004 .
3. Liu, C. S., A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain’s Characteristic Length. CMES, vol. 21, p. 53-65, 2007.
4. Liu, C. S., A Highly AccurateMCTMfor Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains. CMES, vol. 35, p. 97-111, 2008.
5. Liu, C. S., A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains. Numerical Methods for Partial Differential Equations, vol. 24, p. 179-192, 2008.
6. Liu, C. S., Yeih, W. C., and Satya N. Atluri, On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz ExpansionsWith Multiple Length Scales. CMES, vol. 44, p. 281-311, 2009.
7. Chen, Y. W., Liu, C. S., and Chang, J. R., Applications of the modified Trefftz method for the Laplace equation. Engineering Analysis with Boundary Elements, vol. 33, p. 137-146, 2009.
8. Chen, J.T., Kao, S. K., Lee, W. M., and Lee, Y. T., Eigensolutions of the Helmholtz equation for a multiply connected domain with circular boundaries using the multipole Trefftz method. Engineering Analysis with Boundary Elements, vol. 34, p. 463-470 , 2010.
9. Yeih, W. C., Liu, C. S., Kuo, C. L. and Satya N. Atluri, On Solving the Direct/Inverse Cauchy Problems of Laplace Equation in a Multiply Connected Domain, Using the Generalized Multiple-Source-Point Boundary-Collocation Trefftz Method & Characteristic Lengths. CMC, vol. 17, p. 275-302, 2010.
10. Fan, C. M. and Chan, H. F., Modified Collocation Trefftz Method for the Geometry Boundary Identification Problem of Heat Conduction. Numerical Heat Transfer, Part B: Fundamentals, vol. 59, p. 58-75m, 2011.
11. Liu, C. S., S. N. Atluri, Numerical solution of the Laplacian Cauchy problem by using a better postconditioning collocation Trefftz method. Engineering Analysis with Boundary Elements, vol. 37, p. 74-83, 2013.
12. Ku, C. Y., Three-dimensional Laplacian Problems trefftz CMES, vol. 98, p. 509-514, 2014.
13. Kuo, C. L., Yeih, W. C., Liu, C. S., Chang, J. R., Solving Helmholtz equation with high wave number and ill-posed inverse problem using the multiple scales Trefftz collocation method. Engineering Analysis with Boundary Elements, vol. 61: p. 145-152, 2015.
14. Aitchison, J., Numerical Treatment of a Singularity in a Free Boundary Problem. JProc. R. Soc. Lond. A, vol. 330, p. 573-580, 1972.
15. J. T. Oden, N. Kikuchui, Theory of variational inequalities with applications to problems of flow through porous media. Int. J. Engng Sci, vol. 18, p. 1173-1284, 1980.
16. Lee, K. K., D. I. L., Simulation of a free-surface and seepage face using boundary-fitted coordinate system method. Journal of Hydrology, vol. 196, p. 297-309, 1997.
17. Wang, K. P., J. C. B., Finite element adaptive mesh analysis using a cluster of workstations. International journal for numerical methods in fliuds, vol. 27: p. 179-192, 1998.
18. J. P. Bardet, T. Tobita, A practical method for solving free-surface seepage problems. Computers and Geotechnics, vol. 29, p. 451-475, 2002.
19. Jie, Y. X., Jie, G. Z., Mao, Z.Y., Li, G. X., Seepage analysis based on boundary-fitted coordinate transformation method. Computers and Geotechnics, vol. 31, p. 279-283, 2004.
20. Chen, J. T., Hsiao, C. C., Chiu, Y. P., Lee, Y. T., Study of free-surface seepage problems using hypersingular equations. Communications in Numerical Methods in Engineering, vol. 23, p. 755-769, 2006.
21. Herreros, M. I., M. Mabssout, and M. Pastor, Application of level-set approach to moving interfaces and free surface problems in flow through porous media. Computer Methods in Applied Mechanics and Engineering, vol. 195, p. 1-25, 2006.
22. Darbandi, M., Torabi, S. O., Saadat, M., Daghighi, Y., and Jarrahbashi, D., A moving-mesh finite-volume method to solve free-surface seepage problem in arbitrary geometries. International Journal for Numerical and Analytical Methods in Geomechanics, vol. 31, p. 1609-1629, 2007.
23. Tamer Ayvaz, M. and H. Karahan, Modeling three-dimensional free-surface flows using multiple spreadsheets. Computers and Geotechnics, vol. 34, p. 112-123, 2007.
24. Ahmed, A. A., Stochastic analysis of free surface flow through earth dams. Computers and Geotechnics, vol. 36, p. 1186-1190, 2009.
25. Chaiyo, K., P. Rattanadecho, and S. Chantasiriwan, The method of fundamental solutions for solving free boundary saturated seepage problem. International Communications in Heat and Mass Transfer, vol. 38, p. 249-254, 2011.
26. Bazyar, M. H. and A. Graili, A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows. International Journal for Numerical and Analytical Methods in Geomechanics, vol. 36, p. 1793-1812, 2012.
27. Jie, Y. X. and Liu, Y., Simulated annealing based algorithm for node generation in seepage analysis with meshless method. Mechanics Research Communications, vol. 43, p. 96-100, 2012.
28. Kazemzadeh-Parsi, M. J. and F. Daneshmand, Unconfined seepage analysis in earth dams using smoothed fixed grid finite element method. International Journal for Numerical and Analytical Methods in Geomechanics, vol. 36, p. 780-797, 2012.
29. Wu, M. X., Yang, L. Z., and Yu, T., Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field. Science China Physics, Mechanics and Astronomy, vol. 56, p. 1139-1147, 2013.
30. Bazyar, M. H. and A. Talebi, Locating the Free Surface Flow in Porous Media Using the Scaled Boundary Finite-Element Method. International Journal of Chemical Engineering and Applications, vol. 5, p. 155-160, 2014.
31. Athani, Shivakumar S., Shivamanth, Solanki, C. H., and Dodagoudar, G. R., Seepage and Stability Analyses of Earth Dam Using Finite Element Method. Aquatic Procedia, vol. 4, p. 876-883, 2015 .
32. Zhang, Y. and J. Wang, Solving the seepage problems with free surface by mathematical programming method. Numerical Algebra, Control and Optimization, vol. 5, p. 351-357, 2015.
33. Wang, Y., Hu, M. S., Zhou, Q. L., Rutqvist Jonny, A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains. Applied Mathematical Modelling, vol. 40, p. 1427-1445, 2016.
34. Jaime J. S. P. Cabral1 and Luiz C. WrobeP, Unconfined flow through porous media using B-SFLINE boundary elements, J. Hydraul. Eng., vol. 117, pp. 1479-1494, 1991.
35. Carastoian Andreea, Unsaturated Slope Stability and Seepage Analysis of a Dam, Energy Procedia, vol. 85, pp. 93-98, 2016
36. 郭仲倫,二維多連通區域的拉普拉斯內外域研究,國立臺灣海洋大學機械與機電學系碩士論文,2006。
37. 蘇群川,以擬時間積分法求解地下水滲流問題之研究,國立臺灣海洋大學河海工程研究所碩士論文,2010。
38. 王書翰,Trefftz法應用於三維穩態地下水滲流問題之研究,國立臺灣海洋大學河海工程研究所碩士論文,2013。
39. 蕭靖恩,應用基本解法求解互層土壤地下水滲流問題之研究,國立臺灣海洋大學河海工程研究所碩士論文,2015。
40. 宋希尚,地下水之研究,八版,中正書局,台北,1970。
41. 王如意、易任,應用水文學,國立編譯館出版,1983。

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