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研究生:洪立萍
研究生(外文):Hung Li-Ping
論文名稱:應用邊界積分法求解二維勢流場問題
論文名稱(外文):Boundary Integral Method in 2-D Potential problem
指導教授:黃維信黃維信引用關係
指導教授(外文):Hwang , W.S.
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:造船及海洋工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2000
畢業學年度:88
語文別:中文
論文頁數:76
中文關鍵詞:邊界積分法無奇異性邊界積分式
外文關鍵詞:boundary integral methodnon-singular boundary integral equation
相關次數:
  • 被引用被引用:6
  • 點閱點閱:274
  • 評分評分:
  • 下載下載:28
  • 收藏至我的研究室書目清單書目收藏:0
本文旨在建立無奇異性邊界積分式的推導。利用高斯通量定理以及將積分式中之奇異性核函數加入一項使其奇異性消除,在將加入函數的解析積分值減回原方程式。經過去除奇異性的步驟後,無奇異性邊界積分方程式即可直接在積分邊界離散。離散方式為直接將分布於積分邊界的積分點視為節點,其滿足邊界條件並組成影響係數矩陣,以求的流場中之速度勢。本文中並探討邊界積分法在平滑邊界流場與非平滑邊界流場中之特性。
This study presents a general non-singular boundary integral equation for potential flow. The singularities of Green’s function and its normal derivative are desingularized theoretically, using a subtracting and add back technique, and Gauss flux theorem, so that any numerical integration methods can be applied directly evaluate all the integrals without any difficulty. The collocation points are chosen to be the nodes of numerical integration. Several numerical examples are calculated with smooth boundary and non-smooth boundary by boundary integral method.
摘要………………………………………………………………….. …I
目錄……………………………………………………………………III
圖目錄………………………………………………………………….V
表目錄………………………………………………………………..VII
第一章 導論……………………………………………………………1
1.1 研究動機……………………………………………………………1
1.2 文獻回顧…………………………………………………………….2
1.3 研究內容及方法…………………………………………………….4
第二章 邊界積分法…………………………………………………….6
2.1 勢流場理論……………………………………………………7
2.2 積分方程式理論……………………………………………….9
2.3 邊界積分方程式………………………………………………11
第三章 數值計算方法與結果…………………………………………26
3.1 外流場邊界離散式……………………………………………26
3.2 內流場邊界離散式……………………………………………28
3.2.1平滑邊界…………………………………………………………..28
3.2.2 非平滑邊界……………………………………………………….30
3.3 例題計算………………………………………………………32
3.3.1 平滑邊界流場算例……………………………………………….33
3.3.2 非平滑邊界流場算例…………………………………………….38
3.4 非平滑邊界之奇異性處理……………………………………40
3.5邊界元素法與邊界積分法的比較…………………………….44
第四章 結論……………………………………………………………46
參考文獻………………………………………………………………..48
附圖……………………………………………………………………..51
附表……………………………………………………………………..56
附錄一…………………………………………………………………...57
附錄二……………………………………………………………..…….59
附錄三…………………………………………………………………...75
1. Lamb H. , Hydrodynamics . Dover : New York , 1945.
2. Hess J.L. and Smith A.M. , ‘Calculation of nonlifting potential flow about arbitraty three-dimensional smooth bodies ,’ Journal of Ship Research 1964 ; 8 : 22-44.
3. Rizzo F.J. , ‘An integral equation approach to boundary value problems of classical elastostatics ,’ Quarterly of Applied Mathematics 1967 ; 25 : 83-95.
4. Cruse T.A. , ‘Numerical solutions in three dimension elastostatics ,’ Int. J. Solids and Structures 1969 ; 5 : 1259-1274.
5. Morino L. and Kuo C.C. , ‘Subsonic potential aerodynamics for complex configurations : a general theory ,’ AIAA J. 1974 ; 12 : 191-197.
6. Djojodihardjo R.H. and Widnall S.E. , ‘A numerical method for the calculation of nonlinear unsteady lifting potential flow problems ,’ AIAA J. 1969 ; 7(10) : 2001-2009.
7. Sarpkaya T. , ‘Computational methods with vortices-the 1988 Freeman Scholar Lecture ,’ Journal of Fluids Engineering 1989 ; 111 : 5-52.
8. Joseph K. and Plotkin A. , Low-Speed Areodynamics From Wing Theory to Panel Methods . McGraw-Hill : New York , 1991.
9. Lachat J.C. and Watson J.O. , ‘Effective numerical treatment of boundary integral equations : a formulation for three-dimensional elasto-statics ,’ Int. J. Numer. Methods Eng. 1976 ; 10 : 991-1005.
10. Rizzo F.J. and Shippy D.J. , ‘An advanced boundary integral equation method for the three-dimensional thermo-elasticity ,’ Int. J. Numer. Methods Eng. 1977 ; 11 : 1753-1768.
11. Zang Y.L. , Cheng Y.M. and Zhang W. , ‘A higher-order boundary element method for three-dimensional potential problems ,’ Int. J. Numer. Methods Fluid 1995 ; 21 : 331-321.
12. Amini S. and Wilton D.T., ‘An investigation of boundary element methods for the exterior acoustic problem ,’ Comput Methods Appl. Mech. Eng. 1986 ; 54 : 49-65.
13. Grilli S.T. and Svendsen I.A., ‘Corner problems and global accuracy in the boundary element solution of nonlinear wave flows ,’ Engineering Analysis with Boundary Elements 1990 ; 7(4) :178-195.
14. Newman J.N. , ‘Distributions of source and normal dipoles over a quadrilateral panel ,’ J. Eng. Math 1986 ; 20 : 113-126.
15. Landweber L. and Macagno M. , ‘Irrotational flow about ship forms ,’ IHHR report , Iowa , No.123 , 1969.
16. Webster W.C. , ‘The flow about arbitrary three-dimension smooth bodies ,’ J. Ship Res. 1975 ; 19 : 206-218.
17. Heise U. , ‘Numerical properties of integral equation in which the given boundary values and the solutions are defined on different curves ,’ Comput. Struct. 1978 ; 8 : 199-205.
18. Han P.S. and Olson M.S. , ‘An adaptive boundary element method ,’ Int. J. Numer. Methods Eng. 1987 ; 24 : 1187-1202.
19. Johnson R.L. and Fairweather G. , ‘The method of fundamental solutions for problem in potential flow ,’ Appl. Math Modeling 1984 ; 8 : 265-270.
20. Schultz W.W. and Hong S.W. , ‘Solution of potential problems using an overdetermined complex boundary integral method ,’ J. Comput. Phys. 1989 ; 84 : 414-440.
21. Cao Y. , Schultz W.W. and Beck R.F. , ‘Three-dimension desingularized boundary integral methods for potential problems ,’ Int. J. Numer. Methods Fluid 1991 ; 12 : 785-803.
22. Hwang W.S. , ‘Hypersingular boundary integral equations for exterior acoustic problems ,’ J. Acoust. Soc. Am. 1997 ; 101(6) : 3336-3342.
23. Hwang W.S. and Huang Y.Y. , ‘Non-singular direct formulation of boundary integral equations for potential flows,’ Int. J. Numer. Mech. Fluids 1998 ; 26 :627-635.
24. Chang J.M. , ‘Numerical studies on desingularized Cauchy’s formula with applications to interior potential problems ,’ Int. J. Numer. Mech. Engng. 1999 ; 46 : 805-824.
25. Yang S.A. , ‘On the singularities of Green’s formula and its normal derivative with an application to surface-wave-body interaction problems ,’ Int. J. Numer. Mech. Engng. 2000 ; 47(11) : 1841-1864.
26. Huang Q. and Cruse T.A. , ‘Some notes on singular integral techniques in boundary element analysis ,’ Int. J. Numer. Methods Eng. 1993 ; 36 : 2643-2659.
27. Johnston P.R. , ‘Semi-sigmoidal transformations for evaluation weakly singular boundary element integrals ,’ Int. J. Numer. Mech. Engng. 2000 ; 47 : 1709-1730.
28. Johnston P.R. and Elliott D. , ‘Error estimation of quadrature rules for evaluating singular integrals in boundary element problems,’ Int. J. Numer. Mech. Engng. 2000 ; 48 : 949-962.
29. Saranen J. , ‘The modified quadrature method for logarithmic-kernel integral equations on closed curves ,’ Journal of Integral Equations and Applications 1991 ; 3(4) : 575-600..
30. Greenberg M.D. , Application of Green’s Functions in Science and Engineering. : Prentice-Hall, 1971.
31. Brebbia C.A. and Dominguez J. , Boundary Elements : An Introductory Course. Computational Mechanics Publications : Southampton , 1989.
32. Becker A.A. , The Boundary Element Methods in Engineering : An Complete Course. McGraw-Hill : New York , 1992.
33. Liu P.L.-F. and Hsu H.W. , ‘Applications of boundary integral equation methods for two-dimensional non-linear water wave problems ,’ Int. J. Numer. Mech. Fluids 1992 ; 15 : 1119-1141.
34. Atkinson K.E. , An Introduction to Numerical Analysis. Second Edition. Willy : New York , 1989.
35. Kopal Z. , Numerical Analysis. Chapman & Hall Ltd.: London , 1955.
36. Currie I.G. , Fundamenral Mechanics of Fluids. McGraw-Hill : New York , 1975.
37. Kythe P.K. , A Introduction to Boundary Element Methods. CRC Press, Inc. : Boca Raton , 1995.
38. Sarpkaya T. and Isaacson M. , Mechanics of Wave Forces on Offshore Structures. Van Nostrand Reinhold Company : New York , 1981.
39. 黃裕洋,「無奇異性邊界元素法求解勢流場之研究」,國立臺灣大學博士論文,1998。
40. 葛家豪,「邊界元素法對三維水沖激問題之數值模擬」,國立臺灣大學碩士論文,1998。
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