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Date: Jan. 13, 2010 Time: 11:50~12:10 Place: Lectrue Theater F

National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering. Null-field boundary integral equation approach for hydrodynamic scattering by multiple circular and elliptical cylinders. Jai-Wei Lee and Jeng-Tzong Chen. Date: Jan. 13, 2010 Time: 11:50~12:10

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Date: Jan. 13, 2010 Time: 11:50~12:10 Place: Lectrue Theater F

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  1. National Taiwan Ocean University MSVLAB Department of Harbor and River Engineering Null-field boundary integral equation approach for hydrodynamic scattering by multiple circular and elliptical cylinders Jai-Wei Lee and Jeng-Tzong Chen Date: Jan. 13, 2010 Time: 11:50~12:10 Place: Lectrue Theater F

  2. Outline • Introduction of NTOU/MSV group • Motivation and problem statement • Method of solution • Illustrative examples • Conclusions

  3. Outline • Introduction of NTOU/MSV group • Motivation and problem statement • Method of solution • Illustrative examples • Conclusions

  4. The 8th ACFD Conference in HK, 2010.1. 10~14 Keelung HKUST NTOU

  5. 1978 1983 1985 1987 1986 1987 1988 1985 NTOU/MSV Group members (2010) 1959 1955 1962 1962 1971 1972 1975 1976

  6. 陳俊賢 (J S Chen, UCLA) Jeong-Guon Ih (KAIST, Korea) (黃晉, China) 陳 鞏(USA, Texas A M) (M.Tanaka, Japan) 余德浩 中國科學院 程宏達 (Alex H.-D. Cheng, USA) 陳清祥 (C. S. Chen, USA) 姚振漢 (Yao Z H, China) 美國 中國 NTOU/MSV visitors 杜慶華 (Q. H. Du,China) 吳漢津 (H C Wu, Iowa, USA) 日 本 南 韓 吳鼎文 (T. W. Wu, USA) 祝家麟 (J. L. Zhu, China)

  7. Outline • Introduction of NTOU/MSV group • Motivation and problem statement • Method of solution • Illustrative examples • Conclusions

  8. Introduction of water wave problem(single cylinder) Analytical solution circular elliptical MacCamy and Fuchs (1954) Goda and Yoshimura (1972)

  9. Introduction of water wave problem(multiple cylinders) y 3 7 1 4 2b 2 x Analytical solutions are not available Semi-analytical methods Spring and Monkmeyer (1974) Multipole expansion Linton and Evans (1990) Chatjigeorgio and Mavrakos (2009) AOR (2009) Meshless method Present method Boundary type (Null-field BIEM)

  10. Introduction of water wave problem(multiple cylinders) OK Multipole expansion OK (Null-field BIEM) ? Multipole expansion To the authors’ best knowledge

  11. Problem statement (3D) constant water depth Governing equation Linearized wave theory and method of separation variables

  12. Reduction to 2D Problem Incident wave field Radiation field Governing equation Boundary condition Governing equation Boundary condition

  13. Outline • Introduction of NTOU/MSV group • Motivation and problem statement • Method of solution • Illustrative examples • Conclusions

  14. Boundary integral equation and null-field boundary integral equation Interior case Exterior case Degenerate (separable) form

  15. Degenerate (separable) form of fundamental solution (2D) Ellipse Extension Circle

  16. Degenerate kernels Addition theorem (Morse and Feshbach’s book) Methods of Theoretical Physics, 1953, p.1421 Normalized constants Modified Mathieu functions of the third kind (norm) Analytical study

  17. Contour plots of the closed-form fundamental solution and the degenerate kernel Re Im Abs Closed-form fundamental solution Degenerate kernel

  18. Degenerate kernels (polar coordinates) (elliptic coordinates)

  19. Expansions of boundary densities and incident plane wave for circular boundaries Boundary densities Fourier series Incident plane wave Polar coordinates

  20. Expansions of boundary densities and incident plane wave for elliptical boundaries Boundary densities Eigenfunction expansion (Mathieu functions) Incident plane wave Elliptic coordinates

  21. Keypoint for solving the problem with elliptical boundaries Orthogonal relations are reserved

  22. Adaptive observer systems and linear algebraic equations Collocation point Boundary contour integration

  23. Outline • Introduction of NTOU/MSV group • Motivation and problem statement • Method of solution • Illustrative examples • Conclusions

  24. Illustrative examples • Case 1: A single elliptical cylinder • Case 2: Two parallel identical elliptical cylinders • Case 3: One circular and one elliptical cylinders

  25. Case 1:A single elliptical cylinder

  26. Resultant forces of an elliptical cylinder Number of degree of freedom [3] Au M. C. and Brebbia C. A., “Diffraction of water waves for vertical cylinders using boundary elements”, Applied Mathematical Modelling, Vol. 7, (1983), pp 106-114.

  27. Resultant forces of an elliptical cylinder Number of degree of freedom [3] Au M. C. and Brebbia C. A., “Diffraction of water waves for vertical cylinders using boundary elements”, Applied Mathematical Modelling, Vol. 7, (1983), pp 106-114.

  28. Case 2: Two parallel identical elliptical cylinders

  29. Resultant forces of two parallel identical elliptical cylinders

  30. Case 3: One circular and one elliptical cylinders

  31. Resultant forces of two cylinders containing one circular and one elliptical cylinder

  32. Outline • Introduction of NTOU/MSV group • Motivation and problem statement • Method of solution • Illustrative examples • Conclusions

  33. Conclusions 1.The higher accurate and faster convergence rate of the present method over the EBM is observed 2.Null-field BIEM in conjunction with adaptive observer system and the degenerate kernel can solve water wave problems containing circular and elliptical cylinders in a semi-analytical way. 3. This method also belongs to a meshless methodsince collocation points on the boundaries are only required.

  34. The end Thanks for your kind attentions Welcome to visit the web site of MSVLAB/NTOU http://msvlab.hre.ntou.edu.tw/

  35. Extension (circle to ellipse) Expand fundamental solution by using the degenerate kernel

  36. Degenerate kernels(polar coordinates) Page 36 2010/01/13

  37. Four degenerate kernels(elliptic coordinates) Page 37 2010/01/13

  38. Adaptive observer systems and linear algebraic equations Collocation point Collocation point Boundary contour integration Boundary contour integration

  39. 國立台灣海洋大學力學聲響振動實驗室(NTOU/MSV Lab) 冰箱 微波爐 信封 講義 論文 書 櫃 敬啟者： 若本人不在辦公室請勞駕至 河工二館三樓三○六實驗室 分機：六一七七 歡迎蒞臨指導 陳正宗敬啟 電腦相關 論文 講義 討論桌 SEVER 大學部 蕭宇志 (國科案) 陳力豪 休 息 區 陳正宗 陳義麟 陳桂鴻 徐文信 周克勳 呂學育 李為民 書 櫃 資 料 庫 茶水 期刊論文 伙 食 期刊論文 期刊論文 期刊論文 期刊論文 工 作 台 大學部 蕭宇志 (國科案) 陳力豪 論 文 論 文 影 本 會 議 資 料 吳建鋒 蔡振鈞 紀志昌 程 式 文具櫃 高聖凱 書櫃 投 影 片 徐胤祥 解 答 沙 發 休 息 區 李文哲 書櫃 李家瑋 軟 體 負責老師：陳正宗 終身特聘教授 (海洋大學河海工程學系) 地點：河工二館 HR2306 室 　陳義麟 副教授 (高雄海洋科技大學造船學系) 聯絡電話：886-2-24622192 ext.6177 or 6140 李為民 副教授 (中華技術學院機械系) URL：http://ind.ntou.edu.tw/~msvlab 呂學育 助理教授 (中華技術學院航空機械系) E-mail：jtchen@mail.ntou.edu.tw 陳桂鴻 副教授 (國立宜蘭大學土木系) Fax：886-2-24632375 　 徐文信 助理教授 (屏東科技大學教學資源中心) 范佳銘 助理教授 (海洋大學河海工程學系) 木櫃 期刊雜誌 技術報告 博碩士論文 論文資料 MSC/NASTRAN 鐵櫃 CTEX 軟體使用手冊 圖書文具 入口

  40. Elliptic coordinates and Mathieu function angular coordinate radial coordinate Mathieu function Modified Mathieu function

  41. Resultant forces of a circular cylinder Number of degree of freedom

  42. Degenerate (separable) form of fundamental solution (1D) jump continuous

  43. Elliptic coordinates and Mathieu function angular coordinate radial coordinate Mathieu function Modified Mathieu function

  44. Difference between the 33rd CTAM and present work Water wave problems Eigenproblems Interior problem Interior problem 33rd CTAM Present work

  45. Resultant forces of an elliptical cylinder [3] Au M. C. and Brebbia C. A., “Diffraction of water waves for vertical cylinders using boundary elements”, Applied Mathematical Modelling, Vol. 7, (1983), pp 106-114.

  46. Boundary densities Expand boundary densities by using the Fourier series andeigenfunction expansion Circular boundaries Elliptical boundaries

  47. Expansions of incident plane wave using the polar and the elliptic coordinates Circular boundaries Elliptical boundaries

  48. Boundary densities Expand boundary densities by using the eigenfunction expansion is a constants along the elliptical boundary

  49. Successful experiences in 2-D eigenproblems with circular boundaries Complex-valued kernel Kernel UT or LM Real-part Inner boundary Imaginary-part Degenerate kernel (Polar coordinates) UT equation (Singular) LM equation (Hypersingular) Spurious eigenvalues Spurious eigenvalues Chen et al. Proc. R. Soc. Lond., Ser. A, 2002 & 2003 Kuo et al. Int. J. Numer. Meth. Engng. 2000 (Found and treated) Key point

  50. Elliptic coordinates and Mathieu function angular coordinate radial coordinate Mathieu function Modified Mathieu function

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