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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃維信 | zh_TW |
| dc.contributor.advisor | Wei-Shien Hwang | en |
| dc.contributor.author | 許晴 | zh_TW |
| dc.contributor.author | Ching Hsu | en |
| dc.date.accessioned | 2023-11-20T16:17:06Z | - |
| dc.date.available | 2023-11-21 | - |
| dc.date.copyright | 2023-11-20 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-11-07 | - |
| dc.identifier.citation | [1] M. Abramowitz, I. A. Stegun, and R. H. Romer. Handbook of mathematical functions with formulas, graphs, and mathematical tables, 1988.
[2] P. K. Banerjee and B. R. Boundary element method in geomechanics. Chapter 16 in Finite element in geo-mechanics (Ed. G. Gudehus), John Wiley and Sons, New York, 1977. [3] C. A. Brebbia. The boundary element method for engineers. Pentech Press,London, 1978. [4] C. A. Brebbia. Progress in boundary element method. Pentech Press,London, 1, 1981. [5] C. A. Brebbia. Progress in boundary element method. Pentech Press,London, 2, 1983. [6] C. A. Brebbia. Progress in boundary element method. Pentech Press,London, 3, 1984. [7] C. A. Brebbia. Progress in boundary element method. Pentech Press,London, 4, 1984. [8] C. A. Brebbia and S. Walker. Boundary element techniques in engineering. Pentech Press,London, 1980. [9] Y. Cao, W. W. Schultz, and R. F. Beck. Three-dimensional desingularized boundary integral methods for potential problems. International Journal for Numerical Methods in Fluids, 12(8):785–803, 1991. [10] S. K. Chow, A. Y. Hou, and L. Landweber. Hydrodynamic forces and moments acting on a body emerging from an infinite plane. The Physics of Fluids, 19(10):1439–1449, 1976. [11] T. A. Cruse. Numerical solutions in three dimensional elastostatics. International journal of solids and structures, 5(12):1259–1274, 1969. [12] T. A. Cruse, D. W. Snow, and R. B. Wilson. Numerical solutions in axisymmetric elasticity. Computers & Structures, 7(3):445–451, 1977. [13] E. I. Fredholm. Sur une classe d’equations fonctionnelles. Acta Math, 27:365–390, 1903. [14] U. Heise. Numerical properties of integral equations in which the given boundary values and the sought solutions are defined on different curves. Computers & Structures, 8(2):199–205, 1978. [15] J. L. Hess and A. M. O. Smith. Calculation of nonlifting potential flow about arbitrary three-dimensional bodies. Journal of ship research, 8(04):22–44, 1964. [16] C. C. Huang. Experimental study and boundary element method prediction of wave forces on large fixed submerged structures. Texas A&M University, 1988. [17] W. S. Hwang. A regularized boundary integral method in potential theory. Computer Methods in Applied Mechanics and Engineering, 259:123–129, 2013. [18] W. S. Hwang and Y. Y. Huang. Non-singular direct formulation of boundary integral equations for potential flows. International journal for numerical methods in fluids, 26(6):627–635, 1998. [19] M. A. Jaswon. Integral equation methods in potential theory.1. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 275(1360):23–32, 1963. [20] R. L. Johnston and G. Fairweather. The method of fundamental solutions for problems in potential flow. Applied Mathematical Modelling, 8(4):265–270, 1984. [21] O. D. Kellogg. Foundations of potential theory. Springer, Berlin, 1900. [22] J. C. Lachat and J. O. Watson. A second generation boundary integral equation program for three-dimensional elastic analysis. Boundary-integral equation method: Computational applications in applied mechanics, pages 85–100, 1975. [23] H. Lamb. Hydrodynamics. Dover, New York, 57, 1945. [24] L. Landweber and M. Macagno. Irrotational flow about ship forms. Iowa institute of hydraulic research, 1969. [25] S. G. Mikhlin, N. Sneddon, and S. Ulam. Integral equations. international series of monographs on pure and applied mathematics 4. Pergamon Press, London, 1957. [26] F. J. Rizzo. An integral equation approach to boundary value problems of classical elastostatics. Quarterly of applied mathematics, 25(1):83–95, 1967. [27] W. W. Schultz and S. W. Hong. Solution of potential problems using an overdetermined complex boundary integral method. Journal of Computational Physics, 84(2):414–440, 1989. [28] G. D. Smith. Numerical solution of partial differential equations: finite difference methods. Oxford university press, 1985. [29] G. Symm. Integral equation methods in potential theory. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 275(1360):33–46, 1963. [30] W. H. Tsao and W. S. Hwang. Regularized boundary integral methods for threedimensional potential flows. Engineering Analysis with Boundary Elements, 77:49–60, 2017. [31] W. C. Webster. The flow about arbitrary, three-dimensional smooth bodies. Journal of Ship Research, 19(04):206–218, 1975. [32] O. C. Zienkiewicz and P. Morice. The finite element method in engineering science. McGraw-hill London, 1977, 1971. [33] 廖健凱. 邊界元素法對二維翼型之流場分析. 國立臺灣大學碩士論文, 2011. [34] 施育宏. 利用最小方差法對二維翼型之跡流定位. 國立臺灣大學碩士論文, 2012. [35] 李兆芳. 邊界元素法精確上手. 天空數位圖書出版, 2020. [36] 洪立萍. 應用邊界積分法求解二維勢流場問題. 國立臺灣大學碩士論文, 2000. [37] 游騰岳. 邊界積分法對螺槳尾端跡流場之研究. 國立臺灣大學碩士論文, 2017. [38] 鄭人愷. 快速多極點加速之無奇異性邊界積分方程. 國立臺灣大學碩士論文, 2018. [39] 陳正宗，洪宏基. 邊界元素法. 第二版，新世界出版社, 1992. [40] 陳誠宗. 時間領域三維非線性波浪場邊界元素法模擬. 國立成功大學博士論文, 2012. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/91178 | - |
| dc.description.abstract | 本文利用正規化邊界積分法以及邊界元素法兩種數值分析方法對三維流場問題進行探討，並針對奇異點問題以不同方法進行計算，討論其在數值結果上之差異。本研究假設三維流場內之流體滿足勢流理論，並以兩種方法進行討論。其一，利用邊界元素法描繪幾何邊界上之物理量分佈情形，接著以高斯積分對離散後的積分方程式進行積分並組成核函數矩陣。其二，以邊界積分法的佈點概念結合面積權重的計算求得核函數矩陣之數值，以獲得模型表面上之未知物理量。利用此兩種方法結合不同元素之節點分佈方式，計算三維球體及橢球體模型之內、外流場問題，比較及討論其計算結果之均方根誤差、運算時間以及計算複雜度。 | zh_TW |
| dc.description.abstract | There are two numerical analysis methods are used in this paper to discuss the three-dimensional flow field problem. They are the regularized boundary integral method and the boundary element method respectively. We also use different methods to calculate the singular point problem and discuss the differences in numerical results. Assume the fluid in the three-dimensional flow field satisfies the potential flow theory. First, the boundary element method is used to describe the distribution of physical quantities on the boundary. Then, using Gaussian integral to integrate the discretized integral equation and form a kernel function matrix. Second, we use the point distribution concept of the boundary integral method combines with the calculation of weights to obtain the value of the kernel function matrix. With the matrix, we are able to obtain the unknown physical quantities on the model surface.These two methods are combines with the node distribution of different elements to calculate the internal and external flow field problems of the three-dimensional sphere and ellipsoid model. Furthermore, the root mean square error, calculation time and computational complexity of the calculation results are also compared. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-11-20T16:17:06Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-11-20T16:17:06Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝ii
摘要iii Abstract iv 目次v 圖次vii 表次xiii 第一章緒論1 1.1 研究動機及背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 研究目的與方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 第二章基本理論6 2.1 基本假設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 高斯散度定理及格林定理. . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 邊界積分方程式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 流場公式推導. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.1 外流場問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4.2 內流場問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 第三章數值方法17 3.1 邊界元素法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.1 分割元素及形狀函數. . . . . . . . . . . . . . . . . . . . . . . . 18 3.1.2 建立核函數矩陣. . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1.3 數值積分. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.4 奇異點處理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 正規化邊界積分法. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.1 節點佈點. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.2 建立核函數矩陣. . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.3 奇異點處理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 第四章數值分析結果42 4.1 模型一：球體案例分析. . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.1 外流場問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.1.2 內流場問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.1.3 特殊案例計算：外流場. . . . . . . . . . . . . . . . . . . . . . . 72 4.2 模型二：橢球體案例分析. . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1 外流場問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.2 內流場問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.3 小結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 第五章結論與未來展望104 5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 參考文獻107 | - |
| dc.language.iso | zh_TW | - |
| dc.subject | 邊界元素法 | zh_TW |
| dc.subject | 正規化 | zh_TW |
| dc.subject | 勢流理論 | zh_TW |
| dc.subject | 邊界元素法 | zh_TW |
| dc.subject | 邊界積分法 | zh_TW |
| dc.subject | 正規化 | zh_TW |
| dc.subject | 勢流理論 | zh_TW |
| dc.subject | 邊界積分法 | zh_TW |
| dc.subject | Potential Flow Theory | en |
| dc.subject | Boundary Element Method | en |
| dc.subject | Boundary Integral Method | en |
| dc.subject | Regularization | en |
| dc.subject | Potential Flow Theory | en |
| dc.subject | Boundary Integral Method | en |
| dc.subject | Boundary Element Method | en |
| dc.subject | Regularization | en |
| dc.title | 正規化邊界積分法及邊界元素法對三維流場之研究 | zh_TW |
| dc.title | Analysis of Three-Dimensional Potential Flows Using Regularized Boundary Integral Method and Boundary Element Method | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 王昭男;羅弘岳;范佳銘 | zh_TW |
| dc.contributor.oralexamcommittee | Chao-Nan Wang;Hong-Yueh Lo;Chia-Ming Fan | en |
| dc.subject.keyword | 邊界積分法,邊界元素法,勢流理論,正規化, | zh_TW |
| dc.subject.keyword | Boundary Integral Method,Boundary Element Method,Potential Flow Theory,Regularization, | en |
| dc.relation.page | 110 | - |
| dc.identifier.doi | 10.6342/NTU202304398 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2023-11-08 | - |
| dc.contributor.author-college | 工學院 | - |
| dc.contributor.author-dept | 工程科學及海洋工程學系 | - |
| dc.date.embargo-lift | 2025-12-31 | - |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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