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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 | 才士欽 | zh_TW |
| dc.contributor.author | Shr-Chin Tsai | en |
| dc.date.accessioned | 2025-08-20T16:07:36Z | - |
| dc.date.available | 2025-08-21 | - |
| dc.date.copyright | 2025-08-20 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-08-13 | - |
| dc.identifier.citation | [1] E. I. Fredholm. Sur une classe d’equations fonctionnelles. Acta Math, 27:365–390, 1903.
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A BEM formulation using B-splines: I-uniform blending functions. Engineering Analysis with Boundary Elements, 7(3):136–144, 1990. [15] L. Landweber and M. Macagno. Irrotational flow about ship forms. Iowa Institute of Hydraulic Research, 1969. [16] F. J. Rizzo and D. J. Shippy. An advanced boundary integral equation method for three-dimensional thermoelasticity. International Journal for Numerical Methods in Engineering, 11:1753–1768, 1977. [17] S. Amini and D. T. Wilton. An investigation of boundary element methods for the exterior acoustic problem. Computer Methods in Applied Mechanics and Engineering, 54(1):49–65, 1986. [18] Y. L. Zang, Y. M. Cheng, and W. Zhang. A higher-order boundary element method for three-dimensional potential problems. International Journal for Numerical Methods in fluids, 21(4):311–321, 1995. [19] R. L. Johnson and G. Fairweather. The method of fundamental solutions for problems in potential flow. Applied Mathematical Modelling, 8(4):265–270, 1984. [20] P. S. Han and M. D. Olson. An adaptive boundary element method. International Journal for Numerical Methods in Engineering, 24(6):1187–1202, 1987. [21] Y. S. Cao, W. W. Schultz, and R. F. Beck. Three-dimensional desingularized boundary integral methods for potential problems. International Journal for Numerical Methods in Fluids, 12:785–803, 1991. [22] 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. [23] W. S. Hwang. A boundary integral method for acoustic radiation and scattering. The Journal of the Acoustical Society of America, 101(6):3330–3335, 1997. [24] W. S. Hwang. Hypersingular boundary integral equations for exterior acoustic problems. The Journal of the Acoustical Society of America, 101(6):3336–3342, 1997. [25] 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. [26] W. S. Hwang. A regularized boundary integral method in potential theory. Computer Methods in Applied Mechanics and Engineering, 259:123–129, 2013. [27] W. H. Tsao and W. S. Hwang. Regularized boundary integral methods for three-dimensional potential flows. Engineering Analysis with Boundary Elements, 77:49–60, 2017. [28] D. A. Dunavant. High degree efficient symmetrical Gaussian quadrature rules for the triangle. International Journal for Numerical Methods in Engineering, 21:1129–1148, 1985. [29] L. N. Trefethen and J. A. C. Weideman. The Exponentially Convergent Trapezoidal Rule. Society for Industrial and Applied Mathematics, 56(3):385–458, 2014. [30] 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. [31] 黃盈翔. 非奇異性邊界積分法對二維矩形流場之數值模擬. 國立臺灣大學碩士論文, 2004. [32] 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. [33] 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. [34] 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. [35] 許晴. 正規化邊界積分法及邊界元素法對三維流場之研究. 國立臺灣大學碩士論文, 2023. [36] 石惠予. 用於流體動力計算之半點高階小板法開發. 國立臺灣海洋大學碩士論文, 2023. [37] 陳正宗、洪宏基. 邊界元素法. 第二版, 新世界出版社, 1992. [38] 李兆芳. 邊界元素法精確上手. 天空數位圖書出版, 2020. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98877 | - |
| dc.description.abstract | 本文對三維流場問題分別以邊界元素法以及正規化邊界積分法進行分析，並且針對不同方法的數值分析結果進行探討。其中，兩種分析方法皆以邊界積分方程式作為理論基礎。本研究假設流場內之流體滿足勢流理論之基本假設，並且針對單位球體分別以不同的數值分析方法計算出球體表面的未知物理量。邊界元素法計算方面，使用了二次元素以進行計算，並且探討不同階數形狀函數的分析結果。邊界積分法計算方面，透過不同的數值積分理論改變計算節點的分布方式，以及節點所對應的權重因子。針對不同分析方法的均方根誤差、計算時間進行互相比較，並且探討出計算效率最高的分析方法。 | zh_TW |
| dc.description.abstract | This paper analyzes the three-dimensional flow field problem using two numerical methods, and discusses the results of different methods. They are the boundary element method and the boundary integral method both of which use boundary integral equations as rationale, respectively. In the study, we assume the fluid in the flow field satisfies the potential flow theory, and calculate the unknown physical quantities on the surface of the unit sphere using different numerical analysis methods. In the boundary element method, quadratic elements are used for calculation, and the analysis results of different orders of shape functions are discussed. In the boundary integral method, different numerical integration theories are applied to change the distribution of calculation nodes and the weight factors corresponding to the nodes. The root mean square error and calculation time of different analysis methods are compared with each other to find out the analysis method with the highest calculation efficiency. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-08-20T16:07:36Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-08-20T16:07:36Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝…….......…………………………………………………………………………. i
摘要…….......………………………………………………………………………… ii Abstract.…………………………………………………………………………….. iii 目次...…….......……………………………………………………………………… iv 圖次...…….......……………………………………………………………………... vii 表次…………………………………………………………………………………... x 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 內流場問題……………………………………………………………… 11 2.5 外流場問題……………………………………………………………… 11 第三章 數值積分方法……………………………………………………………. 16 3.1 邊界元素法……………………………………………………………… 16 3.1.1 元素分割與形狀函數……………………………………………. 16 3.1.2 核函數矩陣………………………………………………………. 22 3.1.3 數值積分…………………………………………………………. 24 3.1.4 奇異性問題………………………………………………………. 29 3.2 正規化邊界積分法……………………………………………………… 33 3.2.1 核函數矩陣………………………………………………………. 33 3.2.2 奇異性問題………………………………………………………. 34 第四章 數值分析結果……………………………………………………………. 38 4.1 外流場問題……………………………………………………………… 40 4.1.1 三角形元素………………………………………………………. 40 4.1.2 四邊形元素………………………………………………………. 49 4.1.3 特殊佈點情形……………………………………………………. 53 4.2 內流場問題……………………………………………………………… 59 4.2.1 三角形元素………………………………………………………. 59 4.2.2 四邊形元素………………………………………………………. 62 第五章 結論與未來展望...……………………………………………………….. 65 5.1 結論……………………………………………………………………… 65 5.2 未來展望………………………………………………………………… 66 參考文獻……………………………………………………………………………. 67 | - |
| dc.language.iso | 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 | Potential Flow Theory | en |
| dc.subject | Regularization | en |
| dc.subject | Boundary Element Method | en |
| dc.subject | Boundary Integral Method | en |
| dc.title | 邊界元素法及正規化邊界積分法對三維流體之計算分析 | zh_TW |
| dc.title | Analysis of Three-Dimensional Fluid Using Boundary Element Method and Regularized Boundary Integral Method | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 王昭男;辛敬業 | zh_TW |
| dc.contributor.oralexamcommittee | Chao-Nan Wang;Ching-Yeh Hsin | en |
| dc.subject.keyword | 邊界元素法,邊界積分法,正規化,勢流理論, | zh_TW |
| dc.subject.keyword | Boundary Element Method,Boundary Integral Method,Regularization,Potential Flow Theory, | en |
| dc.relation.page | 71 | - |
| dc.identifier.doi | 10.6342/NTU202504274 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2025-08-15 | - |
| 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 | N/A | - |
| 顯示於系所單位： | 工程科學及海洋工程學系 | |
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