請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46752
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 蔡丁貴(Ting-Kuei Tsay) | |
dc.contributor.author | Tun-Chi Yang | en |
dc.contributor.author | 楊敦琪 | zh_TW |
dc.date.accessioned | 2021-06-15T05:27:30Z | - |
dc.date.available | 2011-08-22 | |
dc.date.copyright | 2011-08-22 | |
dc.date.issued | 2011 | |
dc.date.submitted | 2011-08-17 | |
dc.identifier.citation | E. Oñate, S. Idelsohn, O.C. Zienkiewicz, R.L. Taylor, “A finite point method in computational mechanics. Applications to convective transport and fluid flow”, International Journal for Numerical Methods in Engineering, 39, 3839-3866, 1996.
E .Oñate, Idelsohn S, Zienkiewicz OC, Taylor RL, Sacco C, “A stabilized finite point method for analysis of fluid mechanics problems”, Computer Methods in Applied Mechanics and Engineering, 139,315-346,1996. E. Ortega, E. Oñate, S. Idelsohn, “An improved finite point method for tridimensional potential flows”, Computational Mechanics, 40, 949-963, 2007. J.A. Liggett, P.L.-F. Liu, “The Boundary integral element method for porous media flow”, Allen & Unwin: Locdon, 1983. J.F. Thompson, Z.U.A. Warsi, C.W. Mastin, “Boundary-fitted coordinate system for numerical solution of partial differential equations-a review”, Journal of Computational Physics, 47, 1-108, 1982. J.F. Thompson, Z.U.A. Warsi, C.W. Mastin, “Numerical grid generation, Foundation and Applications”, North-Holland: Amsterdam, 1985. John Wang, Ting-Kuei Tsay, Fu-Ru Lin, “A short review of conformal grid generation in an irregular area”, NONLINEAR WAVE DYNAMICS : Selected Papers of the Symposium Held in Honor of Philip L-F Liu’s 60th Birthday, 199 -221 , 11,2008. N.J. Wu, T.K. Tsay, “A Modified Finite Point Method”, International Journal for Numerical Methods in Engineering, 2011. (submitted) T.K. Tsay, B.A. Ebersole, P.L.-F. Liu, “Numerical modeling of wave propagation using parabolic approximation with a boundary-fitted coordinate system”, International Journal for Numerical Methods in Engineering, 27, 37-55, 1989. T.K. Tsay, F.S. Hsu, “Numerical grid generation of an irregular region”, International Journal for Numerical Methods in Engineering, 40, 343-356, 1997. T.K. Tsay, J. Wang, “Analytical evaluation and application of the singularities in boundary element method”, Engineering Analysis with Boundary Elements, 29, 241-256, 2005. T.K.Tsay, J. Wang, Y.T. Huang, “Numerical generation and grid controls of boundary-fitted conformal grids in multiply connected regions”, International Journal for Numerical Methods in Engineering, 67, 1045-1062, 2006. Yaoxin Zhang, Yafei Jia, Sam S.Y. Wang, “2D nearly orthogonal mesh generation with controls on distortion function”, Journal of Computational Physics,218,549-571,2006. 王鄭翰,'應用邊界元素法產生邊界符合保角網格系統及相關奇異性問題研析',國立臺灣大學土木工程學硏究所博士論文,2004。 徐福盛,'區域數值轉換之研究',國立國立臺灣大學土木工程學硏究所碩士論文,1995。 黃永德,'複連通區域多區塊之符合邊界正交網格建立',國立國立臺灣大學土木工程學硏究所碩士論文,1998。 賴俊達,'自動調整微小網格在污染物傳輸計算之硏究',國立國立臺灣大學土木工程學硏究所碩士論文,1998。 羅威麟,'全域轉換法於二維彈性力學之應用',國立國立臺灣大學土木工程學硏究所碩士論文,2007。 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/46752 | - |
dc.description.abstract | 本文旨為在二維圖形中產生符合邊界正交數值網格,以應用於後續其他需要網格的數值方法使用。需要網格的數值方法發展久遠且完善,有其不可被忽略的地位,但建置網格的前置作業困難,尤其在不規則區域,且網格有無符合邊界和是否正交都會影響後續的數值計算結果,因此網格建置很重要。
藉由柯西里曼條件(Cauchy-Riemann condition)的正交性,形成拉普拉斯方程式(Laplace equation),可將二維不規則圖形轉成矩形區域,於矩形區域中建置網格後再經反轉換回原幾何圖形,即可在原幾何圖形中得到正交網格。 使用的方法為無網格法中的修正有限配點法(Modified finite point method, MFPM),為利用相對位置的關係,藉由局部多項式(Local polynomial method)來近似連續函數,以解二維拉普拉斯方程式,優點為其偏導數可直接得到且精準,有利於正交網格的形成,且對於不規則的圖形,無網格法比較容易佈點計算。而修正有限配點法中的參數選擇,使用多目標規劃(Multiple Objective Programming, MOP)挑選出最適合的組合,本文以有解析解的半圓形環狀當做率定的案例。雖然採用無網格法產生網格,但仍不影響本文的價值。 在驗證方面,本文以半圓形環狀、三角標形、圓形環狀、星形、幸運草形以及台灣形狀六個範例為例,與解析解比較或計算相對誤差驗證正交性。本模式的計算成果,除了計算區域內角為鈍角時其鈍角附近計算會有誤差外,其餘皆可得到正確的正交網格,且內角為零度的情況亦可。 | zh_TW |
dc.description.abstract | The purpose of this study is to generate two dimensional orthogonal grids in irregular regions for further computations of grid-based numerical methods. This is because grid-based numerical methods have been fully developed and most numerical models in common uses are still coded with grid-based methods. Grid generation techniques to provide input grid information is essential.
Making use of the orthogonality of Cauchy-Riemann condition, grid generation of the forward and inverse transformations were formulated by solving Laplace equation . The numerical method in this study is a meshless numerical method, namely, modified finite point method (MFPM). Based on collocation, this method uses polynomials as the local solution form needed in the collocation approach. The advantage of this method is not only the values of the solution but also the values of its derivatives can be easily obtained. The meshless numerical method is easier to generate computational points especially in irregular regions for its flexibility in distribution of the grid. In modified finite point method, there are parameters to be determined, and Multiple Objective Programming (MOP) is used. Though the method used in this study to solve the coordinate transformation equation is a meshless one, it shows at least merits of present work with other numerical methods. There are six benchmark problems tested in this study, including a semi-annulus, an area bounded by two triangles, a full annulus, a four-pointed star, a flower like irregular region, and the surrounding area of Taiwan. Correctness of present model is verified by checking the orthogonality of the generated results or comparing with exact solutions. In present model, except at the corner of an obtuse angle, the generated results are very accurate. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T05:27:30Z (GMT). No. of bitstreams: 1 ntu-100-R98521317-1.pdf: 2307401 bytes, checksum: 0745a74dab069523b235c7dd91d5ec59 (MD5) Previous issue date: 2011 | en |
dc.description.tableofcontents | 致謝 ii
摘要 iii Abstract iv 目錄 vi 圖目錄 vii 表目錄 viii 第一章 緒論 1 1.1 研究目的 1 1.2 文獻回顧 1 第二章 研究方法 5 2.1 數值網格轉換的方法 5 2.2 數值方法 16 2.2.1 傳統有限配點法(FPM) 16 2.2.2 修正有限配點法(MFPM) 21 2.3 數值結果驗證 24 2.4 多目標規劃評選 25 第三章 網格形成及結果驗算 28 3.1 範例1半圓形環狀 28 3.2 範例2三角標形 37 3.3 範例3圓形環狀 42 3.4 範例4星形 47 3.5 範例5幸運草形 50 3.6 範例6台灣形狀 54 第四章 結論與建議 59 4.1 結論 59 4.2 建議 60 參考文獻 62 | |
dc.language.iso | zh-TW | |
dc.title | 利用修正有限配點法產生符合邊界的二維正交網格 | zh_TW |
dc.title | 2D Orthogonal Grid Generation of an Irregular Region Using Modified Finite Point Method | en |
dc.type | Thesis | |
dc.date.schoolyear | 99-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 楊德良(De-Liang Young),吳光鐘(Kuang-Chong Wu) | |
dc.subject.keyword | 網格轉換,正交性,柯西里曼條件,拉普拉斯方程式,無網格法,修正有限配點法,多目標規劃, | zh_TW |
dc.subject.keyword | grid generation,orthogonal,Cauchy-Riemann condition,Laplace equation,meshless,modified finite point method,local polynomial approximation,multiple objective programming, | en |
dc.relation.page | 65 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2011-08-18 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 土木工程學研究所 | zh_TW |
顯示於系所單位: | 土木工程學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-100-1.pdf 目前未授權公開取用 | 2.25 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。