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論文名稱 Title |
邊界近似法求解Stoke流體問題 Boundary Approximation Method for Stoke's Flows |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
43 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2007-06-29 |
繳交日期 Date of Submission |
2007-07-20 |
關鍵字 Keywords |
邊界近似法、滯滑作用、重調和方程 Boundary Approximation Method, Stick-slip, Biharmonic, Stokes flow |
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統計 Statistics |
本論文已被瀏覽 5774 次,被下載 1593 次 The thesis/dissertation has been browsed 5774 times, has been downloaded 1593 times. |
中文摘要 |
我們使用邊界近似法解決流體力學上的滯滑作用。這是一個Stoke’s流體在二維空間中的邊界奇異值問題,我們利用奇異點的附近的邊界條件找出近似的流體方程。邊界近似法隨著基底項數增多、收斂的速度極快,找出的首項係數解也非常準確。 在第二章的部份,stoke’s流體在平滑的平面滑動下產生運動,流經一個有孔洞的平面,底層為一固定的平面。滑動的情形與底層平面跟孔洞平面的距離有關,我們利用兩種不一樣的基底,特徵方程式法與一組極座標特解來找出它的數值解。 |
Abstract |
none |
目次 Table of Contents |
1 Stick-Slip Problem 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Stick-Slip Problem . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Boundary Approximation Method . . . . . . . . . . . . . . . . 9 1.4 Numerical Experiment . . . . . . . . . . . . . . . . . . . . . . 12 1.5 Varied Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 Stokes Flow Across the Slotted Plate 22 2.1 Physical Problem . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2 Particular Solution in Rectangular coordinates . . . . . . . . . 22 2.3 Particular Solution in polar coordinates . . . . . . . . . . . . . 27 2.4 Boundary Approximation Method . . . . . . . . . . . . . . . . 30 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 |
參考文獻 References |
[1] Z.C. Li, T.T. Lu, H.Y. Hu and A.H.D. Cheng, Trefftz and collocation methods, WIT Press, Southampton (2006). [2] F.S. Sherman, Viscous Flow, McGraw-Hill, New York (1990). [3] A.D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC (2002). [4] Z. C. Li, R. Mathon and P. Sermer, Boundary methods for solving el- liptic problem with singularities and interfaces, SIAM J. Numer. Anal. 24, 487-498 (1987). [5] S. Richardson, A stick-slip problem related to the motion of a free jet at low Reynold numbers, Proc. Camb. Phil. Soc. 67, 477-489 (1970). [6] G.C Georgiou, L.G. Olson, W.W. Schultz and S. Sagan, A singular finite element for Stokes flow: the stick-slip problem, Int. J. Numer. Methods in Fluids 9, 1353-1367 (1989). [7] A. Poullikkas, A. Karageorghis and G. Georgiou, Method of fundamen- tal solutions for harmonic and biharmonic boundary value problems, Computational Mechanics 21, 416-423 (1998). [8] M. Elliotis, G. Georgiou and C. Xenophontos, Solution of the planar Newtonian stick-slip problem with the singular function boundary inte- gral method, Internat. J. Numer. Methods Fluids 48, no. 9, 1001-1021 (2005). [9] W.R. Dean and P.E. Montagnon, On the steady motion of viscous liquid in a corner, Proc. Camb. Phil. Soc. 45, 389-394 (1994). [10] M. A. Kelmanson, Boundary integral equation solution of viscous flows with free surfaces, J. Eng. Math. 17,329 (1983). [11] Z.C. Li, H.T. Huang and J.T. Chen, Effective condition number for collo- cation Trefftz methods, Technical Report, Department of Applied Math- ematics, National Sun Yat-sen University, Kaohsiung, Taiwan (2005). [12] C.Y. Wang, Stokes flow due to the sliding of a smooth plate over a slotted plate, Eur. J. Mech. B - Fluids 20, 651-656 (2001). [13] C.Y. Wang, The stokes drag due to the sliding of a smooth plate over a finned plate, Phys. Fluids 6, 2248-2252 (1994). |
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