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博碩士論文 etd-0720107-131045 詳細資訊
Title page for etd-0720107-131045
論文名稱
Title
邊界近似法求解Stoke流體問題
Boundary Approximation Method for Stoke's Flows
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
43
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
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
統計
Statistics
本論文已被瀏覽 5774 次,被下載 1593
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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