在過去的研究中，學者對於橫流通過圓柱或運動圓柱在靜止水中之研究，特別有興趣。尤其在海岸工程及土木工程或熱傳設計方面尤被重視。過去二十年中，實驗及數值為兩大方法解圓柱受力過程。在本研究擬以二維之有限差分法來討論黏性流體通過運動圓柱之流場變化。除分析前人所深入關於可移動圓柱在靜止流場、或均勻橫流條件下之流場分析外，並分析圓柱受力情況；本文採用與時間無關之網格，應用有限差分法解二維橫流通過固定或水平移動之圓柱。目前研究比對了前人兩種模式：Re= 100， KC = 5 和Re = 200，KC = 4，之數值結果都相當吻合。所以此數值方法能容易應用在黏性流體和運動圓柱之間的分析上。
前人多分析均勻橫流之流體，流體經過結構體後依不同雷諾數下之運動狀態分析。在此，我們考慮振動橫流狀態，流經一可移動與彈簧聯繫之圓柱，圓柱從初始位置零點釋放後，會因振動流場施與圓柱作用力而驅使圓柱運動。由於加入彈簧與阻尼效應的影響，使圓柱產生阻力及回復力，此發展的數值模式將容易應用在探討流場流經運動圓柱後，產生之流體與結構互制反應分析。

In the present study, circular cylinders in the cross-flow or the motions of circular cylinders in a fluid at rest are especially of interest in fields, such as offshore and civil engineering or heat exchanger. For last two decades, the researches of the force caused by the fluid on the cylinder surface are mainly studied by the ways of experiment and numerical methods. A time-independent finite different method is developed to solve the two-dimensional fixed or transversely oscillating cylinder passing by a cross flow. The present study focuses on the cylinder under a cross flow with only two kinds of conditions, which are Re = 100, KC = 5 and Re=200, KC=4. The benchmark tests of the present numerical results are made and validated by the reported numerical simulation and experimental results, for instant, the flow visualization of the vorticity contours and the in-line force for a flow across a moving circular cylinder. The developed numerical method can easily apply on the analyses of interactions between viscous flow and motion cylinder. Besides, we also consider the oscillatory flow passes a circular cylinder connecting with a spring. The spring -linking cylinder is released in the beginning on the position of zero deflection of the spring and stares moving due to the influence of the in-line force acting on the cylinder. We can find that the spring-linking cylinder under a oscillating flow produces restoring force and drag force due to considering the influence of the spring and damping effect, the developed numerical method can easily apply on the analyses of interactions between viscous flow and oscillating cylinder.

中文摘要 I
目錄 III
圖表目錄 V
符號表 VII
第1章 概論 1
1.1 前言 1
1.2 文獻回顧 2
1.3研究目的 5
第2章 理論分析 6
2.1 問題分析 6
2.2座標轉換 8
2.3控制方程式 10
2.4邊界條件與初始條件 13
2.4-1 圓柱表面之邊界條件 13
2.4-2 無限遠處之邊界條件 14
2.4-3 初始條件 15
2.5無因次化 16
第3章 數值方法 21
3.1 網格形式 21
3.2 有限差分之數值解法 23
3.2-1時間項的處理 23
3.2-2聯立方程式的求解 23
3.2-3對流項處理方法 24
3.2-4積分方法 25
3.2-5移動座標相對加速度處理 25
3.3 控制方程式的有限差分式 27
3.4 邊界條件的有限差分式 32
3.4-1圓柱表面邊界 32
3.4-2無限遠處邊界 33
3.5 RUNGE-KUTTA 法 33
3.6 數值解的收斂條件 37
3.7 計算流程 38
第4章 結果與討論 39
4.1無線遠處邊界及網格驗證 39
4.2模式驗證 42
4.2-1流體流經強制水平震動圓柱 42
4.2-2靜止流場中圓柱水平週期震動 47
4.2-3驗證週期震動流場中圓柱之流場變化 52
4.2-4週期震動流場中，彈簧與阻尼對
可水平移動圓柱之影響 56
第五章 結論與建議 63
5.1 結論 63
5.2 建議 64
參考文獻 65
附錄A 係數轉換 68
附錄B 70

Anagnostopoulos, P. (1989). "Numerical solution for laminar two-dimensional flow about a fixed and transversely oscillating cylinder in a uniform stream." Journal of Computational Physics v85( Issue 2): Pages 257-505.

ANAGNOSTOPOULOS, P., ILIADIS, G. & RASOUL, J. (1993). Numerical solution of oscillatory flow around a circular cylinder at low Reynolds and Keulegan-Carpenter numbers. In Proceedings of the Eight International Conference on Finite Elements in Fluids (eds K. Morgan, E. Onate, J. Periaux, J. Peraire & O. C. Zienkiewicz): Pages. 258+267. Barcelona, Spain.

ANAGNOSTOPOULOS, P. (1994). Numerical investigation of response and wake characteristics of a vortex excited cylinder in a uniform stream. Journal of Fluids and Structures v8: Pages 367+390.

ANAGNOSTOPOULOS, P., ILIADIS G. & GANOULIS, J. (1995). Flow and response parameters of a circular cylinder vibrating in-line with the oscillating stream. In Proceedings of the 6th International Conference on Flow-Induced »ibration (ed. P. W. Bearman), pp. 167+179. London, U.K.

Anagnostopoulos, P. and G. ILIADIS (1998). “Numerical study of the flow pattern and the in-line response of a flexible cylinder in an oscillating stream.” Journal of Fluids and Structures 12: Pages 225-258.

Baba, N. & Miyata, H. (1987). Higher-order accurate difference solutions of vortex generation from a circular cylinder in an oscillatory flow. Journal of Computational Physics v69: Pages363+396.
Chia-Shun Yih,Corrected Edition,(1979). FLUID MECHANICS. A concise introduction to the theory. Pages 598-616.

Chang, C. C., Chern, R. L. (1991). “A numerical study of flow around an impulsively started circular cylinder by a deterministic vorteFluid Mechanics v 473, n 473: Pages 147-166.
GRAHAM, J. M. R. & DJAHANSOUZI, B. (1989). Hydrodynamic damping of structural elements. In Proceedings of the 8th International Conference on Offshore Mechanics and Arctic Engineering (eds J. S. Chung, H. Maeda & T. Huang), v 2: Pages 289+293. The Hague, The Netherlands.

Govardhan, R. A. E. D., Indian Institute of Technology; Williamson, C.H.K. (2002). "Resonance forever: Existence of a critical mass and an infinite regime of resonance in vortex-induced vibration." Journal of Fluid Mechanics v473,n473: Pages 147-166.

H. Du¨tsch, F. D., S. becker and H. Lienhart (1998). "Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers." J. Fluid Mech. v360: Pages 249-271.

ILIADIS, G. and P. Anagnostopoulos (1998). "Viscous oscillatory flow around a circular cylinder at low Keulegan-Carpenter numbers and frequency parameters." International Journal For Numerical Methods In Fluids v26: Pages 403-442

Loc, T. P. and R. Bouar d (1985). "Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder：a comparison with experimental visualization and measurement." Journal of Fluid Mechanics v160: Pages 93-117.

Mittal, S. A. H.-P. C. R. C. and T. E. Tezduyar (Nov 15, 1992). "A finite element study of incompressible flows past oscillating cylinders and aerofoils." International Journal for Numerical Methods in Fluids v 15, n 9: Pages1073-1118
Okamoto, Shiki; Kondo, Yoshinobu (2002). “Fluid force acting on two-dimensional square cylinder in lock-in phenomenon.” Nippon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B, v 68, n 667, March, Pages 726-732

Sarpkaya, T. (1986). "Force on a circular cylinder in viscous oscillatory flow at low Keulegan-Carpenter numbers. " J. Fluid Mech. v165, Pages61-71

SKOMEDAL, N. G., VADA, T. & SORTLAND, B. (1989). "Viscous forces on one and two circular cylinders in planar oscillatory flow. " Applied Ocean Research 11: Pages 114+134.

SMITH, P. A. & STANSBY, P. K. (1991). "Viscous oscillatory flows around cylindrical bodies at low Keulegan-Carpenter numbers using the vortex method. " Journal of Fluids and Structures 5: Pages339+361.

Tatsuno, M. and Bearman, P. W. (1990). "A visual study of the flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers and low Stokes numbers." J. Fluid Mech. v211:Pages157-182.

WANG, X. & DALTON, C. (1991). "Oscillating flow past a rigid circular cylinder: a finite difference calculation. " ASME Journal of Fluids Engineering 113: Pages 377+383.

于弋翔 (2000).”真實流體通過移動圓柱之流場變化分析”國立中山大學海洋環境及工程學系碩士論文