當均勻穩態不可壓縮黏性流體通過單一圓柱時，常在圓柱兩側產生分離流動，並在後方形成非穩態尾流。分離和尾流之流況均與雷諾數有關，並密切影響圓柱所受之阻力。而柱體強制振動於靜止黏滯流體中，與均勻流流經圓柱形成流場極為相似，且固體邊界位移函數若隨時間有非線性變化，則考慮座標隨時間變化情形易在內部流場計算上有誤差累積的嚴重問題，因此文中以相對運動關係考慮流場計算，由流體流入流出物理範圍，以絕對座標計算流場，輸出時則以相對座標決定位置，以邊界速度的變化控制流場計算內部。

本文旨在應用數值方法，探討不同雷諾數下，柱體強制振盪產生非穩態層流流況。流場模式使用流函數與渦度函數，以高精度有限解析法離散，並根據轉換函數直接計算幾何係數(而不用差分法近似計算微分項)，文中分別就格網系統、均勻流通過圓柱流場及柱體振動致流流場3項目做一比較驗證。本文將先就不同雷諾數下流體通過圓柱流場之計算流況與Van Dyke(1982)實驗照片比較驗證，再就柱體振動圓柱形成流況分析討論結果。

在傳統的二維黏滯流體力學理論發展，經常使用流函數-渦度函數方程組來求解，並得到相當良好之結果。基於流函數-渦度法具有流函數為純量易處理、所得解必滿足質量守恆、且本方程組可避免Navier-Stokes壓力項之困擾、能敏感地表現流場對流與擴散之情況等等好處，因此本研究便以流函數-渦度函數法來建立數學模式，並考慮開放性邊界條件，以有限解析法求解內部流場之流函數與渦度，來建立圓柱振盪的數值模式，試圖適當地簡化問題，以期能提供一般非穩定、黏性流場的數值模式供實際上之應用。

　While the stable viscous incompressible flow cross through a single circular cylinder, it always result in the separated streaming and unsteady vortex streaming generated behind the circular cylinder. The separate and vortex streaming is relative to the Reynolds Number and the effect of the drift on the circular cylinder closely. The forced oscillation of the circular cylinder in the rest liquid is similar to the streaming field induced by the uniform flow through a circular cylinder. If the displacement function of the solid boundary had nonlinear evolution by time, then the count error would be a serious problem which accumulated by the grid alteration. There for, we consider the comparative motion with the field computation. This field simulated by input and output the flow in the physical region. We compute the field in absolute grid and consider the comparative grid to output data, and control the boundary velocity to computing.

The purpose in this paper is to employ the numerical method to discuss the flow field induced by forcing oscillation circular cylinder in various Reynolds number. The model is built by stream-function and vorticity-function, discretized by finite-analytic method, and differs the geometry coefficient without difference. The thesis would compares the grid systems and the uniform flow pass a circular cylinder flow field and the flow field induced by a forcing oscillation circular cylinder. We would compare the uniform flow through a circular cylinder flow field at different Reynolds number with Van Dyke(1982), then discuss the result which induced by the forcing oscillation circular cylinder.

In the traditional two dimension fluid dynamic evolution process usually obtain the result which is not bad that solved problems by stream-vorticity function. In oder to the stream-vorticity function is scalar, it must be satisfied with the conservation of mass, and the function avoiding the pressure in Navier-Stokes equation, and performs the characteristic of the flow field sensitively, and diffusion phenomenon via. Hence, we build the math method by stream-vorticity function, and consider with the open boundary condition. To solve the stream-function and vorticity-function in the flow field by finite-analytic method, and build the numerical method attempt to simplify the problem. And anticipate providing the normal unsteady-viscous flow field numerical method in actuality application.

1、Bertelsen A. F.,(1974)，” An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders ,” Journal of Fluid mechanics, 64(3), 589-597.
2、Bertelsen A. F., Svardal A. and Tjotta S. (1973)，” Nonlinear streaming effects associated with Oscillating cylinders,” Journal of Fluid mechanics, 59(3), 493-511.
3、Van Dyke. M. (1982), “ An album of fluid motion, ” The Parabolic Press, Stanford.
4、Zhang J. and Dalton C. (1993), ” A numerical comparison of morison equation coefficients for low keulegancarpenter number flows : both sinusoidal and nonsinusoidal, ” Journal of Fluids and Structures, 7, 39-56.
5、Fujisawa N. (2001), ” Feedback control of Vortex Shedding from a circular cylinder by Rotational Oscillations, ” Journal of Fluids and Structures, (15)23-37.
6、Guilmineau E. and Queutey P. (2002),” A Numerical Simulation of Vortex Shedding from an Oscillationing circular cylinder, ” Journal of Fluids and Structures, 16(6), 773–794.
7、Haddon E. W. and Riley N. (1979). ”The Steady Streaming induced between Oscillating circular cylinders, ” Q. J.Mech. Appl. Math., 11, 264-282.
8、Lyn D. A.,(2004)，“ Steady and Unsteady Simulations of Turbulent Flow and Transport in Ultraviolet Disinfection Channels, ” Journal of Hydraulic Engineering, 130(8), 762-770.
9、Lyn D. A., Chiu, K., and Blatchley III, E. R.(1999). “ Numerical modeling of flow and disinfection in UV disinfection channels, ” J. Environ. Eng., 125(1), 17-26.
10、Riley N. (1965). ” Oscillating viscous flows, ” Mathematica, 23, 161-175.
11、Riley N. (1967). ” Oscillatory Viscous Flows, Review and Extension, ” J. Inst. Math. Appl., 3, 419-434
12、Riley N. (1975). ” Unsteady Laminar Boundary Layers, ” SIAM Review, 17, 271-297.
13、Stuart J. T. (1965). “ Double boundary layers in oscillatory viscous flow, ” J. Fluid Mech., 24(4) , 673-687.
14、Telionis D. P.(1981), “ Unsteady Viscous Flows ”, New York.
15、Uchiyama T. (2001), “ALE finite element method for gas–liquid two-phase flow including moving boundary based on an incompressible two-fluid model, ” Nuclear Engineering and Design, 205,69–82.
16、Van Dyke M. (1962)." Approximations in boundary-layer theory, " J.Fluid Mech., 5, 161-177.
17、張志華(1997)，「孤立波與結構物在黏性流體中互制作用之研究」，博士論文，國立成功大學水利及海洋工程研究所，台南。
18、張志華(1992)，「孤立波與水工結構物互制的動態分析」，碩士論文，國立成功大學水利及海洋工程研究所，台南。