本文旨在建議一個代數格網生成方法，以計算圓柱體於大型圓形液槽內水平振動之流場。此格網生成法利用代數分解各格點之位置向量至多個簡單的向量函數，以簡單之代數函數關係構建所需格網。以此流場問題為例，本文將使用兩個向量，一為線性向量一為極座標向量，其中線性向量表示由極座標向量於固定半徑下所描繪之偏心圓(η格線)圓心位置，並由此得到正交於偏心圓之另一族格線(ξ格線)。藉由此方式，格網可由調整兩向量之長度與角度構成，故模擬圓柱振動產生之流場擾動時，我們只要隨時間改變圓柱體圓心之位置(即線性向量之長度)，則可瞬時構建格網。更佳的是，我們已經得到流場所需之解析幾何轉換關係。流場方程式使用流函數-渦度模式，以有限解析法進行離散，求解內部的流函數、渦度等變數，為加快收斂速度，使用對角矩陣法與超鬆弛收斂法進行疊代，並使用均勻流流經固定圓柱的問題作為模式測試工具，檢驗流場的正確性。驗證結果與流場可視化實驗結果相一致，而對不同流場條件下之圓柱體振動問題進行研究，可觀察出較特別的部份為圓柱周圍的震盪邊界層(Oscillatory Boundary Layer) 和與其相鄰的穩態致流邊界層(Streaming Boundary Layer)。計算出之質點追跡結果亦與前人流場可視化結果相近似，此外進行了大位移振動問題之模擬，亦給了我們不少有用的資訊。

The thesis suggests an algebraic grid generation method for calculating the transient flow problem of a small rigid circular cylinder oscillating rectilinearly inside a large circular fluid tank. This grid method based on decomposition of position vectors at all grid points into several vectors enables easy representation by simple algebraic functions, leading to a tractable scheme to constructed the desired grid system. For this flow example, two decomposed vectors were used, one linear and the other polar. The linear vector describes the displacement center of an eccentric circle that is described by the second polar vector of fixed radial distance to form a circular grid line ( -line). On this circle, we then obtained the grid points so that another family of grid lines ( -lines) passing through them are orthogonal to the circle. By this way, an orthogonal grid system can be constructed by adjustment of the length and radius of two vectors. To simulate the flow disturbed by a cylinder in oscillation, we just adjusted the cylinder center (the length of linear vector) and the grid was constructed immediately. Even better than all, we had analytic geometry relations for the transformed flow equations. Moreover, the flow was modeled by streamfunction-vorticity formulation which was discretized by the finite analytic (FA) method. To accelerate the convergence of numerical solution, the tri-diagonal matrix algorithm with successive over-relaxation (SOR) technique was also applied. The problem of a uniform flow passing over a fixed circular cylinder was first adopted to validate our method. The consistent result with experimental visualization confirmed this validation. The problem with the oscillating cylinder in the tank was then studied under various flow conditions. They show the special flow pattern of the oscillatory boundary layer surrounded by outer streaming boundary layers around the cylinder. The calculated path lines were comparable with the flow visualization in the present study. The extension to large deformation of fluid-structure interaction problem indeed gave useful information in our simulation.

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