本文之目的在於以數值方法來模擬多元流體下之自由液面流場，並研究不同參數選擇對多元流體下之自由液面流場之影響。數值方法以三階向風有限體積法計算不可壓縮奈威-斯托克方程式(Navier-Stokes Equations)。並利用每個單位體績之體積佔有率來描述多元流體之佔有率。由於自由液面之界面類似震波之鋒面；而本文採用斜率修正法，能精確的捕捉自由液面之界面。並計算多元流體內鋼體運動之速度，以模擬鋼體運動之流場
在物理問題方面，我們選取了幾個簡單的例子：二維水壩潰堤問題、二維水滴掉落問題、阿基米得自由落體模型、和二維鋼體運動問題等。首先先驗證在本文中數值方法的準確性，再來改變雷諾數以分析與討論流場上的變化進而得到雷諾數對多元流體下之自由液面流場之影響。

A numerical method is developed to simulate the free-surface flows and is used to investigate the effects of different parameters, such as Reynolds number and density ratio. The numerical method is uses a third-order upwind finite-volume method to solve the steady Navier-Stoke equations. The artificial compressibility method is applied in the continuity equations and different kinds of fluid sate described by using the ratio volume of fluid occupied in an unit volume. Because the interface of free surface alikes the front of a shock wave; the slope modification method is used to exactly capture the interface of free surface. Also, the formulas of the speed of rigid body motion is derived to simulate the flow field of rigid body motion.

Several problems are chosen: two dimensional broken dam problem, two dimensional fall droplet, Archimedes’ model, and two dimensional rigid body motion. In the broken dam problem, the effect of Reynolds number is investigated. In the Archimedes’ model, the accuracy of the formulas of the speed of rigid body motion is analyzed.

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