本研究發展一個清晰界面算法計算模擬不可壓縮且不混溶之兩相流場。對於界面追蹤的部分，在流體體積法(VOF)的架構下，利用一個通量揉合策略結合上風與下風算則對每個網格格面決定其對流通量，並藉此保持界面的清晰度與形狀。同時，從流體體積函數重建一個符號距離函數，並藉此準確得到界面的曲率與法向向量。基於符號距離函數的資訊，使用一個質量回復技巧(MRT)來消除大於一或小於零之非物理量並同時保持質量守恆。在數值求解暫態不可壓縮之那威爾-史托克方程式方面，使用四步分步算法運用在同心結構網格系統並結合一個動量內插技巧去避免壓力棋盤狀之擾動現象。
在界面流問題當中，界面僞流之生成是一個經典的課題。據我所知，可歸因於三個因素：(1)由連續表面張力(CSF)模型所引進之有限厚度界面區域(2)界面幾何資訊的不準確性(3)界面的表面張力與壓力梯度的數值量之不平衡。在本研究中，奇異的表面張力被直接轉換成壓降形式，且不引進虛擬的界面厚度，同時將在界面不連續之動力黏度給平滑化。並使用鬼流體方法的陡降離散技巧來處理其他物理量之不連續性，同時壓降條件可藉由清晰界面張力(SSF)模型改寫成源項。
一個力量平衡的技巧被發展來確保界面的表面張力與壓力梯度的數值量之平衡。類似於壓力邊界法(PBM)的做法，藉由求解一個狄利克雷問題來獲得離散相中的毛細壓力場，並在數值計算上平衡表面張力，同時使用一個動態壓力場來滿足連續方程式。表面張力所導致之壓力不連續將使壓力的數值邊界條件變得更加複雜，尤其在出口邊界。但可藉由毛細與動態壓力場對壓力的數值邊界條件做出良好的定義與處理。在數值一致性方面，表面張力項與壓力梯度項皆在網格格面上做離散化，並在每一個時間步結合在一起做計算。
藉由各種標準測試範例驗證此計算方法之效率與準確度。本方法可成功計算二維T型管微管流，並進一步研究T 型管中液滴生成與分裂之物理問題。

A sharp interface method for simulating incompressible immiscible two-phase flows is presented in this thesis. Within the framework of volume of fluid (VOF), a flux-blending strategy based on the high resolution upwind and downwind schemes is utilized to determine the convective flux through each cell face and preserve both the interface sharpness and shape. A signed distance function is reconstructed from the VOF function to accurately obtain the interface curvature and normal vector. A mass recover technique, based on the distance information, is proposed to eliminate the overshoot/undershoot problem under the premise of mass conservation. The four-step fractional-step method, applied to a collocated structured grid system, is adopted to solve unsteady incompressible Navier-Stokes equations and coupling with a momentum interpolation technique to avoid the pressure checkerboard phenomenon.
In the interfacial flow problem, the generation of spurious currents near the interface is a classical issue. In our knowledge, it is attributed to three reasons: (i) the finite thickness interface region introduced by the continuous surface tension force (CSF) model,(ii) the inaccurate estimation of geometrical information, (iii) a numerical imbalance between the surface tension force and the associated pressure gradient. In this study, the singular surface tension force is directly transformed into the form of a pressure jump without introducing a fictitious interface thickness while numerically smearing out the dynamic viscosity jump condition. A sharp discretization technique of the ghost fluid method (GFM) is employed to deal with the discontinuous jump of material properties while the pressure jump condition can be rewritten as a source term by a sharp surface tension force (SSF) model.
A balanced-force technique is developed to ensure the numerical balance between the surface tension force and the associated pressure gradient. Similar to the pressure boundary method (PBM), a capillary pressure field within the dispersed phase is obtained from a Dirichlet problem to numerically balance the surface tension force while a dynamic pressure field is used to satisfy the continuity equation. After considering the discontinuity effect induced by the surface tension force, the numerical boundary condition for pressure becomes more complicated, especially in the outlet boundary, and can be well defined by these two pressure fields (capillary and dynamic). For numerical consistency, the surface tension force term and the pressure gradient are both discretized at the cell face and evaluated together at every time step.
The efficiency and accuracy of our method are validated by various benchmark problems. The presented numerical algorithm successfully simulates the two dimensional, microfluidic channels at T-junction and is used to investigate the droplet formation and the droplet breakup problems.

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