在本研究中使用Lee與Lin所提出的晶格波茲曼模型進行三維的多相流模擬計算，並在多張圖形顯示卡叢集上運行以獲得液珠撞擊液膜的結果。經由一系列的三維基準測試，驗證目前使用的晶格波茲曼方程方法，包括靜止液珠、單顆液珠撞擊液膜、質量守恆定律與在旋轉流場中開槽球體介面的演化過程。對於各種不同的表面張力下，靜止液珠所產生的內外壓差的數值結果與拉普拉斯定律的理論結果也相符合。而液珠撞擊液膜的模擬，發現擴散半徑隨著時間演變得過程也與理論預測符合。此外，為了提高計算效率，除了將二維平行切割應用在多圖形顯示卡叢集，還採用Allen-Cahn方程的晶格波茲曼模型，得知使用Allen-Cahn方程的晶格波茲曼模型更穩定。

This thesis presents a simulation of a single droplet impact on a thin liquid film using Lee and Lin's three-dimensional two-phase lattice Boltzmann model on the graphics processing unit (GPU) cluster platform. In a series of 3D benchmarks, tests were conducted for validation of the present lattice Boltzmann equation (LBE) method, including a stationary droplet, the impact of a single droplet on a liquid film, the law of conservation of mass and the evolution of an interface in the form of a slotted sphere in a rotational flow field. The numerical results for stationary droplets at different pressures at the droplet interface for various surface tensions agree well with the theoretical solution based on Laplace law. In the simulation of a droplet impact, the time evolution of the crown radius is in good agreement with theoretical predictions. Also, in order to improve computational efficiency, the LBM for the Allen-Cahn equation was conducted. The results show that the LB model for the Allen-Cahn equation is more accurate and more stable.

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