本文利用簡化的晶格波茲曼方法(LB Model)來處理採用Boussinesq 模式為浮力項的晶格波茲曼方程式，並針對二維自然對流在封閉空穴幾何下，在不同的紐森數(Knudsen number) 、瑞里數(Rayleigh number)，以及在固定的普蘭特常數(Prandtl number)為空氣(Pr=0.71)的條件下，探討流體行為以及其不穩定現象。在本研究中，紐森數範圍設定為Kn = 10^(−4)~ 10^(−2)，瑞里數範圍設定在Ra <=4×10^5。針對從巨觀到介觀的流體行為及其不穩定現象做分析及探討。在使用晶格波茲曼方法來模擬自然對流的問題中，對於選擇適當的浮力速度( )是非常重要的。因此，本研究提出由kinetic theory為基礎所推導出來的特徵浮力速度來模擬自然對流的問題，並且利用頻譜分析(spectrum analysis)技術來分析非穩態流場的週期性(periodic)之流體不穩定行為。再利用紐賽數(Nusselt number) 及瑞里數(Rayleigh number)來判定發生非穩態且不穩定流體行為的產生機制及範圍。從本研究的相關結果中可以得知，流體穩定行為與紐森數(Knudsen number) 、瑞里數(Rayleigh number)等，有很大的關聯。尤其是紐森數(Knudsen number)，其影響流體發生不穩定現象的效應更是明顯。最後，找出紐森數與發生二次不穩定現象之臨界瑞里數(Second Critical Rayleigh number)之關係。

In many scientific and industrial applications, natural convection inside a closed cavity is one of the interesting and extensive problem. Many kinds of numerical methods have been applied to analyze this problem. The lattice Boltzmann method (LBM), one of the most powerful computational fluid dynamics (CFD) methods in recent years, was used in this problem. Using a simple LB model with the Boussinesq approximation, this study investigates the 2D natural convection problem inside a rectangular cavity at different Rayleigh numbers and Knudsen numbers when the Prandtl number is fixed as within the range of Ra <=4×10^5 from macroscopic scale to mesoscopic scale Kn = 10^(−4)~ 10^(−2) respectively. The flow structures with instability phenomena from macroscopic scale to mesoscopic scale are compared and analyzed. A model for choosing the appropriate value of the velocity scale in simulating the natural convection problems, i.e. , is important by the LBM. Current work presents a model to determine the value of characteristic velocity (V) based on kinetic theory. A spectrum analysis is performed to identify the frequency of the unsteady periodic oscillatory flow. The relationship between the Nusselt number and the Rayleigh number is also explored. The simulation results show that the onset of the instable flow is dependent on both the Rayleigh numbers and Knudsen numbers. The Knudsen number plays a significant role to influence the oscillatory flow structures. Finally, the relation between the Kundsen numbers and the secondary critical Rayleigh number of generating secondary instability is established by a curve fitting technique.

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