本論文之主要目的以二維非穩態數值計算平台，模擬傾斜式方形閉合空穴內臨界Ra值10^7到10^9的流場行爲，採用步進演算法計算N-S方程式，由二維的數值模擬，了解傾斜角135°下方形閉合式空穴內不穩定發生的行爲。本研究數值方法採用步進(Fractional Step Method)演算法，將N-S方程式中的速度與壓力分別處理，求解壓力Poisson方程式，並配合理想氣體方程式獲得密度值，再由質量流率中求得速度值，在二維非穩態的數值計算中把密度變化考慮到方程式，可以獲得更正確的結果。在時間項與非線性對流項分別以二階準確Adams-Bashforth方法與QUICK方法處理之。判斷混沌方面則是使用相軌跡方法(phase trajectory method)與頻譜分析(frequency spectrum)，可以看出週期或是爲混沌行爲。研究之流場範圍自當10^7到10^9，傾斜角度Φ=135°，依研究數值顯示，傾斜封閉空穴內的流場在Ra=10^7仍爲層流場，當Ra=10^8時流場進入到週期流，將Ra值提高到4×10^8時流場內部分位置進入混沌的行爲，提高Ra值達到6×10^8部分區域將變成紊亂之流場，Ra值達到10^9時流場紊亂的情形更剧烈。

The objective of the present study is to explore when and how the instability of 2-D natural convection in a tilted cavity. The time-dependent governing equations are solved by using the fractional step method. The time-advancement sequence is treated using the second-order Adams-Bashforth scheme, while the spatial discretization is made by the second-order QUICK scheme. The problem to be investigated is the natural convection in 2-D dimensions under the formulation without any approximations. The problem is the natural convection in a two-dimensional tilted cavity for a range of Ra from 10^7 to 10^9 with inclined angle Φ=135°. The cavity flows at Ra=10^7 is steady, laminar. As the Ra reached the values of 10^8 or 4×10^8 the flows become periodic/period doubling. As the Ra being up to 6×10^8 or larger, the flows present chaotic motion. When the Ra reached the values of 10^9, the flows exhibit turbulent motion in some region of cavity.