臺灣博碩士論文加值系統

本論文之研究為建立一數值模擬程式，藉以分析不可壓縮流之流場。
在數值方法的選擇上，吾人不以傳統求解不可壓縮流的SIMPLE法，而採以同為原始變數表示法(Primitive-Variable formulation)的人工壓縮法(Artificial Compressibility method) 配合可壓縮流領域中發展出的加權型基本不震盪(Weighted Essentially Non-Oscillatory) 算則直接求解不可壓縮型式的Navier-Stokes方程式。而程式撰寫技巧上採用具增強數值穩定性的Lower-Upper Symmetric-Gauss-Seidel Method ( LU-SGS method ) 以求更快的收斂。文中選擇了兩個典型的不可壓縮流測試範例-空穴流及背向階梯流來測試所撰寫程式的可靠性，其結果顯示都有不錯的精確度。

A numerical simulation program to analyze incompressible flow has been developed. The artificial compressibility method of primitive variable formulation, which has been developed for compressible flow, was used in this work. Specifically, the governing Navier-Stokes equations were solved with weighted essentially non-oscillatory (WENO) scheme. In addition, the Lower-Upper Symmetric-Gauss-Seidel (LU-SGS) method was adopted to enhance numerical stability and to achieve fast convergence.
Two classical incompressible flow, cavity flow and backward —step flow, where examined to validate the numerical simulation program. Good agreement between the numerical simulation results and the published experimental data in the literature was obtained.

英文摘要 …………………….…………………………… I
中文摘要 …………………………………………………. II
誌 謝 …………………………………………………. III
目 錄 …………………………………………………. IV
圖 目 錄 …………………………………………………. Ⅵ
符號說明 …………………………………………………. Ⅷ
第一章 緒 論 …………….………………………….. 1
1.1 引 言 ……………………………………….. 1
1.2 文獻回顧 ……………………………………… 1
1.3 章節簡介 ……………………………………… 5
第二章 物理問題 ………………………………………. 6
2.1 物理現象簡述 ……………………………….... 6
2.2 物理問題假設 ………………………………… 7
2.3 二維統御方程式 ……………..……….……… 7
第三章 數值方法 ……………………………………...… 10
3.1 人工壓縮法 ……………………………………… 10
3.2 空間離散 ……………………………………… 12
3.3 WENO算則 …………..………………………. 16
3.3.1 WENO2 ………………………………… 17
3.3.2 WENO3 ………………………………… 19
3.4 時間離散 ……………………………………… 21
3.5 LU-SGS隱式法 ………………………………. 23
3.6 網格之建立 ……………………………………. 25
3.7 邊界條件 ………………………………………. 26
第四章 結果分析 ……..…………………………………. 29
4.1 二維空穴流 …………….……………………… 29
4.2 背向階梯流 ………………………………..… 30
第五章 結論與未來展望 ……………………………… 31
參考文獻 ………………………………………………… 32

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