劉氏保群算法於高雷諾數Burgers方程之應用及探討

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姓名

李苡珊(E-Shan Lee) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

劉氏保群算法於高雷諾數Burgers方程之應用及探討

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摘要(中)

本文探討劉氏於2006年發表關於計算高雷諾數之保存群性質數值方法[30]。此篇文章在探討高雷諾數數值解部分採用雙曲線函數座標轉換，本文則採用指數函數座標轉換與之對比，另外，也用傳統數值方法RK4與劉氏GPS(LGPS)計算出之數值結果做一詳細之比較。此外，我們也考慮網格點數量之多寡對RK4與LGPS之影響，最後，我們嘗試使用牛頓插值公式找出R-A關係式，如此，雷諾數值一旦改變即可不必重新尋找A值了。

摘要(英)

This article explores Professor Liu C.S. published in 2006 on the calculation of the preservation group nature of high Reynolds number numerical methods [30]. This article to explore the numerical solution of partial high Reynolds coordinate transformation using hyperbolic functions, exponential functions are used herein coordinate transformations contrast. In addition, the traditional numerical methods RK4 and Liu GPS (LGPS) calculated the numerical results do a detailed comparison. Moreover, we also consider the number of grid points of the amount of the impact on RK4 and LGPS. Finally, we try to use Newton’s interpolation formula to identify RA relationships, so, once the Reynolds number can be changed without re looking for A worth it.

關鍵字(中)

★ 劉氏保群算法

關鍵字(英)

★ Burgers 方程

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VI
表目錄 XIII
符號表 XIV
第一章緒論 1
第二章 Burgers 方程之簡介 3
第三章差分公式
3.1 空間軸上的離散 6
3.2 Fourth-Order Runge-Kutta Method , RK4 11
3.3 Group Preserving Scheme , GPS 13
第四章計算範例
4.1 網格轉換後公式之替換 19
4.1.1 雙曲線函數座標轉換之應用 21
4.1.2 指數函數座標轉換之應用 44
4.2 網格數目的增減 53
4.2.1 RK4與GPS測試雙曲線x-y轉換函數功效 53
4.2.2 RK4與GPS測試指數x-y轉換函數功效 62
4.3 R與A關係的數學公式
4.3.1 RK4與GPS計算雙曲線函數 71
4.3.2 RK4與GPS計算指數函數 78
第五章結論 82
第六章參考文獻 83

參考文獻

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指導教授

李顯智(Hin-Chi Lei)

審核日期

2013-7-18

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