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研究生:蔡尚熹
研究生(外文):Shangsi, Tsai
論文名稱:相對論氣體動力學之通量向量分離法算則
論文名稱(外文):A kinetic flux vector splitting scheme for the relativisitc gas dynamics
指導教授:楊照彥
指導教授(外文):Jaw-Yen, Yang
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:101
中文關鍵詞:通量向量分離法相對論氣體動力學高解析算則特徵曲線理論
外文關鍵詞:KFVS methodrelativisitc gas dynamicshigh resolution schemecharacterisitic theoryconservation relations
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以特殊相對論及氣體動力論為理論基礎,由羅倫茲轉換及平衡態速度分布函數定義不同慣性參考座標系中各項巨觀物理量,藉由相對論波茲曼方程式的尤拉極限建立相對論守恆律方程組,推導相對論氣體動力論守恆律方程組積分形式的通量向量分離法算則,由物理觀點定義該算則導出的各項巨觀物理量的傳遞速度,討論因傳遞速度的差異造成該算則的不守恆特性。同時發展一階與MUSCL-type高階算則,並應用於計算一維Sod相對論震波管問題與二維爆炸波問題。
The relativistic kinetic flux vector splitting (KFVS) method is derived based on the special theory of relativity, the relativistic Boltzmann equation and the equilibrium, i.e., the Jüttner-Maxwell distribution function. The numerical first-order and the MUSCL-type second order schemes with van Leer limiters are developed in local rest frame and their counterparts in other inertial moving frames are obtained by Lorentz transformation, whose general transformation matrix is given in Appendix A and is formulated according to the one-dimensional Lorentz transformation in associated with the three-dimensional coordinate rotations. Both schemes are validated by the problems of one-dimensional Sod’s shock tube with different initial conditions and are applied to the two-dimensional spherical explosive waves.
The intrinsic flaw of the original KFVS method is investigated. Due to the splitting of integration intervals for the distribution function, the propagation velocities of the macroscopic physical quantities are discrepant, which results in the breakdown of the conservation relations. The modified intervals of integration and the conditions for the KFVS method satisfying the conservation relations are proposed both for the classical and relativistic gas dynamics.
摘要
目錄
附圖目錄
第一章 緒論
1.1. 引言
1.2. 文獻回顧
1.3. 內容簡介
第二章 特殊相對論與氣體動力學之基本理
2.1. 簡介
2.2. 特殊相對論與羅倫茲轉換
2.3. 慣性座標系間的物理量轉換
2.4. 相對論之氣體動力論
2.4.1. 分布函數的羅倫茲不變性
2.4.2. 傳輸方程式
2.4.3. 巨觀物理量的定義
2.4.4. 相對論尤拉方程式
2.4.5. 平衡態分布函數
2.5. 守恆律方程組與相對論流體力學
2.5.1. 黎曼不變量
2.5.2. 突升條件
第三章 相對論通量向量分離法
3.1. 簡介
3.2. 相對論通量向量分離法算則之基本物理量
3.2.1. 靜止座標系
3.2.2. 一般座標系
3.2.3. 討論
3.3. 相對論通量向量分離法之守恆律方程式
3.3.1. 一維通量分離法之守恆律方程式
3.3.2. 二維通量向量分離法之守恆律方程式
3.4. 相對論通量向量分離法算則之描述
3.4.1. 通量傳遞速度
3.4.2. CFL條件
3.4.3. 通量向量分離法一階算則之建構
3.4.4. 通量向量分離法二階算則之建構
3.4.5. 討論
第四章 相對論通量向量分離法算則之應用
4.1. 簡介
4.2. 一維震波管問題
4.3. 二維爆炸波問題
4.4. 討論
第五章 結論與展望
參考文獻
附錄A. 羅倫茲轉換
附錄B. 第二類修正型Bessel函數
附錄C. van Leer斜率限制函數的單調性
附圖
附表4.1. 二維爆炸波等高線分布範圍與數目
附圖目錄
圖3.1. 傳遞速度分布圖
圖3.2. 特徵速度馬赫數分布圖
圖3.3. 二維計算網格
圖4.1.(a) 通量向量分離法Sod震波管算例一-一階算則
圖4.1.(b) 通量向量分離法Sod震波管算例一-二階算則
圖4.2.(a) 通量向量分離法Sod震波管算例二-一階算則
圖4.2.(b) 通量向量分離法Sod震波管算例二-二階算則
圖4.3.(a) 通量向量分離法二維爆炸波密度分布-一階算則
圖4.3.(b) 通量向量分離法二維爆炸波壓力分布-一階算則
圖4.3.(c) 通量向量分離法二維爆炸波速度分布-一階算則
圖4.4.(a) 通量向量分離法二維爆炸波密度分布-二階算則
圖4.4.(b) 通量向量分離法二維爆炸波壓力分布-二階算則
圖4.4.(c) 通量向量分離法二維爆炸波速度分布-二階算則
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