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研究生:黃玟瑜
研究生(外文):Wun-Yu Huang
論文名稱:半古典Shakhov模型格子波茲曼法之發展與流場模擬
論文名稱(外文):Development of Semiclassical Lattice Boltzmann Method with Shakhov Model for Flow Simulation
指導教授:楊照彥
口試委員:黃美嬌黃俊誠湯國樑
口試日期:2015-06-24
學位類別:碩士
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:2015
畢業學年度:103
語文別:中文
論文頁數:117
中文關鍵詞:格子波茲曼法半古典Shakhov模型格子波茲曼法半古典格子波茲曼法波茲曼BGK方程式Shakhov模型D2Q9格子速度模型方腔流
外文關鍵詞:Lattice Boltzmann MethodSemiclassical Lattice Boltzmann Method with Shakhov ModelSemiclassical Lattice Boltzmann MethodBoltzmann BGK EquationShakhov ModelD2Q9 Lattice ModelLid Driven Cavity Flows
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本研究發展出半古典Shakhov模型格子波茲曼法,是基於Shakhov模型格子波茲曼方程式與半古典格子波茲曼方程式推導而來,以修正普朗特數(Prandtl Number)且考慮量子氣體為目的,使得適用性更為廣泛,計算流場更趨於真實性。此方法利用Hermite展開法,得到半古典Shakhov模型平衡態分布函數的Hermite展開式,並透過Chapman-Enskog展開得到其鬆弛時間與黏滯係數之間的關係,以半古典Shakhov模型格子波茲曼方程式來模擬計算流場。本文透過此方法,以D2Q9格子速度模型和反彈邊界為基礎,模擬方腔流流場問題,由不同普朗特數以及不同雷諾數的條件下模擬Bose-Einstein統計與Fermi-Dirac統計和Maxwell-Boltzmann統計的粒子,展示半古典Shakhov模型格子波茲曼法在各流場的狀態,並由模擬結果比較半古典Shakhov模型格子波茲曼法與半古典格子波茲曼法之差異性。

A Semiclassical Lattice Boltzmann Method with Shakhov Model based on Shakhov Model Lattice Boltzmann equations and Semiclassical Lattice Boltzmann equations is presented. In order to take the Prandtl number and the quantum effect into consideration for approximate exact solution. The equilibrium distribution function is expanded by the Semiclassical Shakhov Model in term of Hermite polynomials, and the relationship between relaxation time and viscosity is obtained by using Chapman-Enskog expansion. Simulation of the lid driven cavity flows based on D2Q9 lattice model and Bounce-Back boundary condition are studied under Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics with different Parndtl number and Reynolds numbers in the thesis. Based on the result of simulations, a comparison between Semiclassical Lattice Boltzmann Method with Shakhov Model and Semiclassical Lattice Boltzmann Method is made.

摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖目錄 VII
表目錄 IX
第一章 緒論 1
1-1 計算流體力學 1
1-2 格子波茲曼法(LATTICE BOLTZMANN METHOD)簡介 1
1-3 格子波茲曼法(LATTICE BOLTZMANN METHOD)文獻回顧 2
1-4 本文目的 3
1-5 本文架構 3
第二章 理論與統御方程式 5
2-1 氣體動力論 5
2-2 分布函數 7
2-3 波茲曼方程式 8
2-4 波茲曼H定理 11
2-5 MAXWELL分布 13
2-6 波茲曼BGK方程式 15
2-7 平衡態分布函數HERMITE展開 16
2-8 格子波茲曼方程式與速度模型 18
第三章 SHAKHOV模型格子波茲曼法理論 22
3-1 SHAKHOV模型格子波茲曼方程式 22
3-2 SHAKHOV模型格子波茲曼法之宏觀物理量求法 27
3-3 SHAKHOV模型格子波茲曼法之CHAPMAN-ENSKOG分析 27
第四章 半古典格子波茲曼法理論 33
4-1 理想量子氣體 33
4-2 半古典格子波茲曼方程式 34
4-3 半古典波茲曼法之宏觀物理量求法 43
4-4 半古典格子波茲曼法之CHAPMAN-ENSKOG分析 45
第五章 半古典SHAKHOV模型格子波茲曼法理論 51
5-1 半古典SHAKHOV模型格子波茲曼方程式 51
5-2 半古典SHAKHOV模型格子波茲曼法之宏觀物理量求法 61
5-3 半古典SHAKHOV模型格子波茲曼法之CHAPMAN-ENSKOG分析 62
第六章 基本模型與邊界處理方法 68
6-1 半古典SHAKHOV模型格子波茲曼法 68
6-2 邊界條件 68
6-3 收斂條件與計算流程 69
第七章 模擬結果與討論 71
7-1 方腔流 71
7-2 問題描述 72
7-3 模擬結果討論 75
第八章 結論與展望 114
8-1 結論 114
8-2 未來展望 115
參考文獻 116


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