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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊照彥(Jaw-Yen Yang) | |
| dc.contributor.author | Po-Chen Tsai | en |
| dc.contributor.author | 蔡博臣 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:43:51Z | - |
| dc.date.available | 2014-07-18 | |
| dc.date.copyright | 2013-07-18 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-10 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62365 | - |
| dc.description.abstract | 基於Uehling-Uhlenbeck Boltzmann-BGK方程（Uehling-Uhlenbeck Boltzmann Bhatnagar-Gross-Krook Equation）和橢圓統計BGK方程（Ellipsoidal Statistical BGK equation，ES-BGK）為基礎發展出半古典橢圓統計波茲曼方程之格子波茲曼法。此方法從氣體動力學理論出發，成功地藉由Hermite多項式與D2Q9格子速度模型近似推導而得到。本文利用此方法模擬二維方腔流，雙平板流流場問題， 由不同的雷諾數和三種不同的量子氣體分別遵循Bose-Einstein統計與Fermi-Dirac統計和Maxwell-Boltzmann統計呈現了此方法，並從不同的量子統計以及雷諾數的模擬結果分析比較BGK碰撞模型和ES-BGK碰撞模型的差異。
從模擬方腔流場(Cavity Flows)結果可以清楚地看出方腔流場中流線函數在BGK和ES-BGK碰撞模型(b值為-0.5 ,0 , 0.5)的差異在於上游次渦漩的呈現，隨著b值增加，上游次渦漩會越趨於完整；而考慮三種量子統計下之流線函數圖則就無明顯地不同。方腔流場中等壓圖以及壓力張量圖的低壓區域隨著b值增加，形狀與位置則會有明顯地不同；而考慮三種量子統計下之等壓圖以及壓力張量圖的低壓區域的形狀與位置亦有明顯地不同。此外，模擬雙平板流場(Couette Flows)結果可以看出b值增加或是依序BE、MB、FD量子統計下，流場的最高溫均會增大。值得注意的是ES-BGK碰撞模型在b值為-0.5時，可以修正BGK碰撞模型的普朗特數(1→2/3)，因此，對於MB統計下可以比較雙平板流場在上下邊界上有速度與溫差下之解析解，可以發現在靠近邊界上時有些許偏移。 | zh_TW |
| dc.description.abstract | A semiclassical lattice Boltzmann–Ellipsoidal Statistical method based on the Uehling-Uhlenbeck Boltzmann-BGK equation and Ellipsoidal Statistical BGK equation is presented. According to gas kinetic theories, the kinetic governing equation for Ellipsoidal Statistical method is directly derived by the Hermite polynomials expansion and lattice velocity model. By using lattice Boltzmann method, this work successfully demonstrates the lid driven cavity flows and Couette flows with different collision operator, BGK and ES-BGK models. Simulations not only shows the similarity and the difference between BGK and ES-BGK collision models but also presents the result for different Reynolds numbers and three quantum particles that obeying Bose-Einstein and Fermi-Dirac and Maxwell-Boltzmann statistics. It is clear to notice that the shapes of the upper upstream secondary eddy of streamlines for three quantum particles from cavity simulation are different between BGK and ES-BGK collision models (the value of b equal -0.5, 0, 0.5), the shape of the upper upstream secondary eddy is more complete as the value of b increases, the shape and position of low pressure center and pressure tensor for three quantum particles from cavity simulations are also different as the value of b is varied. Moreover, simulation for Couette flows not only shows the velocity and temperature distribution but also presents the pressure and pressure tensor contour for three quantum particles. Because ES-BGK collision models (when the value of b equal -0.5) will recover the correct Prandtl number (1→2/3), we also compare our simulations for Maxwell-Boltzmann statistics with exact solution of Couette flows with velocity and temperature difference boundary condition and the result can be found slightly error near the boundary. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:43:51Z (GMT). No. of bitstreams: 1 ntu-102-R00543009-1.pdf: 12911307 bytes, checksum: 5cb0ed94252693c3f9ad4559bba6818c (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 目錄
中文摘要.…………………………………………………………………………Ⅰ Abstract ……………………………………………………………………Ⅱ 誌謝…………………………………………………………………………………Ⅲ 目錄……………………………………………………………………………………Ⅳ 圖目錄………………………………………………………………………………Ⅶ 第一章 緒論 1 1-1 格子Boltzmann 法介紹 1 1-2 Boltzmann法之文獻回顧 2 1-3 本文目的 3 1-4 本文架構 3 第二章 Boltzmann方程式 5 2-1 氣體運動理論(Gas Kinetic Theory) 5 2-2 分布函數(Distribution Function) 7 2-3 Liouville 方程 8 2-4 Boltzmann方程 9 2-5 Boltzmann H定理 10 2-6 Maxwell分布 12 2-7 Boltzmann BGK方程 14 2-8 格子Boltzmann方程與特殊速度離散模型 14 2-9 平衡態分布函數的Hermite展開 17 第三章 半古典格子Boltzmann法的理論 22 3-1 理想量子氣體 22 3-2 半古典格子Boltzmann方程 22 3-3 宏觀物理量的求法 28 3-4 格子Boltzmann-BGK方程之Chapman-Enskog分析 29 第四章 半古典橢圓統計格子Boltzmann方法的理論 33 4-1 Boltzmann-ESBGK方程式： 33 4-2 宏觀物理量的求法 39 4-3 格子Boltzmann-ESBGK方程之Chapman-Enskog分析 40 第五章 基本模型與邊界處理方法 44 5-1 橢圓統計格子Boltzmann法 44 5-2 邊界條件 45 5-3 收斂條件與計算流程 47 第六章 模擬結果與討論 49 6-1 方腔流(Lid Driven Flow) 49 6-2 方腔流問題描述 50 6-3 平板流(Couette Flow) 51 6-4 平板流問題描述 52 6-5 模擬結果分析與討論 54 第七章 結論與展望 100 7-1 結論 100 7-2 展望 101 參考文獻 103 | |
| dc.language.iso | zh-TW | |
| dc.title | 基於半古典橢圓統計波茲曼方程之格子波茲曼法 | zh_TW |
| dc.title | A Semiclassical Lattice Boltzmann–Ellipsoidal Statistical Method for Hydrodynamics of Quantum Gases | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳朝光(Chao-kuang Chen),楊玉姿(Yue-Tzu Yang),洪立昕(Li-Hsin Hung) | |
| dc.subject.keyword | 半古典格子波茲曼方法,橢圓統計BGK方程,D2Q9格子模型,方腔流,雙平板流,氣體動力學,格子波茲曼方法, | zh_TW |
| dc.subject.keyword | Semiclassical lattice Boltzmann method,Ellipsoidal statistical BGK equation,D2Q9 lattice model,Cavity flows,Couette flows,Gas kinetic theories, | en |
| dc.relation.page | 106 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-10 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
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