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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊照彥(Jaw-Yen Yang) | |
dc.contributor.author | Sheng-Hsin Hu | en |
dc.contributor.author | 胡聖鑫 | zh_TW |
dc.date.accessioned | 2021-06-15T01:13:54Z | - |
dc.date.available | 2012-08-12 | |
dc.date.copyright | 2009-08-12 | |
dc.date.issued | 2009 | |
dc.date.submitted | 2009-07-29 | |
dc.identifier.citation | [1] Bird, G. A. (1994) Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press Oxford.
[2] Chen, H., Chen, S. & Matthaeus, W. H. (1992) Recovery of the Navier-Stokes Equation Using a Lattice Boltzmann Method, Physical Review A, 45, pp. 5339-5342. [3] Chen, S., Martinez, D. & Mei, R. (1996) On Boundary Conditions in Lattice Boltzmann Methods, Physics of Fluids, 8, 2527. [4] Filippova, O. & Hamel, D. (1998) Grid Refinement for Lattice-BGK Models, Journal of Computational Physics, 147, pp. 219-228. [5] He, X., Luo, L.-S. & Dembo, M. (1997) Some Progress in Lattice Boltzmann Method., Part Ⅰ. Nonuniform Mesh Grids, Journal of Computational Physics, 129, pp. 357-363. [6] He, X., & Luo, L.-S. (1997) A Priori Derivation of the Lattice Boltzmann Equation, Physical Review E, 55, pp. 6333-6336. [7] Higuera, F. & Jimenez, J. (1989) Boltzmann Approach to Lattice Gas Simulation, Europhysics Letters, 9, pp. 663-668 [8] Inamuro, T., Yoshino, M. & Ogino, F. (1995) A Non-slip Boundary Condition for Lattice Boltzmann Simulation, Physics of Fluids, 7, pp. 2928-2930. [9] Knudsen, M. (1909) Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren, Annalen der Physik, 28,75. [10] Lim, Y. C., Shu, C., Niu, X. D. & Chew Y. T. (2002) Application of Lattice Boltzmann Method to Simulation Microchannel Flows, Physics of Fluids, 14(7) 2299. [11] Lockerby, D. A., Reese, J. M. & Gallis, M. A. (2005) The Usefulness of High-order Constitutive Relation for Describing the Knudsen Layer, Physics of Fluids, 17 100609. [12] McNamara, G. & Zanetti, G. (1988) Use of the Boltzmann Equation to Simulate Lattice-Gas Automata, Physical Review, 61, pp.2332-2335. [13] Mei, R., Lou, L. S. & Shyy, W. (1999) An Accurate Curved Boundary Treatment in the Lattice Boltzmann Method, Journal of Computational Physics, 155, pp. 307-330. [14] Qian, T. H., D’Humieres, D. & Lallemand, P. (1992) Lattice BGK Models for Navier-Stokes Equation, Europhysics Letters 17, pp. 479-484 [15] Shan, X., Yuan, X.-F. & Chen, H., (2006) Kinetic Theory Representation of Hydrodynamics: A Way Beyond the Navier-Stokes Equation, Journal of Fluid Mechanics, 550, pp. 413-441. [16] Succi, S. (2001) The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford Science Publications. [17] Tang, G.-H. Zhang, Y. & Emerson, D. R. (2008) Lattice Boltzmann Models for Nonequilibrium Gas Flows, Physical Review E, 77, 046701. [18] Uehling, E. A. & Uhlenbeck, E. G. (1933) Transport Phenomena in Einstein-Bose and Fermi-Dirac Gases. Ⅰ, Physical Review, 43, pp. 552-561. [19] Wagner, A. J. (2008) A Practical Introduction to the Lattice Boltzmann Method, Department of Physics North Dakota State University. [20] Zhang, Y. H., Gu, X. J., Barber, R. W. & Emerson, D.R. (2006) Capturing Knudsen Layer Phenomena Using Lattice Boltzmann Model, Physical Review E, 74, 046704. [21] Zhang, Y. Qin, R. & Emerson, D. R. (2005) Lattice Boltzmann simulation of Rarefied Gas Flows in Microchannels, Physical Review E, 71, 047702. [22] Zhang, R., Shan X. & Chen, H. (2006) Efficient Kinetic Method for Fluid Simulation Beyond the Navier-Stokes Equation, Physical Review E, 74, 046703. [23] Zhou, Y., Zhang, R., Staroselsky, I., Chen, H., Kim, W. T. & Jhon, M. S. (2006) Simulation of Micro- and Nano-scale Flows Via the Lattice Boltzmann Method, Physica A: Statistical Mechanics and its Applications, 362(1), pp. 68-77. [24] Zou, Q. & He, X. (1997) On Pressure and Velocity Boundary Condition for the Lattice Boltzmann BGK Model, Physics of Fluids, 9, 1591. [25] 何雅玲、王勇、李慶 (2009) 格子Boltzmann方法的原理及應用(Lattice Boltzmann Method: Theory and Applications),科學出版社。 [26] 沈清 (2003) 稀薄氣體動力學(Rarefied Gas Dynamics),國防工業出版社。 [27] 郭照立、鄭楚光 (2009) 格子Boltzmann方法的原理及應用(Theory and Applications of Lattice Boltzmann Method),科學出版社。 [28] 鄭以禎 (2003) 巨觀與統計熱力學,偉明圖書公司出版。 [29] 謝澤揚 (2007) 聲子熱傳輸與理想量子氣體動力學之高解析算則,國立台灣大學工學院應用力學所博士論文,台北。 [30] 顏子翔 (2006) 應用晶格波茲曼法與場協同理論於不同阻礙物之背向階梯管道熱流分析,國立成功大學工學院機械工程學系博士論文,台南。 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42445 | - |
dc.description.abstract | 在近十年間,格子Boltzmann法(Lattice Boltzmann Method, LBM)已發展成為相當重要的一項研究流體流動的工具。在本文的研究中,我們使用格子Boltzmann法來計算模擬流體在二維微流道管中,在不同的Knudsen數,包含了滑移區跟過渡流區,並使用新發展的半古典格子Boltzmann法,來模擬量子氣體。
半古典格子Boltzmann法是利用Uehling-Uhlenbeck Boltzmann-BGK方程式,藉由Hermite多項式展開推導而得到的。根據邊界上的滑移運動,採用了一個調和係數(accommodation coefficient)來模擬氣體在邊界上的交互作用。 不同的Knudsen數,包含了滑移區跟過渡流區中,模擬了三種不同的粒子統計,計算而得到質量流率跟速度分佈曲線,最後順利發現Knudsen minimum現象的存在。由發現Knudsen minimum現象的展現可做為演算法驗證的方式,並和本研究使用量子統計得出結果做為比較。 | zh_TW |
dc.description.abstract | In the last decade, Lattice Boltzmann Method, an useful and powerful tool for general fluid flow simulation, has been developed. The two-dimensional micro-channel flow of gas of arbitrary statistics in the slip and transition regimes as characterized by the Knudsen number are studied using a newly developed semiclassical lattice Boltzmann method.
The semiclassical lattice Boltzmann method is derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials using moment expansion method. To take into account the slip motion at wall surface, the Maxwellian scattering kernel is adopted to model the gas surface interactions with an accommodation coefficient. The mass flow rates and the velocity profiles are calculated for the three particle statistics over the slip and transition regimes Knudsen numbers. The results indicate that the Knudsen minimum can be captured and distinct characteristics of the effect of quantum statistics can be delineated. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T01:13:54Z (GMT). No. of bitstreams: 1 ntu-98-R96543053-1.pdf: 1074517 bytes, checksum: 7910501f2293e1f8be01911eb77bdd17 (MD5) Previous issue date: 2009 | en |
dc.description.tableofcontents | 摘要 I
Abstract II 誌謝 III 目錄 IV 圖目錄 VI 第一章、緒論 1 1-1 格子Boltzmann法(Lattice Boltzmann Method)簡介 1 1-2 格子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 Liouville方程 6 2-3 Boltzmann方程 7 2-4 BGK模型 9 2-5 連續體模型方程 10 2-6 平衡態分佈函數的Hermite展開 12 第三章、半古典格子Boltzmann法的理論 18 3-1 理想量子氣體動力學 18 3-1-1 理想量子氣體平衡分佈函數 18 3-1-2 三種統計 18 3-2 半古典格子Boltzmann方程 19 3-3 2-D的D2Q9Chapmen-Enskog分析 24 第四章、基本模型與邊界處理方法 29 4-1 格子Boltzmann法 29 4-2 格子Boltzmann方法的邊界條件 30 4-2-1 固體邊界 31 4-2-2 開放邊界 32 第五章、模擬結果與討論 39 5-1 平行板間穩定層流 39 5-2 問題描述 40 5-3 圖表中使用到的參數及收斂條件 41 5-4 模擬結果分析與討論 42 第六章、結論與展望 60 6-1 結論 60 6-2 展望 61 參考文獻 63 | |
dc.language.iso | zh-TW | |
dc.title | 使用半古典格子波茲曼法之微流道流場模擬 | zh_TW |
dc.title | Simulation of Microchannel Flow Using Semiclassical Lattice Boltzmann Method | en |
dc.type | Thesis | |
dc.date.schoolyear | 97-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 黃美嬌,黃俊誠,石育炘 | |
dc.subject.keyword | 格子Boltzmann法,半古典格子Boltzmann法,微流道,Knudsen minimum, | zh_TW |
dc.subject.keyword | Lattice Boltzmann Method,Semiclassical lattice Boltzmann method,Microchannel,Knudsen minimum, | en |
dc.relation.page | 66 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2009-07-29 | |
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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