請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/17648
完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊照彥 | |
dc.contributor.author | Bo-Yao Huang | en |
dc.contributor.author | 黃柏堯 | zh_TW |
dc.date.accessioned | 2021-06-08T00:27:41Z | - |
dc.date.copyright | 2013-07-11 | |
dc.date.issued | 2013 | |
dc.date.submitted | 2013-07-09 | |
dc.identifier.citation | [1] 何雅玲、王勇、李慶 格子Boltzmann方法的原理及應用(Lattice Boltzmann Method: Theory and Applications),科學出版社(2009)。
[2] Yang, J. Y, & Hung, L.H., “Lattice Uehling-Uhlenbeck Boltzmann Bhatnagar- Gross-Krook Hydrodynamics of Quantum Gases.” Phys. Rev. E, vol. 79, p.056708, (2009). [3] d’Humieres, D., Ginzburg, I., Krafczyk, M., Lallemand, P. & Lou, L.S. “Multiple-Relaxation-Time Lattice Boltzmann Models in Three Dimensions.” Phil. Trans. R. Soc., vol. 360, pp.437–451, (2002). [4] 郭照立、鄭楚光 格子Boltzmann方法的原理及應用(Theory and Applications of Lattice Boltzmann Method),科學出版社(2009)。 [5] Chen, S.Y., Martinez, D. & Mei, R.W. “On Boundary Conditions in Lattice Boltzmann Methods.” Physics of Fluids, vol. 8, pp.2257–2536, (1996). [6] Zou, Q.S. & He, X.Y. “On Pressure and Velocity Boundary Conditions for The Lattice Boltzmann BGK Model.” Physics of Fluids, vol. 9, pp.1591–1598, (1997). [7] McNamara, G. & Zanetti, G. “Use of The Boltzmann Equation to Simulate Lattice-Gas Automata,” Phys. Rev. E, vol. 61, pp.2332–2335, (1988). [8] Higuera, F. & Jimenez, J. “Boltzmann Approach to Lattice Gas Simulation,” Europhys. Lett., vol.9, pp.663–668, (1989). [9] Qian, Y., d’Humieres, D. & Lallemand, P. “Lattice BGK Models for Navier - Stokes Equation,” Europhys. Lett., vol.17, pp.479–484, (1992). [10] Shan, X., Yuan, X.F. & Chen, Y. H. “Kinetic Theory Representation of Hydrodynamics: A Waybeyond the Navier–Stokes Equation,” J. Fluid Mech., vol. 550, pp.413–441, (2006). [11] Yang, J. Y. & Hung, L.H. “Lattice Uehling-Uhlenbeck Boltzmann Bhatnagar- Gross-Krook Hydrodynamics of Quantum Gases.” Phys. Rev. E, vol. 79, p.056708, (2009). [12] Luo, L.S., Liao, W., Chen, X.W., Peng, Y. & Zhang, W. “Numerics of The Lattice Boltzmann Method: Effects of Collision Models on The Lattice Boltzmann Simulations,” Phys. Rev. E, vol. 83, p.056710, (2011). [13] Chen, S.Y., “Development of Semiclassical Lattice Boltzmann Method Using Multi Relaxation Time Scheme for Flow Field Simulation”(2012) [14] 沈清 稀薄氣體動力學(Rarefied Gas Dynamics),國防工業出版社(2003)。 [15] 洪立昕 半古典晶格波滋曼方法,國立台灣大學工學院應用力學所博士論文,台北(2011)。 [16] Ginzburg, I., Verhaeghe, F. & d’Humieres, D. “Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization,Velocity, Pressure and Mixed Boundary Conditions,” Commun. Comput. Phys., vol. 3, pp.427–478, (2008). [17] Ginzburg, I., “Equilibrium-Type and Link-Type Lattice Boltzmann Models for Generic Advection and Anisotropic-Dispersion Equation,” Advances in Water Resources, vol. 28, pp.1171–1195, (2005). [18] He, X. & Luo, L.S., “Theory of The Lattice Boltzmann Method: From the Boltzmann Equation to The Lattice Boltzmann Equation,” Phys. Rev. E, vol. 56, pp.6811–6817, (1997). [19] Chen, H., Chen, S. & Matthaeus, W.H. “Recovery of The Navier-Stokes Equation Using a Lattice Boltzmann Method,” Phys. Rev. E, vol. 45, pp.5339–5342, (1992). [20] He, X., Chen, S. & Doolen, G.D. “A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit,” J. Comput. Phys., vol. 146, pp.282–300, (1998). [21] Ansumali, S. & Karlin, I.V. “Single Relaxation Time Model for Entropic Lattice Boltzmann Methods,” Phys. Rev. E, vol. 65, p.056312, (2001). [22] Patil, D.V., Lakshmisha, K.N. & Rogg, B. “Lattice Boltzmann Simulation of Lid-Driven Flow in Deep Cavities,” Computers & Fluids, vol. 35, pp.1116–1125, (2006). [23] Lutsko, J.F., “Chapman-Enskog Expansion about Nonequilibrium States with Application to The Sheared Granular Fluid,” Phys. Rev. E, vol. 73, p.021302, (2006). [24] Du, R., Shi, B. & Chen, X.W. “Multi-Relaxation-Time Lattice Boltzmann Model for Incompressible Flow,” Physics Letters A, vol. 359, Issue 6, pp.564–572, (2006). [25] Mezrhab, A., Moussaoui, M. A. & Jami, M. “Double MRT Thermal Lattice Boltzmann Method for Simulating Convective Flows,” Physics Letters A, vol. 374, pp.3499–3507, (2010). [26] Wu, S.J. & Shao, Y.L. “Simulation of Lid-Driven Cavity Flows by Parallel Lattice Boltzmann Method Using Multi-Relaxation-Time Scheme,” Int. J. Numer. Meth. Fluids, vol. 46, pp.921–937, (2004). [27] Lin, L.S., Chen, Y.C. & Lin, C.A. “Multi Relaxation Time Lattice Boltzmann Simulations of Deep Lid Driven Cavity Flows at Different Aspect Ratios,” Computers & Fluids, vol. 45, pp.233–240, (2011). [28] Yang, H.B., Liu, Y., Xu, Y.S. & Kou, J.L. “Numerical Simulation of Two - Dimensional Flow over Three Cylinders by Lattice Boltzmann Method,” Commun. Theor. Phys., vol. 54, pp.886–892, (2010). [29] Lallemand, P. & Luo, L.S. “Theory of The Lattice Boltzmann Method: Dispersion, Dissipation,Isotropy,Galilean Invariance, and Stability,” Phys. Rev. E, vol. 61, pp.6546–6562, (2000). | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/17648 | - |
dc.description.abstract | 發展基於Uehling-Uhlenbeck Boltzmann-BGK(Uehling-Uhlenbeck Boltzmann Bhatnagar-Gross-Krook Equation)方程的三維多鬆弛時間半古典格子Boltzmann法。此種方法藉由Hermite展開法得到離散半古典平衡態分布函數的Hermite展開形式,並且引入多鬆弛時間的概念,推導出三維半古典平衡態分布函數的矩空間形式,最後藉由此半古典矩空間平衡態分布函數加以計算便可得到各種巨觀物理量。
以D3Q19速度模型模擬方腔流,使用單一Re數,比較三維多鬆弛時間半古典格子Boltzmann法和三維單鬆弛時間半古典格子Boltzmann法的結果後,可以發現多鬆弛時間模擬的流場結構更為完整;並且為了更加了解多鬆弛時間半古典格子Boltzmann法的可行性,以二維D2Q9速度模型模擬長寬比例為1:2與2:1長方腔流流場問題,經由幾種Re數與三種遵循Bose-Einstein統計、Fermi-Dirac統計與Maxwell-Boltzmann統計的粒子模擬下,由結果分析可以明確展示下游次渦流在不同量子效應下產生不同的變化形態;最後經由各種邊界條件的計算後確定了此種方法的穩定性及準確性。 | zh_TW |
dc.description.abstract | According to two dimensional multiple-relaxation-time semiclassical lattice Boltzmann method, a three dimensional multiple-relaxation-time semiclassical lattice Boltzmann based on the Uehling-Uhlenbeck Boltzmann-BGK equation has been successfully developed by using D3Q19 lattice model. The method is derived by expanding the equilibrium distribution function in term of Hermite polynomials. Then, we combine the concept of multiple-relaxation-time with lattice Boltzmann method to obtain the moment matrix and various physical quantities.
Simulations with SRT and MRT for the lid-driven cavity flows based on D3Q19 lattice model have been carried out for three quantum particles including Bose-Einstein , Fermi-Dirac and Maxwell-Boltzmann statistics. Simulations show the streamline and pressure contour of 3D lid-driven cubic cavity flows. The result can be found in the multi-relaxation time simulation of the flow field structure is more complete. Moreover, comparing with different length and width of cavity flows such as 1:2 and 2:1, it is easy to notice that the shape of downstream eddy of rectangle flows are different for three quantum particles. Finally, after testing various boundary conditions, the stability and the accuracy of this method is illustrated. | en |
dc.description.provenance | Made available in DSpace on 2021-06-08T00:27:41Z (GMT). No. of bitstreams: 1 ntu-102-R00543069-1.pdf: 2680989 bytes, checksum: eee47362c468af855cd5f1ad376ea94e (MD5) Previous issue date: 2013 | en |
dc.description.tableofcontents | 目錄
中文摘要……………………………………………………………………………Ⅰ Abstract……………………………………………………………………………Ⅱ 致謝…………………………………………………………………………………Ⅲ 目錄…………………………………………………………………………………Ⅳ 圖目錄………………………………………………………………………………Ⅵ 符號…………………………………………………………………………………Ⅷ 第一章 緒論…………………………………………………………………………1 1-1 計算流體力學………………………………………………………………1 1-2 格子Boltzmann法簡介與文獻回顧………………………………………1 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 Boltzmann方程……………………………………………………………8 2-4 Boltzmann H 定理…………………………………………………………12 2-5 Maxwell 分布………………………………………………………………15 2-6 Boltzmann BGK 方程………………………………………………………17 2-7 格子Boltzmann方程與速度模型…………………………………………18 2-9 平衡態分布函數的Hermite展開…………………………………………21 第三章 半古典格子Boltzmann法理論……………………………………………25 3-1 理想量子氣體的分類………………………………………………………25 3-1-1 包立不相容原理(Pauli Exclusion Principle) …………………………25 3-1-2 三種統計……………………………………………………………………26 3-2 半古典格子Boltzmann方程………………………………………………27 3-3 單鬆弛時間Chapman-Enskog分析………………………………………34 第四章 多鬆弛時間半古典格子Boltzmann法理論………………………………39 4-1 Multiple-Relaxation-Time LBM 基本原理……………………………39 4-2 使用D3Q19速度模型的多鬆弛時間半古典格子Boltzmann法……………44 第五章 基本模型邊界處理方法……………………………………………………49 5-1 多鬆弛時間格子Boltzmann法……………………………………………49 5-2 邊界條件……………………………………………………………………49 5-3 收斂條件……………………………………………………………………50 5-4 計算流程……………………………………………………………………51 第六章 模擬問題結果與討論………………………………………………………52 6-1 方腔流………………………………………………………………………52 6-2 問題描述……………………………………………………………………53 6-3 模擬結果分析與討論………………………………………………………56 第七章 結論與展望…………………………………………………………………78 7-1 展望…………………………………………………………………………79 參考文獻……………………………………………………………………………80 | |
dc.language.iso | zh-TW | |
dc.title | 三維多鬆弛時間半古典格子波茲曼法之流場模擬 | zh_TW |
dc.title | A Three-Dimensional Semiclassical Lattice Boltzmann Method Using Multiple Relaxation Times For Quantum Hydrodynamic Flow Simulations | en |
dc.type | Thesis | |
dc.date.schoolyear | 101-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 陳朝光,楊玉姿,洪立昕 | |
dc.subject.keyword | 多鬆弛時間,D2Q9,D3Q19速度模型,方腔流,格子波茲曼法,半古典格子波茲曼法, | zh_TW |
dc.subject.keyword | Mutiple-relaxation-time,D3Q19 lattice model,Cavity flows,Semiclassical lattice Boltzmann method,Lattice Boltzmann method, | en |
dc.relation.page | 83 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2013-07-09 | |
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 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-102-1.pdf 目前未授權公開取用 | 2.62 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。