雙分佈函數半古典格子波茲曼法之熱流場模擬

Chih-Yun Liu; 劉之昀

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61601

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	Chih-Yun Liu	en
dc.contributor.author	劉之昀	zh_TW
dc.date.accessioned	2021-06-16T13:06:59Z	-
dc.date.available	2018-08-09
dc.date.copyright	2013-08-09
dc.date.issued	2013
dc.date.submitted	2013-08-01
dc.identifier.citation	[1] Bird, G. A., Molecular gas dynamics and the direct simulation of gas flows, Clarendon Press Oxford, (1994). [2] Yang, J. Y. and Hung, L.H., “Lattice Uehling-Uhlenbeck Boltzmann Bhatnagar- Gross-Krook hydrodynamics of quantum gases,” Phys. Rev. E, vol. 79, 056708, (2009). [3] Woods, L. C., An introduction to the kinetic theory of gases and magnetoplasmas. London: Cambridge University Press, (1993) . [4] Chen, S.Y., Martinez, D., and Mei, R.W., “On boundary conditions in lattice Boltzmann methods,” Physics of Fluids, vol. 8, pp.2257–2536, (1996). [5] Luo, L.S., “Unified theory of lattice Boltzmann models for nonideal gases,” Phys. Rev. Lett., vol. 81, pp. 1618~1621, (1998). [6] He, X. and 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). [7] Xiaoyi He, Shiyi Chen, and Gary D. Doolen, “A novel thermal model for the lattice Boltzmann method in incompressible limit,” Journal of Computational Physic, vol. 146, pp. 282–300, (1998). [8] McNamara, G. and Zanetti, G., “Use of the Boltzmann equation to simulate lattice-gas automata,” Phys. Rev. E, vol. 61, pp.2332–2335, (1988). [9] Higuera, F. and Jimenez, J., “Boltzmann approach to lattice gas simulation,” Europhys. Lett., vol.9, pp.663–668, (1989). [10] Qian, Y., d’Humieres, D., and Lallemand, P., “Lattice BGK models for Navier-Stokes Equation,” Europhys. Lett., vol.17, pp.479–484, (1992). [11] Z. L. Guo, C.G. Zheng, and B.C. Shi, “Thermal lattice Boltzmann equation for low Mach number flows: decoupling model,” Phys. Rev. E, vol.75, 036704, (2007). [12] X. Shan., “Simulation of Rayleigh–Benard convection using a lattice Boltzmann method,” Phys. Rev. E, vol.55, pp.2780–2788, (1997). [13] Shan, X., Yuan, X.F., and Chen, Y. H., “Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation,” J. Fluid Mech., vol.550, pp.413–441, (2006). [14] Z. L. Guo, C.G. Zheng, and B.C. Shi, “ A coupled lattice BGK model for the Boussinesq equations,” Int. J. Numer. Meth. Fluids, vol.39, pp.325-342, (2002). [15] Hung, L.H. and Yang, J. Y., “ A coupled lattice Boltzmann model for thermal flows,” IMA Journal of Applied Mathematics, pp. 1-16, (2011). [16] Lutsko, J.F., “Chapman-Enskog expansion about nonequilibrium states with application to the sheared granular fluid,” Phys. Rev. E, vol. 73, 021302, (2006). [17] Chen, H., Chen, S., and Matthaeus, W.H., “Recovery of the Navier-Stokes equation using a lattice Boltzmann method,” Phys. Rev. E, vol. 45, pp.5339–5342, (1992). [18] Chen, Y., Ohashi, H., and Akiyama, M., “ Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations,” Phys. Rev. E, vol. 50, 2776, (1994). [19] Zou, Q.S. and He, X.Y., “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model,” Physics of Fluids, vol. 9, pp.1591–1598, (1997). [20] Shi, Y., Zhao, T. S., and Guo, Z. L., “ Thermal lattice Bhatnagar-Gross-Krook model for flows with viscous heat dissipation in the incompressible limit,” Phys. Rev. E, vol.70, 066310, (2004). [21] 童長青、何雅玲、王勇、劉迎文封閉方腔自然對流的格子-Boltzmann 方法動態模擬，西安交通大學學報(2007)。 [22] 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)。 [23] 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)。
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61601	-
dc.description.abstract	本文研究中，我們使用耦合半古典格子波茲曼法於雙分佈函數模型下，來計算模擬熱流動問題。在此模型下，藉著速度分佈函數來計算速度場；總能分佈函數計算溫度場。由古典格子波茲曼法推導出半古典格子波茲曼法來模擬量子氣體，其方法是利用 Uehling-Uhlenbeck Boltzmann-BGK 方程，經Hermite多項式根據Grad’s moment展開推得，再由Gauss-Hermite積分得到巨觀物理量(數量密度、動量、能量)。此半古典格子波茲曼法可以模擬三種量子氣體效應(Maxwell-Boltzmann統計、Bose-Einstein統計、Fermi-Dirac統計)。於雙分佈函數下，採用D2Q9格子速度模型探討多種Rayleigh number和不同粒子統計情況，模擬自然對流之封閉方腔流、方形腔體之頂蓋有一恆定驅動速度及Rayleigh-Benard自然對流此三種物理問題。由模擬結果分析可以發現，當Rayleigh Number較小時，主要影響整個流場之熱傳方式為傳導所造成，從流線圖可觀察到渦漩會呈近似圓形；隨著Rayleigh Number增大，在流場內熱交換活動越來越劇烈，主要傳遞熱的方式由原本的傳導，漸漸變成以對流為主，其流線圖中的渦漩會漸漸變成橢圓，根據數值結果與前例可得到驗證。因此，使我們瞭解Rayleigh number與流場變化的關係。	zh_TW
dc.description.abstract	A coupled lattice Boltzmann method is proposed for solving thermal flows in the double-distribution-function framework. In the present, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The semiclassical lattice Boltzmann equation is used for describing the flow of fermions and bosons. This method is derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials using Grad’s moment expansion method. By applying Gauss-Hermite quadrature to the moment integration, we have the macroscopic quantities (the number density, number density flux, and energy density), and get the equilibrium distribution function which including Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics. Simulations of 2D natural convection flows, such as square cavity, lid driven cavity flow, and Rayleigh-Benard thermal convection, based on the two-dimensional nine-velocity (D2Q9) lattice model for several Rayleigh numbers and different particle statistics are shown. For low Rayleigh number, a vortex appears at the center of the cavity. When the Rayleigh number increases, the vortex gradually becomes elliptic. The numerical results are in good agreement with the previous data. The heat is transferred mainly by conduction at small Rayleigh number and by convection at large Rayleigh number. Therefore, we understand the relation of Rayleigh number and the change of the flow.	en
dc.description.provenance	Made available in DSpace on 2021-06-16T13:06:59Z (GMT). No. of bitstreams: 1 ntu-102-R00543078-1.pdf: 5401313 bytes, checksum: b14fb81d56b8992b528a117ba0bbb4f9 (MD5) Previous issue date: 2013	en
dc.description.tableofcontents	致謝 I 中文摘要 II Abstract III 目錄 IV 圖目錄 VI 表目標 VIII 符號 IX 第一章、緒論 1 1-1 格子Boltzmann 方法(Lattice Boltzmann method) 1 1-2 格子Boltzmann 法文獻回顧 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 分佈函數（Distribution function） 7 2-3 Boltzmann 方程 7 2-5 格子Boltzmann方程與速度模型 10 2-4 Boltzmann BGK方程 12 2-6 平衡態分佈函數的Hermite展開 13 2-7 外力項的Hermite展開 18 第三章、熱流體動力學之格子Boltzmann方法 19 3-1 總能分佈函數 19 3-2 Chapman-Enskog分析 21 第四章、雙分佈函數半古典格子Boltzmann法理論 24 4-1 理想量子氣體動力學 24 4-2 雙分佈函數之半古典格子Boltzmann方程 25 4-3 宏觀物理量的求法 33 4-4 Chapman-Enskog分析 34 第五章、邊界處理方法和模擬流程 40 5-1 格子Boltzmann方法之邊界條件 40 5-2 收斂條件 44 5-3 模擬流程 45 第六章、模擬結果與討論 46 6-1 物理問題描述 46 6-2 模擬結果分析與討論 55 第七章、結論與展望 76 7-1 結論 76 7-2 展望 77 參考文獻 78
dc.language.iso	zh-TW
dc.subject	雙分佈函數	zh_TW
dc.subject	自然對流	zh_TW
dc.subject	半古典格子波茲曼方法	zh_TW
dc.subject	natural convection	en
dc.subject	double distribution function	en
dc.subject	semiclassical lattice Boltzmann method	en
dc.title	雙分佈函數半古典格子波茲曼法之熱流場模擬	zh_TW
dc.title	Semiclassical Lattice Boltzmann Modeling of Thermal Flows Using Double Distribution Functions	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	雙分佈函數,半古典格子波茲曼方法,自然對流,	zh_TW
dc.subject.keyword	double distribution function,semiclassical lattice Boltzmann method,natural convection,	en
dc.relation.page	80
dc.rights.note	有償授權
dc.date.accepted	2013-08-02
dc.contributor.author-college	工學院	zh_TW
dc.contributor.author-dept	應用力學研究所	zh_TW
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