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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 | Nan-Huei Jiang | en |
dc.contributor.author | 江南輝 | zh_TW |
dc.date.accessioned | 2021-06-07T23:44:29Z | - |
dc.date.copyright | 2014-07-11 | |
dc.date.issued | 2014 | |
dc.date.submitted | 2014-07-09 | |
dc.identifier.citation | [1] Uehling, E. A. & Uhlenbeck, G. E., (1933) “Transport phenomena in einstein-bose and Fermi-dirac gases, I”, Physical Review, 43, pp. 553-561.
[2] Abramowitz, M. & Stegun, I. A. (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, ninth dover printing, tenth gpo printing edition. [3] van Leer, B., (1979) “Towards the Ultimate Conservative difference scheme V. A second-order sequel to Godunov’s method ” Journal of Computational Physics, 32, pp. 101–136. [4] Yang, J., Liu, Y. & Lomax, H. (1987) “Computation of shock wave reflection by circular cylinders.” AIAA Journal 25, 683-689. [5] Harten, A., Engquist, B., Osher, S. & Chakravarthy, S., (1987) “Uniformly High Order Essentially Non-Oscillatory Schemes, III”, Journal of Computational Physics, 71, pp. 231-303. [6] Shu, C. W. & Osher, S., (1988) “Efficient Implementation of Nonoscillatory Shock Capturing Schemes”, Journal of Computational Physics, 77, pp. 439-471. [7] Shu, C. W. & Osher, S., (1989) “Efficient Implementation of Nonoscillatory Shock Capturing Schemes II”, Journal of Computational Physics, 83, pp. 32-78. [8] Bird, G. A., (1994) Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press Oxford. [9] Liu, X. D., Osher, S. & Chan, T., (1994) “Weighted Essentially NonoscillatorySchemes,” Journal of Computational Physics, 115, pp. 200-212. [10] Cercignani, C., Gamba, I.M., Jerome, J.W. & Shu, C. W., (2000) “Device Benchmark Comparisons via Kinetic, Hydrodynamic, and High-Field Models”, Computer Methods in Applied Mechanics and Engineering, 181, pp. 381-392. [11] Anile, M. A., Carrillo J. A., Gamba, I. M. & Shu, C. W., (2001) “Approximation of the BTE by a Relaxation-time Operator: Simulations for a 50 nm-channel Si Diode”, VLSI Design, 13, pp. 349-354. [12] Henning Struchtrup (2005) Macroscopic Transport Equations for Rarefied Gas Flows, Approximation Methods in Kinetic Theory, Interaction of Mechanics and Mathematics. [13] Muljadi, B. P., Yang, J. Y. (2010) “A direct Boltzmann-BGK equation solver for Arbitrary Statistics using the Conservation Element/Solution Element and Discrete Ordinate Method”, Kuzmin, A. (ed.) Computational Fluid Dynamics 2010, pp. 637–642. [14] Alekseenko, A. M., (2011) “Numerical Properties of High Order Discrete Velocity Solutions to the BGK Kinetic Equation”, Applied Numerical Mathematics, 61, pp. 410–427. [15] Muljadi, B. P., Yang, J. Y. (2011) “Simulation of Shock Wave Diffraction over 90° Sharp Corner in Gases of Arbitrary Statistics”, Journal of Statistical Physics, 145, pp. 1674-1688. [16] Shi, Y. H., Huang, J. C. & Yang, J. Y., (2007) “High Resolution Kinetic Beam Schemes in Generalized Coordinates for Ideal Quantum Gas Dynamics”, Journal of Computational Physics, 222, pp. 573-591. [17] Yang, J. Y., Hsieh, T. Y. & Shi, Y. H., (2007a) “Kinetic Flux Splitting Schemes for Ideal Quantum Gas Dynamics” , SIAM Journal on Scientific Computing, 29, pp. 221-244. [18] Yang, J. Y., Hsieh, T. Y., Shi, Y. H. & Xu, K., (2007b) “High Order Kinetic Flux Vector Splitting Schemes in General Coordinates for Ideal Quantum Gas Dynamics”, Journal of Computational Physics, 227, pp. 967-982. [19] Yang, J. Y., Shi, Y. H. (2008) “A Gas-Kinetic BGK Scheme for Semiclassical Boltzmann Hydrodynamic Transport”, Journal of Computational Physics, 227, pp. 9389-9407. [20] Lei, W., Jianping Meng, Yonghao Zhang (2012) “Kinetic Modeling of the Quantum Gases in the Normal Phase”, The Royal Society, 468, pp.1799-1823 [21] 李念達(2012) 量子統計稀薄氣體直接解法研究,國立臺灣大學工學院應用力學所博士論文,臺北。 [22] 黃俊誠 (1995) 波茲曼模型方程式之數值方法,國立臺灣大學工學院應用力學所博士論文,臺北。 [23] 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,國立臺灣大學工學院應用力學所博士論文,臺北。 [24] 湯國樑 (2005) 波茲曼方程式之高解析數值方法,國立臺灣大學工學院應用力學所博士論文,臺北。 [25] 石育炘 (2008) 半古典波茲曼方程式之動力數值方法-波色子與費米子流體之氣體動力學,國立臺灣大學工學院應用力學所博士論文,臺北。 [26] 顏致遠 (2013) 半古典橢圓波茲曼模型方程式的直接解法,國立臺灣大學工學院應用力學所碩士論文,臺北。 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16724 | - |
dc.description.abstract | 本文利用通量分離法來求解半古典波茲曼BGK模型方程式和半古典波茲曼橢球BGK模型方程式,利用橢球BGK模型中參數來修正BGK模型中的普郎特數,以及調整BGK模型中的鬆弛時間來改變流場的稀薄度,並以不同馬赫數的流場、文獻來驗證本研究模擬的正確性。另外,將卡式座標系統轉換至廣義座標系統,來解決結構網格在曲面型邊界的問題,而本文使用圓柱流場做驗證,並比較在量子氣體,玻色-愛因斯坦統計、費米-狄拉克統計與古典極限的馬克斯威爾-波茲曼統計有何不同。
空間離散所使用之數值方法為高解析算則中的全變量消逝法,其能夠結合高階與低階準確算則的好處,以解決各別在連續解與不連續解的問題;在初始值問題中使用加權型基本不震盪算則來提高在不連續解的準確性。在時間離散中,分別加入顯式算則與隱式算則,來求解在廣義座標系統下的半古典波茲曼BGK模型方程式,模擬震波暫態與穩態的物理問題,而本研究主要以圓柱震波繞射作為驗證。 | zh_TW |
dc.description.abstract | I solved the Semiclassical Boltzmann BGK model equations and Semiclassical Boltzmann Ellipsoidal BGK model equations by flux vector splitting method, and we can adjust Prandtl number is correct by Ellipsoidal BGK model. And then, we can adjust the level of rarefied flow by relaxation time in BGK model. The result of simulation could be validated in different Mach numbers and literature. In addition, we transformed Cartesian coordinate system to generalized coordinate system in order to solve the curved boundary on structure mesh, and compared the difference in Bose–Einstein statistics, Fermi–Dirac statistics, and Maxwell-Boltzmann statistics.
The present numerical methods combined total variation diminishing in discrete space and implicit methods in discrete time, and solved the Semiclassical Boltzmann BGK model equations in generalized coordinate system. Weighted Essentially Non-Oscillatory (WENO) are applied to initial value problem. | en |
dc.description.provenance | Made available in DSpace on 2021-06-07T23:44:29Z (GMT). No. of bitstreams: 1 ntu-103-R01543016-1.pdf: 11136447 bytes, checksum: 21f302aa22fd20979d1ad94f3b3bfc28 (MD5) Previous issue date: 2014 | en |
dc.description.tableofcontents | 誌謝 1
摘要 2 ABSTRACT 3 目錄 4 附圖目錄 6 附表目錄 10 第一章 緒論 12 1-1引言 12 1-2文獻回顧 13 1-3研究目的 14 1-4本文架構 14 第二章 波茲曼方程式 16 2-1 稀薄氣體動力學 16 2-2 分子速度分佈與其巨觀量 17 2-3 LIOUVILLE方程式 20 2-4 BOLTZMANN方程式 21 2-5 鬆弛時間近似 23 2-6 固體壁面的邊界條件 24 第三章 半古典波茲曼方程式 25 3-1 理想氣體動力學 25 3-2 半古典波茲曼方程式 27 3-3 半古典橢球BGK模型波茲曼方程式 31 3-4 無因次化 33 第四章 數值方法 36 4-1分立座標法 36 4-2分立座標法與高斯赫邁積分公式之應用 37 4-3空間與時間離散 39 4-3-1顯式算則 39 4-3-2廣義座標軸系統 40 4-3-3隱式算則 42 4-3-4全量消逝法(TOTAL VARIATION DIMINISHING, TVD) 44 4-3-5加權型基本不震盪算則(WENO) 47 4-4邊界條件 49 4-5初始條件的設置 49 4-6程式流程圖 52 第五章 數值模擬結果與討論 53 第六章 結論與未來展望 127 6-1結論 127 6-2未來展望 128 參考文獻 129 | |
dc.language.iso | zh-TW | |
dc.title | 半古典波茲曼模型方程式在廣義座標下之相空間直接解法 | zh_TW |
dc.title | A Direct Solver in Phase Space for Semiclassical Boltzmann Model Equation in General Coordinates | en |
dc.type | Thesis | |
dc.date.schoolyear | 102-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 黃俊誠(Juan-Chen Huang),陳旻宏(Min-Hung Chen),洪鉦杰(Jeng-Jye Hung),謝澤揚(Tse-Yang Hsieh) | |
dc.subject.keyword | 廣義座標系統,半古典波茲曼BGK模型方程式,半古典波茲曼橢球BGK模型方程式,全變量消逝法,加權型基本不震盪算則,隱式算則, | zh_TW |
dc.subject.keyword | Generalized coordinate system,Semiclassical Boltzmann-BGK model equations,Semiclassical Boltzmann Ellipsoidal-BGK model equations,Total Variation Diminishing,implicit method,Weighted Essentially Non-Oscillatory method, | en |
dc.relation.page | 131 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2014-07-09 | |
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 |
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