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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 楊照彥(Jaw-Yen Yang) | |
| dc.contributor.author | Manuel A. Diaz | en |
| dc.contributor.author | 譚夢寧 | zh_TW |
| dc.date.accessioned | 2021-06-15T13:44:20Z | - |
| dc.date.available | 2016-02-02 | |
| dc.date.copyright | 2016-02-02 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-12-09 | |
| dc.identifier.citation | Abramowitz, M., Stegun, I.A., Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Number 55. Courier Corporation, 1964.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/51681 | - |
| dc.description.abstract | 半古典波茲曼方程式可適用較波茲曼方程式廣泛的傳輸現象, 即適用於遵從量子統計的粒子傳輸現象。半古典波茲曼方程式最初由Nordheim 於 1928 年推導出, 在 1933 年 Uehling 和 Uhlenbeck 擴充。它是能在同一框架下描述古典和量子氣體運動的合適的數學模型。這統一框架雖然形式上簡單, 但實質上卻不是簡單的,並具有非線性量子關係產生很多數值上的挑戰。雖然已有文獻報導許多方法來模擬量子系統的流體問題,量子熱力學關係的非線性性質阻礙了許多方法的運用機會。尤其在量子效應起主要作用,即近簡併狀態。在本文提出一種新的數值方法求解波茲曼 BGK 方程的古典和量子 (Bose-Einstein 和Fermi-Dirac 統計) 氣體問題。此外,利用不連續多項式所發展的數值直解法已完成平行化的工作,應用於模擬量子氣體粒子系統中將大幅增加其計算效率。本研究所提出的數值方法已由氣體動力學基準測試問題得到驗證。本研究是首篇能夠成功呈現包含內部自由度的理想量子氣體運動現象的模式。 | zh_TW |
| dc.description.abstract | The semiclassical Boltzmann equation is a generalization of the classical Boltzmann Equation intended to describe the dynamics of quantum particle system in phase space. Originally formulated by Nordheim in 1928 and extended by Uehling and Uhlenbeck in 1933, it is a suitable mathematical model capable of describing classical and quantum gases under a single framework. This general framework although simple it is not simplistic and possess many numerical challenges due to the non-linear quantum relations that arise in it. Although many approaches to model the hydrodynamic of quantum systems have been reported throughout the literature, the non-linear nature of the quantum thermodynamic relations hinders many methodological opportunities. This is especially true when considering conditions where the quantum effects play a major role, the near-degenerate regimes. In this dissertation, a new numerical methodology is presented to solve the Boltzmann-BGK equation of gas dynamics for the classical and quantum gases described by the Bose-Einstein and Fermi-Dirac statistics. Moreover, an efficient direct solver based on discontinuous polynomial representation is investigated to explore the parallel computing opportunities in modeling quantum gas systems. In this work, the proposed numerical methodology is validated by benchmark problems of gas dynamics. Descriptions of ideal quantum gases including internal degrees of freedom are successfully achieved and reported for the first time. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T13:44:20Z (GMT). No. of bitstreams: 1 ntu-104-F99543083-1.pdf: 5122160 bytes, checksum: eb4dc52f6c4495d201603d951d9406dd (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | CONTENTS
口試委員會審定書(i) Acknowledgments (ii) 中文摘要 (iv) Abstract (v) Contents (vi) List of Figures (ix) Nomenclature (xvi) 1 Introduction (1) 1.1 Overview (1) 1.2 Introduction to Quantum Gases (4) 1.3 Basics of the semiclassical Boltzmann Equation (8) 1.3.1 The Semiclassical Equilibrium States (11) 1.3.2 The Semiclassical Entropy Function and H-Theorem (12) 1.4 The Flow and Physical Regimes (14) 1.5 Contents of the Dissertation (16) 2 The Semiclassical Boltzmann-BGK Model (18) 2.1 Overview (18) 2.2 Semiclassical Boltzmann Equation (21) 2.3 Semiclassical Boltzmann-BGK Model Equation (21) 2.4 Properties of the SB-BGK Model (24) 3 A Unified Treatment (28) 3.1 Overview (28) 3.2 A Unified Treatment for the SB-BGK Model (29) 4 Numerical Implementation (33) 4.1 Overview (33) 4.2 Normalization (34) 4.3 Velocity Domain Discretization (36) 4.4 An Asymptotic-Preserving time integration scheme (37) 4.5 Space Discretization of ∂x Fσ(n) by WENO Methods (39) 4.6 Space Discretization of ∂x Fσ(n) by FR/CPR Method (41) 4.6.1 FR/CPR Formulation (42) 4.6.2 Discontinuity Sensor (45) 4.7 Computing Internal Energy and Fugacity (46) 4.8 Enhancements Strategies (47) 4.8.1 Enforcing Conservation Properties of the BGK Collision Term (47) 4.8.2 Positivity-Preserving Limiter (49) 5 Numerical Investigation (52) 5.1 Overview (52) 5.2 Numerical Verification (53) 5.2.1 Test 1: Mesh Refinement Test (54) 5.2.2 Test 2: CDOM With Shock Tube Test Problems (57) 5.2.3 Test 3: Viscous Shock-Tube Problems (60) 5.3. Numerical Experiments (62) 5.3.1 Experiment 1: 1-D Shock Tube Problems (62) 5.3.2 Experiment 2: Gas Dynamics in the Transition Regime (66) 5.3.3 Experiment 3: 1-D Shock Tube Problem with Bose gas (68) 5.3.4 Experiment 4: 2-D Riemann Problems (71) 6 Conclusions and Future Work (81) 6.1 Overview (81) 6.2 Accomplishments (82) 6.3 Future Work (83) A Extension to the ES-BGK model (85) A.1 Extensions to the Gaussian-BGK model (85) B Tuning the Activation Ramp Parameters (90) B.1 Nodal to Modal Coefficients (90) B.2 Setting the Viscosity Scale (94 C Matlab Codes (97) C.1 The Golub-Welsch Algorithm (97) C.2 Newton-Cotes Quadrature Rules (98) C.3 Polylogarithm Function (100) D Exact Quantum Riemann Solver (103) D.1 Riemann Solver for Quantum Euler Equations (103) Bibliography (114) | |
| dc.language.iso | en | |
| dc.subject | 量子流體動力學 | zh_TW |
| dc.subject | 流量重建 | zh_TW |
| dc.subject | 量子波茲曼方程 | zh_TW |
| dc.subject | Quantum Hydrodynamics | en |
| dc.subject | Flux Reconstruction | en |
| dc.subject | Quantum Boltzmann Equation | en |
| dc.title | 半古典波茲曼 BGK 方程式之任意統計稀薄流模擬 | zh_TW |
| dc.title | Modeling Rarefied Gas Flows of Arbitrary Statistics
with the Semiclassical Boltzmann-BGK equation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 黃俊誠(Juan-Chen Huang),黃美嬌(Mei-Jiau Huang),陳旻宏(Min-Hung Chen),潘國隆(Kuo-Long Pan),牛仰堯(Yang-Yao Ni) | |
| dc.subject.keyword | 量子流體動力學,流量重建,量子波茲曼方程, | zh_TW |
| dc.subject.keyword | Quantum Hydrodynamics,Flux Reconstruction,Quantum Boltzmann Equation, | en |
| dc.relation.page | 120 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2015-12-09 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| Appears in Collections: | 應用力學研究所 | |
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| ntu-104-1.pdf Restricted Access | 5 MB | Adobe PDF |
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