請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56234完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 闕志鴻(Tzihong, Chiueh) | |
| dc.contributor.author | "Chung-Han, Lee" | en |
| dc.contributor.author | 李忠翰 | zh_TW |
| dc.date.accessioned | 2021-06-16T05:19:56Z | - |
| dc.date.available | 2014-08-26 | |
| dc.date.copyright | 2014-08-26 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-15 | |
| dc.identifier.citation | [1] M. Mendoza and J. D. Munoz. Three-dimensional lattice Boltzmann model for electrodynamics. Phys. Rev. E, 82:056708, Nov 2010.
[2] S. M. Hanasoge, S. Succi, and S. A. Orszag. Lattice Boltzmann method for electromagnetic wave propagation. EPL (Europhysics Letters), 96(1):14002, 2011. [3] Yin-Jen Lin. Applications to electromagnetics with lattice Boltzmann method, 2010. [4] Hui Xu and Pierre Sagaut. Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics . Journal of Computational Physics, 230(13):5353 – 5382, 2011. [5] Francois Dubois and Pierre Lallemand. Towards higher order lattice Boltzmann schemes. Journal of Statistical Mechanics, 2009(6):P06006, 2009. [6] A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny. Near-Field Second-Harmonic Generation Induced by Local Field Enhancement. Phys. Rev. Lett., 90:013903, Jan 2003. [7] Hsi-Yu Schive, Yu-Chih Tsai, and Tzihong Chiueh. GAMER: A Graphic Processing Unit Accelerated Adaptive-Mesh-Refinement Code for Astrophysics. The Astrophysical Journal Supplement Series, 186(2):457, 2010. [8] P. A. Skordos. Initial and boundary conditions for the lattice Boltzmann method. Phys. Rev. E, 48:4823–4842, Dec 1993. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56234 | - |
| dc.description.abstract | 晶格波茲曼法是一種傳統上用於模擬流體問題的演算法，在2008年時被應用於電磁學的模擬。波的色散現象是晶格波茲曼法的其中一個缺點，本研究以泰勒展開為基礎，推導出晶格波茲曼法演化中的第三階項，進而修正色散造成的誤差。經過修正後的晶格波茲曼法可以使用自適性網格點的架構使模擬的精度勝於均勻網格點的模擬。為了
提高模擬的效率，本研究也使用了顯示卡的平行運算作為輔助。本研究提出在模擬中加入完美導體網格點所需要的邊界條件，並利用此項邊界條件，模擬與探討偏振分向器、反射式望遠鏡與將細針置於拋物面鏡焦點所產生的近場效應等等問題。 | zh_TW |
| dc.description.abstract | Lattice Boltzmann method(LBM) is traditionally used in the simulation of hydrodynamic problems, and it has been developed to solve electromagnetic wave problems in 2008. The wave dispersion due to grid effects has been known to be a serious problem in the LBM approach. We devised a scheme which bases on third-order Taylor-expansion to correct the dispersion error. The new LBM scheme can naturally incorporate adaptive mesh refinement(AMR) to enhance the accuracy from the uniform grid simulation. We also used graphic processing units(GPU) as a tool to obtain speed-up in computation. This research provides a proper boundary condition for perfect conductor grids. By using this boundary condition, problems like wave polarizer, reflecting telescope and the near-field effect of a needle on the focus of a parabolic mirror are studied by this method. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T05:19:56Z (GMT). No. of bitstreams: 1 ntu-103-R00222078-1.pdf: 4303876 bytes, checksum: 6257448ca34cf0e415543a2f9fa03796 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 1 Introduction 1
1.1 Lattice Boltzmann Method . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Adaptive Mesh Refinement . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Lattice Boltzmann Method In Electrodynamics 5 2.1 Boltzmann Transport Equation . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Model Structure of Lattice Boltzmann Method in Electrodynamics . . . . 6 2.2.1 The discrete velocity and field vectors . . . . . . . . . . . . . . . 6 2.2.2 The procedure of evolution . . . . . . . . . . . . . . . . . . . . . 9 2.3 The Analysis Based on Taylor Expansion to Derive the Evolution Equations 10 2.3.1 Recovering Maxwell’s Equations . . . . . . . . . . . . . . . . . 11 2.3.2 The Third-Order Error Term . . . . . . . . . . . . . . . . . . . . 13 3 Incorporate AMR With LBM 17 3.1 Initialization of The Distribution Functions with Second Order Accuracy . 17 3.2 Remove the second-order error at the coarse-fine boundary . . . . . . . . 23 3.3 Correction Of The Third-Order Dispersion Error . . . . . . . . . . . . . 25 3.3.1 Error prediction and elimination . . . . . . . . . . . . . . . . . . 25 3.3.2 A tiny damping to maintain stability . . . . . . . . . . . . . . . . 34 4 Boundary Condition of Perfectly Conductive Boundary 37 4.1 Regular Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1.1 Specular Reflection . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1.2 Third-order correction in simulations with boundary girds . . . . 40 4.2 Irregular Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2.1 LBM without third-order correction scheme . . . . . . . . . . . . 42 4.2.2 LBM with third-order correction scheme . . . . . . . . . . . . . 43 4.2.3 Using coarser resolution to describe the irregular boundary . . . . 44 4.2.4 Apply A Poisson Solver To Maintain Divergence Free Of Magnetic Field In AMR . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Absorbing Layer in Lattice Boltzmann Method . . . . . . . . . . . . . . 48 5 Application of the LBM with AMR 51 5.1 Wave Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 Reflecting Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.3 Near-field Effect of A Needle on The Focus of A Parabolic Mirror . . . . 59 6 Conclusion 65 Bibliography 69 | |
| dc.language.iso | en | |
| dc.title | 以自適性網格應用於晶格波茲曼之電磁學模擬研究 | zh_TW |
| dc.title | Application of Lattice Boltzmann Method in Electrodynamics with Adaptive Mesh Refinement | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 石明豐(Ming-Feng, Shih),朱士維(Shi-Wei, Chu) | |
| dc.subject.keyword | 晶格波茲曼法,電動力學,自適性網格, | zh_TW |
| dc.subject.keyword | Lattice Boltzmann Method,Electrodynamics,Adaptive Mesh Refinement, | en |
| dc.relation.page | 69 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-08-16 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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