晶格波茲曼法在自適性網格下之線性及非線性光學介質

Nonlinear and Linear Optical Medium in Lattice Boltzmann Method with Adaptive Mesh Refinement

許家榮(Chia-Jung Hsu)

指導教授 ： 闕志鴻

國立臺灣大學/理學院/物理研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.02879

摘要

本篇的內容主要為晶格波茲曼法在電磁波上的模擬研究，針對已在波的色散現象上修正、具有三階精準度的模擬方法，討論在使用鏡面反射表現理想導體的狀況下，如何修正高階修正項的計算；以及在鑲嵌到自適性網格的架構下時，如何保持演算法的穩定性。最後並將在介質中的計算一併放入前述架構中，且測試在非線性介質中的可行性。

關鍵字

晶格波茲曼 ； 自適性網格 ； 電動力學

並列摘要

We base on the lattice Boltzmann method for electrodynamics, whose dispersion error has been removed and is third order accuracy. In this thesis, the way to compute the correction term is modified when we use the specular reflection to represent the perfect conductor. Besides, there is also discussion about the way to keep the stability under the frame of adaptive mesh refinement. Finally, the computation in the medium will also be incorporated with the algorithm above, and test the performance in nonlinear medium.

並列關鍵字

Lattice Boltzmann Method ； Adaptive Mesh Refinement ； Electrodynamics

參考文獻

[1] A Practical Introduction to the Lattice Boltzmann Method. Mar. 2008.

[3] Y.-J. Lin. Applications to Electrodynamics with Lattice Boltzmann Method, Oct. 2010.

[4] M. Mendoza and J. D. Muñoz. Three Dimensional Lattice-Boltzmann Model for Electrodynamics. ArXiv e-prints, June 2008.

[5] H.-Y. Schive, Y.-C. Tsai, and T. Chiueh. GAMER: A Graphic Processing Unit Accelerated Adaptive-Mesh-Refinement Code for Astrophysics. apjs, 186:457–484, Feb.2010.

[2] C.-H. Lee. Application of Lattice Boltzmann Method in Electrodynamics with Adaptive Mesh Refinement, Nov. 2014.