半古典Shakhov模型格子波茲曼法之發展與流場模擬

Development of Semiclassical Lattice Boltzmann Method with Shakhov Model for Flow Simulation

黃玟瑜(Wun-Yu Huang)

指導教授 ： 楊照彥

國立臺灣大學/工學院/應用力學研究所/碩士(2015年)

https://doi.org/10.6342/NTU.2015.02457

摘要

本研究發展出半古典Shakhov模型格子波茲曼法，是基於Shakhov模型格子波茲曼方程式與半古典格子波茲曼方程式推導而來，以修正普朗特數(Prandtl Number)且考慮量子氣體為目的，使得適用性更為廣泛，計算流場更趨於真實性。此方法利用Hermite展開法，得到半古典Shakhov模型平衡態分布函數的Hermite展開式，並透過Chapman-Enskog展開得到其鬆弛時間與黏滯係數之間的關係，以半古典Shakhov模型格子波茲曼方程式來模擬計算流場。本文透過此方法，以D2Q9格子速度模型和反彈邊界為基礎，模擬方腔流流場問題，由不同普朗特數以及不同雷諾數的條件下模擬Bose-Einstein統計與Fermi-Dirac統計和Maxwell-Boltzmann統計的粒子，展示半古典Shakhov模型格子波茲曼法在各流場的狀態，並由模擬結果比較半古典Shakhov模型格子波茲曼法與半古典格子波茲曼法之差異性。

關鍵字

格子波茲曼法 ； 半古典Shakhov模型格子波茲曼法 ； 半古典格子波茲曼法 ； 波茲曼BGK方程式 ； Shakhov模型 ； D2Q9格子速度模型 ； 方腔流

並列摘要

A Semiclassical Lattice Boltzmann Method with Shakhov Model based on Shakhov Model Lattice Boltzmann equations and Semiclassical Lattice Boltzmann equations is presented. In order to take the Prandtl number and the quantum effect into consideration for approximate exact solution. The equilibrium distribution function is expanded by the Semiclassical Shakhov Model in term of Hermite polynomials, and the relationship between relaxation time and viscosity is obtained by using Chapman-Enskog expansion. Simulation of the lid driven cavity flows based on D2Q9 lattice model and Bounce-Back boundary condition are studied under Bose-Einstein, Fermi-Dirac and Maxwell-Boltzmann statistics with different Parndtl number and Reynolds numbers in the thesis. Based on the result of simulations, a comparison between Semiclassical Lattice Boltzmann Method with Shakhov Model and Semiclassical Lattice Boltzmann Method is made.

並列關鍵字

Lattice Boltzmann Method ； Semiclassical Lattice Boltzmann Method with Shakhov Model ； Semiclassical Lattice Boltzmann Method ； Boltzmann BGK Equation ； Shakhov Model ； D2Q9 Lattice Model ； Lid Driven Cavity Flows

參考文獻

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