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Title: | 半古典橢圓波茲曼模型方程式的直接解法 A Direct Solver for Semiclassical Ellipsoidal Statistical Model Boltzmann Equation |
Authors: | Chih-Yuan Yan 顏致遠 |
Advisor: | 楊照彥 |
Keyword: | 波茲曼BGK 方程,橢圓統計BGK 方程,半古典波茲曼BGK 方程,離散座標法,全變量消逝法, ES-BGK model,semiclassical-Boltzmann-BGK equation,discrete ordinate method,TVD method, |
Publication Year : | 2013 |
Degree: | 碩士 |
Abstract: | 對於求解不同統計粒子流動問題本文提出另一種模型,修正了半古典的波茲
曼BGK 方程式中普朗特數的不正確, 此三種統計粒子分別遵循著 Maxwell-Boltzmann、Fermi-Dirac、Bose-Einstein 並且同於BGK 方法,加入了鬆 弛時間來近似處理相空間中廣泛的紐森數之氣體動力學問題。 本文測試了3 種普朗特數(b=0.5,b=0,b=-0.5)在一維激波管和二維激波管問 題上,並且加入了三種統計使得可以觀察在不同普朗特數下不同粒子的分布情況, 主要將流場之密度、壓力、速度、壓力張量等畫出來比較ESBGK 和BGK 模型 方程之差異,同時也驗證了BGK 方程僅是ESBGK 的一種特例,因此改變鬆弛 時間所產生的變化兩者也相同,並且發現兩者在壓力張量部分差距較大。此測詴 驗證了ESBGK 模型可較彈性的調整普朗特數,有效的改善了BGK 模型中普朗 特數的不正確性。 數值方法方面使用了離散座標法處理速度空間的部分,高解析算則全變量消 逝法來處理空間分佈,時間部分則使用顯示算則。 Gas flow problems which include particle statistics namely, Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are simulated by using direct solver for solving Ellipsoidal Statistical-BGK equation. The computational experiments include one -dimensional shock tube problem and two-dimensional Riemann gas flow problems. We can control the value of Prandtl number by adjusting parameter b and it relaxes the fixed Prandtl number assumption in BGK classical model. By observing the results, some obvious difference arises when comparing their pressure tensor distributions. The numerical method is based on applying the discrete ordinate method in velocity space to render a set of linear advection equations in physical space then applying the high-resolution method such as total variation diminishing scheme to solve them. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62211 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 應用力學研究所 |
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ntu-102-1.pdf Restricted Access | 18.26 MB | Adobe PDF |
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