含重力場半古典格子波茲曼法之微流道流場模擬

Abstract

在近十年間，格子Boltzmann法(Lattice Boltzmann Method, LBM)已發展成為相當重要的一項研究流體流動的工具。在本文的研究中，我們使用含重力場格子Boltzmann法來計算模擬流體在二維微流道中，在不同的Knudsen數，包含了滑移區跟過渡流區，並使用新發展的含重力場半古典格子Boltzmann法，來模擬量子氣體。 半古典格子Boltzmann法是利用Uehling-Uhlenbeck Boltzmann-BGK方程式，藉由Hermite多項式展開推導而得到的。根據邊界上的滑移運動，採用了一個調和係數(accommodation coefficient)來模擬氣體在邊界上的交互作用。 不同的Knudsen數，包含了滑移區跟過渡流區中，模擬了三種不同的粒子統計，計算而得到質量流率跟速度分佈曲線，最後順利發現Knudsen minimum現象的存在。由發現Knudsen minimum現象的展現可做為演算法驗證的方式，並和本研究使用量子統計得出結果做為比較。

In the last decade, Lattice Boltzmann Method, an useful and powerful tool for general fluid flow simulation, has been developed. The two-dimensional micro-channel flow of gas of arbitrary statistics in the slip and transition regimes as characterized by the Knudsen number are studied using a newly developed semiclassical lattice Boltzmann method with gravitational field. The semiclassical lattice Boltzmann method is derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials using moment expansion method. To take into account the slip motion at wall surface, the Maxwellian scattering kernel is adopted to model the gas surface interactions with an accommodation coefficient. The mass flow rates and the velocity profiles are calculated for the three particle statistics over the slip and transition regimes Knudsen numbers. The results indicate that the Knudsen minimum can be captured and distinct characteristics of the effect of quantum statistics can be delineated.