多鬆弛時間半古典格子波茲曼法之發展與流場模擬

Abstract

基於Uehling-Uhlenbeck Boltzmann-BGK方程（Uehling-Uhlenbeck Boltzmann Bhatnagar-Gross-Krook Equation）和多鬆弛時間格子波茲曼方法（Multi Relaxation Time Lattice Boltzmann Mathed，MRT-LBM）為基礎的多鬆弛時間半古典格子波茲曼方法。此方法成功地從動力學統御方程式，藉由Hermite多項式與各種氣體動力學近似推導而得到。本文藉由此方法，並以D2Q9格子模型為基礎模擬方腔流流場問題，由多個雷諾數和三種不同的粒子分別遵循Bose-Einstein統計與Fermi-Dirac統計和Maxwell-Boltzmann統計展示了這個方法。模擬結果指出在量子統計中特殊特性的結果。

A Multi Relaxation Time Semiclassical Lattice Boltzmann Method based on the Uehling-Uhlenbeck Boltzmann-BGK equation （Uehling-Uhlenbeck Boltzmann Bhatnagar-Gross-Krook Equation）and Multi Relaxation Time Lattice Boltzmann Method（MRT-LBM）is presented. The method is directly derived by projecting the kinetic governing equation onto the tensor Hermite polynomials and various hydrodynamic approximation orders can be achieved. Simulations of the lid driven cavity flows based on D2Q9 lattice model for several Reynolds numbers and three different particles that obey Bose-Einstein and Fermi-Dirac and Maxwell-Boltzmann statistics are shown to illustrate the method. The results indicate distinct characteristics of the effects of quantum statistics.