基于Boltzmann模型方程的平板Couette流计算

Simulation of planar Couette flows using the gas-kinetic Boltzmann model

将基于Boltzmann模型方程的气体运动论统一算法推广应用于Couette槽道流计算,发展可用于槽道流问题的气体运动论边界条件数学模型及数值处理方法,研究建立模拟不同Knudsen数二维低速槽道流动问题的气体运动论数值算法,通过将近连续流到高稀薄区Couette剪切流计算结果与基于微观分子统计模拟的类DSMC值、基于宏观流体力学滑移Navier-Stokes解和线化Boltzmann近似解比较分析,显示出该文发展的介观Boltzmann简化速度分布函数方程数值算法对不同尺度槽道流问题具有很强的模拟能力。

The gas-kinetic unified algorithm based on the Boltzmann model equation was extended to analyze gas flow in planar Couette flow. Suitable numeric boundary conditions were developed for the gas kinetic equation for channel flows. The algorithm effectively simulates low-speed flows in two-dimensional channels with various Knudsen numbers. The method was verified by comparing solutions for classical Couette flows with approximate solutions of the Boltzmann equation,DSMC results of statistical particle simulations, and slip Navier-Stokes solutions of macroscopic fluid dynamics. The comparisons show that the gas-kinetic algorithm using the mesoseopic Boltzmann simplified velocity distribution equation effectively simulates the gas flows for various size channels.