Macroscopic descriptions of rarefied gases from the elimination of fast variables
Macroscopic descriptions of rarefied gases from the elimination of fast variables
复制标题
快速变量消除对稀薄气体的宏观描述
DOI：
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发表时间：
2007
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影响因子：
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通讯作者：
P. Dellar
中科院分区：
文献类型：
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作者：
P. Dellar
描述稀单原子气体的玻尔兹曼方程等价于分布函数连续矩的无限层次演化方程。给出宏观质量、动量和能量密度的五个力矩不受原子间碰撞的影响，而所有其他力矩在快速碰撞时间尺度上自然演化。我们证明了Chen， Rao和Spiegel的宏观方程[Phys。列托人。[271,87(2000)]，就像我们熟悉的纳维-斯托克斯-傅立叶方程一样，通过使用系统程序来消除较高的矩，留下不受碰撞影响的五个矩的封闭演化方程。这两组方程的不同之处在于它们对温度对动量和能量通量的贡献的处理。矩方程为模型碰撞算子的普朗特数问题提供了一种明确的处理方法，大大减少了推导不同碰撞算子方程的工作量，并明确了模型碰撞算子的作用。
The Boltzmann equation describing a dilute monatomic gas is equivalent to an infinite hierarchy of evolution equations for successive moments of the distribution function. The five moments giving the macroscopic mass, momentum, and energy densities are unaffected by collisions between atoms, while all other moments naturally evolve on a fast collisional time scale. We show that the macroscopic equations of Chen, Rao, and Spiegel [Phys. Lett. A 271, 87 (2000)], like the familiar Navier-Stokes-Fourier equations, emerge from using a systematic procedure to eliminate the higher moments, leaving closed evolution equations for the five moments unaffected by collisions. The two equation sets differ through their treatment of contributions from the temperature to the momentum and energy fluxes. Using moment equations offers a definitive treatment of the Prandtl number problem using model collision operators, greatly reduces the labor of deriving equations for different collision operators, and clarifies the role ...