Higher-order continuum approximation for rarefied gases
Higher-order continuum approximation for rarefied gases
复制标题
稀薄气体的高阶连续谱近似
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Jean
中科院分区：
文献类型：
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作者：
E. Spiegel;Jean
平均飞行时间的动力学方程的Hilbert-Chapman-Enskog展开式被认为是渐近的而不是收敛的。因此，它是不可取的，使用较低的顺序结果来简化目前的近似是在传统的Chapman-Enskog程序中所做的，因为这是一个迭代方法。通过避免这种循环的低阶结果，得到的宏观方程是渐近等价的Chapman-Enskog方法中发现的。新方程包含在Chapman-Enskog方法中被丢弃的高阶项。这些对超声传播等问题的结果产生重大影响。在本文中，它表明，这些结果很好，相对较小的复杂性时，展开进行到第二阶的平均自由时间，为例的松弛或Bhatnagar-Gross-Krook模型的动力学理论。
The Hilbert–Chapman–Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman–Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman–Enskog approach. The new equations contain higher order terms that are discarded in the Chapman–Enskog method. These make a significant impact on the results for such problems as ultrasound propagation. In this paper, it is shown that these results turn out well with relatively little complication when the expansions are carried to second order in the mean free time, for the example of the relaxation or Bhatnagar–Gross–Krook model of kinetic theory.