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arXiv 1701.09052cond-mat.soft
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光滑硬球稀颗粒气体的高阶矩理论

Higher-order moment theories for dilute granular gases of smooth hard-spheres

Vinay Kumar Gupta, Priyanka Shukla, Manuel Torrilhon

摘要:

格拉德的矩量法是用来开发高阶格拉德的矩方程-第一个26矩-颗粒气体(非弹性)玻尔兹曼方程的框架内。本文用Grad的26阶矩方程在半线性化条件下研究了自由冷却颗粒气体的均匀冷却状态,结果表明,在均匀冷却状态下,颗粒温度仍按Haff定律衰减,而其它高阶矩在更快的时间尺度上衰减。应力和热通量的本构关系(Navier-Stokes和傅立叶关系)进行Chapman-Enskog样的扩展的Grad的26阶矩方程,并与文献中存在的。通过将各子系统分解为纵向和横向两个系统,利用Grad的26阶矩系统分析了均质冷却状态的线性稳定性。结果表明,在非弹性气体情况下,纵、横系统中的一个本征模是不稳定的。通过比较各种理论的本征模,它是成立的13矩本征模理论预测,不稳定的本征模保持不稳定的所有波数低于一定的恢复恢复系数,而任何其他高阶矩理论表明,这种模式变得稳定的一些临界波数以上的所有值的恢复恢复系数。特别是,格拉德的26矩理论导致一个光滑的轮廓的临界波数相比,其他考虑的理论。此外,通过梯度26矩和现有的理论得到的临界系统尺寸也非常一致。

英文摘要:

Grad's method of moments is employed to develop higher-order Grad's moment equations---up to first 26-moments---for granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling granular gas is investigated with the Grad's 26-moment equations in a semi-linearized setting and it is shown that the granular temperature in the homogeneous cooling state still decays according to Haff's law while the other higher-order moments decay on a faster time scale. The constitutive relations for stress and heat flux (the Navier--Stokes and Fourier relations) are obtained by performing a Chapman--Enskog-like expansion on the Grad's 26-moment equations and compared with those existing in the literature. The linear stability of the homogeneous cooling state is analyzed through the Grad's 26-moment system and various sub-systems by decomposing them into longitudinal and transverse systems. It is found that one eigenmode in both longitudinal and transverse systems in case of inelastic gases is unstable. By comparing the eigenmodes from various theories, it is established that the 13-moment eigenmode theory predicts that the unstable eigenmode remains unstable for all wavenumbers below a certain coefficient of restitution while any other higher-order moment theory shows that this mode becomes stable above some critical wavenumber for all values of coefficient of restitution. In particular, the Grad's 26-moment theory leads to a smooth profile for the critical wavenumber in contrast to the other considered theories. Furthermore, the critical system size obtained through the Grad 26-moment and existing theories are also in excellent agreement.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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