标题： NiST：稀薄气体动力学中的非局部时空本构关系 显示英文标题

标题： NiST: a non-localized spatial-temporal constitutive relation in rarefied gas dynamics

摘要： 尽管介观玻尔兹曼方程描述了稀薄气体动力学，但在复杂的工程问题中找到其解是具有挑战性的。 因此，在过去一个半世纪里，提出了许多基于少数宏观变量的偏微分方程。 然而，它们不仅形式复杂，而且当克努森数较大时，无法做出令人满意的预测。 在这里，我们为稀薄气体动力学提出了一种非局域的时空（NiST）本构关系，其中在时间$t$和位置$\bm x$处的应力/热通量由附近时空坐标中的速度/温度梯度通过卷积算子确定。 通过使用库埃特/傅里叶流和自发瑞利-布里渊散射的玻尔兹曼方程解，我们提取了非局域性通用参数作为空间和时间克努森数的函数。 在稀薄气体中的声波传播进一步测试表明，NiST 本构关系可以在广泛的克努森数范围内预测稀薄气体流动。 显示英文摘要

摘要： Although the mesoscopic Boltzmann equation describes the rarefied gas dynamics, finding its solutions in complicated engineering problems is challenging. Therefore, over the past one and a half centuries, many partial differential equations based on a few macroscopic variables are proposed. However, they not only have complicated forms, but also cannot make satisfactory prediction when the Knudsen number is large. Here, we propose a non-localized spatial-temporal (NiST) constitutive relation for rarefied gas dynamics, where the stress/heat flux at time $t$ and position $\bm x$ is determined by the velocity/temperature gradient in the nearby spatial-temporal coordinates, via convolution operators. By using the solutions of the Boltzmann equation for the Couette/Fourier flow and the spontaneous Rayleigh-Brillouin scattering, we extract the universal parameters of non-locality as functions of the spatial and temporal Knudsen numbers. Further tests in the sound propagation in rarefied gas show that the NiST constitutive relation can predict the rarefied gas flow over a wide range of Knudsen number.