Moving boundary problems for a rarefied gas: Spatially one-dimensional case
Moving boundary problems for a rarefied gas: Spatially one-dimensional case
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DOI：
10.1016/j.jcp.2013.05.017
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发表时间：
2013-10
期刊：
影响因子：
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通讯作者：
Tetsuro Tsuji;K. Aoki
中科院分区：
文献类型：
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作者：
Tetsuro Tsuji;K. Aoki
基于Boltzmann方程的Bhatnagar-Gross-Krook（BGK）模型，数值研究了无限宽平板法向振动引起的稀薄气体全空间非定常流动。本文的目的是显示固有的性质和困难，在气体动力学理论中使用一个简单的一维设置的移动边界问题。更具体地说，考虑以下两个问题：（问题I）板开始强迫谐波振荡（强迫运动）;（问题II）板，这是服从胡克定律的外部恢复力，从其平衡位置位移和释放（自由运动）。问题I的物理意义在于非线性声波在稀薄气体中的传播，而问题II则在于平板振荡的衰减率。本文在特征线法的基础上发展了一种精确的数值方法，它能描述由振动板引起的奇异性，并应用于上述两个问题。结果，解的非定常行为，如传播的不连续性和一些较弱的奇异性的分子速度分布函数，澄清。一些结果也与基于现有方法的结果进行了比较。
Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hooke’s law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method.