发表机构
Graduate School of Informatics, Kyoto University（京都大学信息研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究数值模拟无限薄圆盘在稀薄气体中的辐射计效应，采用线性化BGK模型并处理边缘不连续性，发现辐射计力随Knudsen数单调增加，终端速度非单调变化，并提供参考解与验证。
AI 中文摘要
辐射计效应是一种自热泳现象，即两侧存在温差的薄物体在稀薄气体中会受到力的作用。我们数值研究了在静止气体中以终端速度自由平移的无限薄圆盘上的这一效应。问题采用Boltzmann方程的线性化Bhatnagar-Gross-Krook模型并施加漫反射边界条件进行公式化。主要困难源于尖锐的圆盘边缘，其在速度分布函数中产生不连续性并向气体中传播。精确分辨这些不连续性对于捕捉近连续区中与辐射计力相关的边缘局部应力至关重要。我们采用基于特征值的数值格式显式处理这些不连续性，并结合无界域的适当远场渐近。在广泛的Knudsen数范围内获得了辐射计力、终端速度以及流场和应力场。无量纲辐射计力随Knudsen数单调增加，在连续极限下按$\mathrm{Kn}^{3/2}$标度，在自由分子极限下趋近常数。终端速度对Knudsen数呈非单调依赖，在中等Knudsen数下略超过其自由分子极限值。在连续极限下，法向应力差的边缘局部变化幅度似乎保持有限，而其特征宽度约为分子平均自由程的量级。所得数值数据也为未来尖锐边缘动力学问题的研究提供了参考解。最后，利用线性化Boltzmann方程的对称关系独立验证了计算得到的辐射计力。
英文摘要
The radiometer effect is a self-thermophoretic phenomenon in which a thin body with a temperature difference between its two sides experiences a force in a rarefied gas. We numerically investigate this effect for an infinitely thin circular disk freely translating at its terminal velocity in an otherwise quiescent gas. The problem is formulated using the linearized Bhatnagar--Gross--Krook model of the Boltzmann equation with the diffuse reflection boundary condition. A major difficulty arises from the sharp disk edge, which generates discontinuities in the velocity distribution function that propagate into the gas. Accurate resolution of these discontinuities is essential for capturing the edge-localized stress associated with the radiometric force in the near-continuum regime. The discontinuities are explicitly accounted for using a characteristic-based numerical scheme, together with the appropriate far-field asymptotics for the unbounded domain. The radiometric force, the terminal velocity, and the flow and stress fields are obtained over a wide range of Knudsen numbers. The dimensionless radiometric force increases monotonically with the Knudsen number, scaling as $\mathrm{Kn}^{3/2}$ in the continuum limit and approaching a constant in the free-molecular limit. The terminal velocity exhibits a nonmonotonic dependence on the Knudsen number and slightly exceeds its free-molecular-limit value at intermediate Knudsen numbers. In the continuum limit, the magnitude of the edge-localized variation of the normal-stress difference appears to remain finite, whereas its characteristic width is of the order of the molecular mean free path. The resulting numerical data also provide reference solutions for future studies of sharp-edge kinetic problems. Finally, the computed radiometric force is independently validated using the symmetric relation for the linearized Boltzmann equation.
Comments24 pages, 10 figures, 4 tables
