时变螺旋对称下的动力学约化与流体动力学
Kinetic Reduction and Hydrodynamics under Time-Dependent Helical Symmetry
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- School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院）
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中文总结 AI 辅助
本文针对时变螺旋对称稀薄气体，采用objective molecular dynamics框架推导约化玻尔兹曼方程并得到对应流体方程，经与直接模拟蒙特卡罗解对比，一阶流体修正可提升应力各向异性与径向温度变化的预测精度。
中文摘要 AI 辅助
平移对称与螺旋对称为自然界和工程中诸多流动提供了理想化描述。尽管平移对称流动已在动力学与连续介质框架下得到广泛研究，但螺旋流动的微观动力学与连续介质行为间的对应关系仍欠发展。本文针对具有时变螺旋对称的稀薄气体研究该对应关系，采用objective molecular dynamics框架推导了保留径向变化且在螺旋对称下保持经典碰撞算子的约化玻尔兹曼方程，通过形式流体动力学展开得到对应的欧拉方程与纳维-斯托克斯-傅里叶方程。所得模型描述了圆柱几何与轴向变形如何影响输运（包括黏性输运与热传导），以及变形如何与碰撞弛豫竞争，沿轴向与垂直轴向产生不等应力。与直接模拟蒙特卡罗解的对比检验了空间均匀与径向变化流动，在所研究案例中，一阶流体修正捕捉了主导应力各向异性并提升了径向温度变化的预测，而更大的努森数则暴露了该近似的局限性。
英文摘要
Translational and helical symmetries provide idealized descriptions of many flows encountered in nature and engineering. While translationally symmetric flows have been extensively studied within kinetic and continuum frameworks, the corresponding connection between microscopic dynamics and continuum behaviour for helical flows is less developed. Here, we investigate this connection for a dilute gas with time-dependent helical symmetry. Using the objective molecular dynamics framework, we derive a reduced Boltzmann equation that retains radial variations while preserving the classical collision operator under helical symmetry. Formal hydrodynamic expansions then yield the corresponding Euler and Navier-Stokes-Fourier equations. The resulting models describe how cylindrical geometry and axial deformation influence transport, including viscous transport and heat conduction, and how deformation generates unequal stresses along and across the axis in competition with collisional relaxation. Comparisons with direct simulation Monte Carlo solutions examine both spatially uniform and radially varying flows. In the cases studied, the first-order fluid corrections capture the leading stress anisotropy and improve the prediction of radial temperature variations, while larger Knudsen numbers expose limitations of the approximation.
