基于推广的多元Boltzmann方程的求解 一组可观察物

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摘要翻译：
我们基于包括每个组分的流体动力学速度和温度在内的可观测量集，给出了多组分Boltzmann动力学方程的摄动解。通过对Enskog提出的形式密度缩放方案进行修正，使各分量的密度独立缩放，从而得到解。由此，我们得到了物种动量平衡方程和能量平衡方程，源项描述了不同组分之间相应量的传递。在零级近似下，这些方程是欧拉方程，动量和热扩散以经典的Maxwell-Stefan扩散项的形式包含。采用一阶近似，得到了一个Navier-Stokes型方程，其中部分粘度和热导率仅包括同一组分颗粒的关联式。计算了对Maxwell-Stefan项的一阶修正，以及对梯度的贡献、梯度的双线性和可观测量的差值。一阶动量源项包含了热扩散。粘度和热导率的非对角分量（在组分指数中）表现为二阶贡献。
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英文标题：
《Solution of the Multicomponent Boltzmann Equation Based on an Extended
  Set of Observables》
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作者：
S.V. Savenko and E.A.J.F. Peters and P.J.A.M. Kerkhof
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
--

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英文摘要：
  We present the perturbative solution of the multicomponent Boltzmann kinetic equation based on the set of observables including the hydrodynamic velocity and temperature for each component. The solution is obtained by modifying the formal density scaling scheme by Enskog, such that the density of each component is scaled independently. As a result we obtain the species momentum and energy balance equations with the source terms describing the transfer of corresponding quantities between different components. In the zero order approximation those are the Euler equations with the momentum and heat diffusion included in the form of the classical Maxwell-Stefan diffusion terms. The first order approximation results in equations of a Navier-Stokes type with the partial viscosity and heat conductivity including only the correlations of the particles of the same component. The first order corrections to the Maxwell-Stefan terms as well as the contributions bilinear in gradients and differences of observables are calculated. The first order momentum source term is shown to include thermal diffusion. The nondiagonal (in component indexes) components of viscosity and heat conductivity appear as second order contributions.
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PDF链接：
https://arxiv.org/pdf/707.3067

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