论文标题
Chapman-Enskog多组件Navier-Stokes方程的推导
Chapman-Enskog derivation of multicomponent Navier-Stokes equations
论文作者
论文摘要
将Navier-Stokes方程的表示形式扩展到多组分系统有几个原因。许多技术应用是基于既不存在于纯元素或二进制混合物中的物理现象。尽管傅立叶定律必须在二进制文件中概括，但只有两个以上的组件才能以简单的形式崩溃。耗散现象的出现也影响了惯性限制融合构型，该构型被设计为未来融合核电站的原型，希望能代替裂变核电站。 自从Snider最近提出的形式主义出版\ textit {phys {phys。 Rev. E} \ TextBf {82}，051201（2010）。它以一种非常自然的方式，用独立的部分密度替代线性依赖的原子分数。然后，对于多组分混合物而言，Chapman-Enskog程序比纯元素更为复杂。此外，Baalrud和Daligault在\ textit {phys中对收敛动力学方程的最新建议。等离子体} \ textbf {26}，082106（2019）表明，具有平均力潜力的玻尔兹曼方程在接近平衡的情况下是一个更好的选择，如navier-stokes方程所述，而不是landau或landau或lanard-balescu方程。 在我们的全面演讲中，我们强调了查普曼·恩斯科（Chapman-Enskog）推导背后的物理论点，并使数学尽可能简单。这不仅是技术非必需方面，因此通过Hermite多项式的扩展，线性化玻尔兹曼方程的解。我们讨论了熵增加的热力学的第二个原理，以及从该博览会中学到的东西。
There are several reasons to extend the presentation of Navier-Stokes equations to multicomponent systems. Many technological applications are based on physical phenomena that are present neither in pure elements nor in binary mixtures. Whereas Fourier's law must already be generalized in binaries, it is only with more than two components that Fick's law breaks down in its simple form. The emergence of dissipative phenomena affects also the inertial confinement fusion configurations, designed as prototypes for the future fusion nuclear plants hopefully replacing the fission ones. This important topic can be described in much simpler terms than in many textbooks since the publication of the formalism put forward recently by Snider in \textit{Phys. Rev. E} \textbf{82}, 051201 (2010). In a very natural way, it replaces the linearly dependent atomic fractions by the independent set of partial densities. Then, the Chapman-Enskog procedure is hardly more complicated for multicomponent mixtures than for pure elements. Moreover, the recent proposal of a convergent kinetic equation by Baalrud and Daligault in \textit{Phys. Plasmas} \textbf{26}, 082106 (2019) demonstrates that Boltzmann equation with the potential of mean force is a far better choice in situations close to equilibrium, as described by the Navier-Stokes equations, than Landau or Lenard-Balescu equations. In our comprehensive presentation, we emphasize the physical arguments behind Chapman-Enskog derivation and keep the mathematics as simple as possible. This excludes as a technical non-essential aspect the solution of the linearized Boltzmann equation through an expansion in Hermite polynomials. We discuss the link with the second principle of Thermodynamics of entropy increase, and what can be learned from this exposition.
