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Regularized moment equations for binary gas mixtures: Derivation and linear analysis

机译：二元混合气的正则矩方程：推导和线性分析

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The applicability of the order of magnitude method [H. Struchtrup, "Stable transport equations for rarefied gases at high orders in the Knudsen number," Phys. Fluids 16, 3921-3934 (2004)] is extended to binary gas mixtures in order to derive various sets of equations-having minimum number of moments at a given order of accuracy in the Knudsen number-for binary mixtures of monatomic-inert-ideal gases interacting with the Maxwell interaction potential. For simplicity, the equations are derived in the linear regime up to third order accuracy in the Knudsen number. At zeroth order, the method produces the Euler equations; at first order, it results into the Fick, Navier-Stokes, and Fourier equations; at second order, it yields a set of 17 moment equations; and at third order, it leads to the regularized 17-moment equations. The transport coefficients in the Fick, Navier-Stokes, and Fourier equations obtained through order of magnitude method are compared with those obtained through the classical Chapman-Enskog expansion method. It is established that the different temperatures of different constituents do not play a role up to second order accurate theories in the Knudsen number, whereas they do contribute to third order accurate theory in the Knudsen number. Furthermore, it is found empirically that the zeroth, first, and second order accurate equations are linearly stable for all binary gas mixtures; however, although the third order accurate regularized 17-moment equations are linearly stable for most of the mixtures, they are linearly unstable for mixtures having extreme difference in molecular masses. (C) 2016 AIP Publishing LLC.
机译：数量级方法的适用性[H． Struchtrup，“努氏数中高阶稀有气体的稳定输运方程式”，物理。流体16，3921-3934（2004）]扩展到二元气体混合物，以便推导各种方程组-在给定的精度下以Knudsen数具有最小的矩数-对于单原子惰性理想的二元混合物气体与麦克斯韦相互作用势相互作用。为简单起见，方程式以线性形式导出，直到Knudsen数达到三阶精度。在零阶时，该方法生成欧拉方程。一阶，它的结果是Fick，Navier-Stokes和Fourier方程;在二阶时，它产生了一组17个矩方程。在三阶，它导致正规化的17矩方程。将通过量级方法获得的Fick，Navier-Stokes和Fourier方程中的输运系数与通过经典Chapman-Enskog展开法获得的输运系数进行比较。可以确定的是，不同成分的不同温度对克努森数的二阶精确度理论不起任何作用，而它们却对克努森数中的三阶精确度理论有贡献。此外，从经验上发现，对于所有二元气体混合物，零阶，一阶和二阶精确方程都是线性稳定的;对于所有二元气体混合物，方程都是线性稳定的。然而，尽管对于大多数混合物，三阶精确正则化的17矩方程是线性稳定的，但是对于分子质量具有极大差异的混合物，它们却是线性不稳定的。 （C）2016 AIP出版有限责任公司。

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