Bendib A, Bendib-Kalache K, Gombert M-M
Laboratoire d'Electronique Quantique, Faculté de Physique, USTHB, El Alia, BP 32, Bab Ezzouar, 16111 Algiers, Algeria.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041201. doi: 10.1103/PhysRevE.80.041201. Epub 2009 Oct 2.
Recently we proposed a method to solve the perturbed Boltzmann equation modeled by the Bhatnagar-Gross-Krook operator [Phys. Rev. E 74, 041204 (2006)]. In this work we use this method to derive linear transport equations in the whole collisionality range. A comparison of the closure relations derived up to the third order in the Knudsen number (super-Burnett) yields the same results as the Chapman-Enskog expansion. The contribution of the projection operators to the transport is investigated. It is pointed out that their contributions are not negligible in the super-Burnett equations and very significant in the collisionless range. The test of stability of the super-Burnett equations is also performed. It is shown that the stability problem can be related to the positivity of the generalized transport coefficients. Using the Padé approximants, nonlocal transport coefficients are proposed which present the desirable stability properties.
最近，我们提出了一种方法来求解由Bhatnagar-Gross-Krook算子建模的微扰玻尔兹曼方程[《物理评论E》74, 041204 (2006)]。在这项工作中，我们使用该方法推导了整个碰撞范围内的线性输运方程。对在克努森数（超伯内特）中高达三阶推导的封闭关系进行比较，得到了与查普曼-恩斯科格展开相同的结果。研究了投影算子对输运的贡献。指出它们在超伯内特方程中的贡献不可忽略，在无碰撞范围内非常显著。还对超伯内特方程的稳定性进行了测试。结果表明，稳定性问题可能与广义输运系数的正定性有关。利用帕德近似，提出了具有理想稳定性性质的非局部输运系数。
