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Particular solutions of the linearized Boltzmann equation for a binary mixture of rigid spheres

机译:刚性球二元混合物的线性化Boltzmann方程的特解

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Particular solutions that correspond to inhomogeneous driving terms in the linearized Boltzmann equation for the case of a binary mixture of rigid spheres are reported. For flow problems (in a plane channel) driven by pressure, temperature, and density gradients, inhomogeneous terms appear in the Boltzmann equation, and it is for these inhomogeneous terms that the particular solutions are developed. The required solutions for temperature and density driven problems are expressed in terms of previously reported generalized (vector-valued) Chapman–Enskog functions. However, for the pressure-driven problem (Poiseuille flow) the required particular solution is expressed in terms of two generalized Burnett functions defined by linear integral equations in which the driving terms are given in terms of the Chapman–Enskog functions. To complete this work, expansions in terms of Hermite cubic splines and a collocation scheme are used to establish numerical solutions for the generalized (vector-valued) Burnett functions.
机译:对于刚性球体的二元混合物,报告了与线性化Boltzmann方程中不均匀驱动项相对应的特定解决方案。对于由压力,温度和密度梯度驱动的流动问题(在平面通道中),在Boltzmann方程中出现非均质项,正是针对这些非均质项开发了特定的解决方案。温度和密度驱动的问题所需的解决方案用以前报道的广义(矢量值)Chapman–Enskog函数表示。但是,对于压力驱动的问题(泊松流动),所需的特定解决方案由线性积分方程式定义的两个广义Burnett函数表示,其中,驱动项根据Chapman–Enskog函数给出。为了完成这项工作,使用了Hermite三次样条和配置方案的扩展来为广义(矢量值)Burnett函数建立数值解。

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