Abstract

This study describes a method for calculating the Darcy friction coefficient in a flat channel formed by two infinite parallel plates as a function of the Reynolds numbers and the gas rarefaction parameter in the channel. Maxwell’s diffuse reflection model is used as a model for the reflection of gas molecules from the channel walls. The isothermal gas flow is due to the presence of a pressure gradient that is small in absolute magnitude and directed along the channel walls. The method proposed in this paper is based on solving a linearized ellipsoidal-statistical Boltzmann kinetic equation with homogeneous boundary conditions using the Chebyshev polynomial approximation. An unknown function that interpolates the solution to this equation is represented as a partial sum of a series in Chebyshev polynomials of the first kind. The properties of finite sums for an orthonormal system of Chebyshev polynomials are used to reduce the problem to a system of linear algebraic equations with respect to the values of the sought function at interpolation nodes. The results obtained in this study are analyzed.

中文翻译：

---

使用椭球统计模型计算的达西摩擦系数

摘要

本研究描述了一种计算由两个无限平行板形成的平坦通道中的达西摩擦系数的方法，该系数是通道中雷诺数和气体稀薄参数的函数。麦克斯韦的漫反射模型用作气体分子从通道壁反射的模型。等温气流是由于存在绝对值较小且沿着通道壁引导的压力梯度。本文提出的方法基于使用切比雪夫多项式近似求解具有齐次边界条件的线性化椭球统计玻尔兹曼动力学方程。对该方程的解进行插值的未知函数表示为第一类切比雪夫多项式中的级数的部分和。切比雪夫多项式正交系统的有限和的性质用于将问题简化为关于插值节点处所寻求函数的值的线性代数方程组。对本研究获得的结果进行了分析。