AN APPLICATION OF THE CHEBYSHEV COLLOCATION METHOD FOR THE CALCULATION OF A MASS FLUX IN A LONG CONCENTRIC ANNULAR CHANNEL

被引：0

作者：

Germider, O., V ^{[1
]}

Popov, V. N. ^{[1
]}

机构：

[1] Northern Arctic Fed Univ, 4 Severnaya Dvina Emb, Arkhangelsk 163002, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2021年 / 18卷

关键词：

linearized BGK model kinetic equation; model of diffuse reflection; collocation method; Chebyshev polynomials; RAREFIED-GAS FLOW; TUBE;

D O I：

10.33048/semi.2021.18.059

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A rarefied gas flow through a long concentric annular channel due to pressure gradient is studied on the basis of the linearized BGK model of the Boltzmann kinetic equation using a Chebyshev collocation method. The method is based on the approximation by the truncated Chebyshev series. The linearized BGK model kinetic equation and boundary conditions are transformed into a matrix equation, which corresponds to a system of linear algebraic equations with the values of the unknown function at the Chebyshev collocation points. The mass flux is calculated as a function of the rarefaction parameter. The accuracy of the results is validated in several ways, including the recovery of the analytical solutions at the hydrodynamic and free molecular limits.

引用

页码：805 / 816

页数：12

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