Geodesic
An application of the Chebyshev collocation method for the calculation of a mass flux in a long concentric annular channel
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 805-816

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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.
Keywords: linearized BGK model kinetic equation, model of diffuse reflection, collocation method, Chebyshev polynomials. 
@article{SEMR_2021_18_2_a57,
     author = {O. V. Germider and V. N. Popov},
     title = {An application of the {Chebyshev} collocation method for the calculation of a mass flux in a long concentric annular channel},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {805--816},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a57/}
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O. V. Germider; V. N. Popov. An application of the Chebyshev collocation method for the calculation of a mass flux in a long concentric annular channel. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 805-816. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a57/