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 Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 7, Pages 1193–1211 (Mi zvmmf9832)

Solution of a kinetic equation for diatomic gas with the use of differential scattering cross sections computed by the method of classical trajectories

Yu. A. Anikin, O. I. Dodulad

Moscow Institute of Physics and Technology

Abstract: A collision integral is constructed taking into account the rotational degrees of freedom of the gas molecules. Its truncation error is shown to be second order in the rotational velocity mesh size. In the solution of the kinetic equation, the resulting collision integral is directly computed using a projection method. Preliminarily, the differential scattering cross sections of nitrogen molecules are computed by applying the method of classical trajectories. The resulting cross section values are tabulated in multimillion data arrays. The one-dimensional problems of shock wave structure and heat transfer between two plates are computed as tests, and the results are compared with experimental data. The convergence of the results with decreasing rotational velocity mesh size is analyzed.

Key words: Boltzmann equation, Wang Chang–Uhlenbeck equation, diatomic gas, molecular dynamics methods, differential scattering cross sections, projection method.

DOI: https://doi.org/10.7868/S0044466913070041

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:7, 1026–1043

Bibliographic databases:

UDC: 519.634

Citation: Yu. A. Anikin, O. I. Dodulad, “Solution of a kinetic equation for diatomic gas with the use of differential scattering cross sections computed by the method of classical trajectories”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1193–1211; Comput. Math. Math. Phys., 53:7 (2013), 1026–1043

Citation in format AMSBIB
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This publication is cited in the following articles:
1. Yu. A. Anikin, O. I. Dodulad, Yu. Yu. Kloss, F. G. Tcheremissine, “Method of calculating the collision integral and solution of the boltzmann kinetic equation for simple gases, gas mixtures and gases with rotational degrees of freedom”, Int. J. Comput. Math., 92:9, SI (2015), 1775–1789
2. O. I. Dodulad, Yu. Yu. Kloss, A. P. Potapov, F. G. Tcheremissine, P. V. Shuvalov, “Simulation of rarefied gas flows on the basis of the Boltzmann kinetic equation solved by applying a conservative projection method”, Comput. Math. Math. Phys., 56:6 (2016), 996–1011
3. Yu. A. Anikin, “Solution of the Wang Chang–Uhlenbeck equation for molecular hydrogen”, Comput. Math. Math. Phys., 57:6 (2017), 1048–1065
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