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

This article is cited in 3 scientific papers (total in 3 papers)

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

Full text: PDF file (763 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:7, 1026–1043

Bibliographic databases:

UDC: 519.634
Received: 22.11.2012

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  crossref  isi  elib
    3. Yu. A. Anikin, “Solution of the Wang Chang–Uhlenbeck equation for molecular hydrogen”, Comput. Math. Math. Phys., 57:6 (2017), 1048–1065  mathnet  crossref  crossref  mathscinet  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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