Numerical and Theoretical Analysis of Model Equations for Multicomponent Rarefied Gas

A. A. Frolova; Фролова А. А.

doi:10.31857/S0044466923120128

Numerical and Theoretical Analysis of Model Equations for Multicomponent Rarefied Gas

Authors: Frolova A.A.¹
Affiliations:
1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Issue: Vol 63, No 12 (2023)
Pages: 1973-1983
Section: Mathematical physics
URL: https://bakhtiniada.ru/0044-4669/article/view/233011
DOI: https://doi.org/10.31857/S0044466923120128
EDN: https://elibrary.ru/TBGJZG
ID: 233011

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Abstract
About the authors
References
Supplementary files
Statistics

Abstract

Model equations approximating the system of Boltzmann equations for a multicomponent gas are investigated. Methods for determining parameters in relaxation terms corresponding to cross-collision integrals are analyzed. Numerical solutions based on three model systems and the Boltzmann equations are compared as applied to the following problems: relaxation of a mixture to equilibrium, shock wave structure, and the dynamics of a vapor-gas cloud generated by pulsed laser irradiation of a target. It is shown that the parameters in the relaxation operators influence the degree of difference in the solutions produced by the various models.

Keywords

kinetic equation, model equations, conservation laws, multicomponent gas, nonstationary problems

About the authors

A. A. Frolova

Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences

Author for correspondence.
Email: aafrolova@yandex.ru
119333, Moscow, Russia

References

Шахов Е.М. Обобщение релаксационного кинетического уравнения Крука // Изв. АН СССР. МЖГ.1968. № 5. С. 142–145.
Holway L.H. New statistical models for kinetic theory: Methods of construction // Phys. Fluids. 1966. V. 9. P. 1658.
Larina I.N., Rykov V.A. Nonlinear nonequilibrium kinetic model of the Boltzmann equation for monatomic gases // Comput. Math. Math. Phys. 2011. V. 51. № 11. P. 1962–1972.
Konopel’ko N.A., Shakhov E.M. Evolution to a steady state for rarefied gas flowing from a tank into a vacuum through a plane channel // Comput. Math. Math. Phys. 2017. V. 57. № 10. P. 1695–1705.
Konopel'ko N.A., Titarev V.A., Shakhov E.M. Unsteady rarefied gas flow in a microchannel driven by a pressure difference // Comput. Math. Math. Phys. 2016. V. 56. № 3. P. 470–482.
Titarev V.A., Shakhov E.M. Efficient method for computing rarefied gas flow in a long finite plane channel // Comput. Math. Math. Phys. 2012. V. 52. № 2 P. 269–284.
Шахов E.М. Течение разреженного газа между коаксиальными цилиндрами под действием градиента давления // Ж. вычисл. матем. и матем. физ. 2003. Т. 43. № 7. С. 1107–1116.
Gross E.P., Krook M. Model for collision processes in gases: small amplitude oscillations of charged two-component systems // Phys. Rev. 1956. V. 102. № 3 . P. 593–604.
Goldman E., Sirovich L. Equations for gas mixtures // Phys. Fluids. 1967. V. 10. № 9. P. 1928–1940.
Morse T.F. Kinetic model equations for a gas mixture // Phys. Fluids. 1964. V. 7. № 12. P. 2012–2013.
Hamel B.B. Kinetic model for binary gas mixtures // Phys. Fluids. 1965. V. 8. № 3. P. 418–425.
Garzo V., Santos A., Brey J.J. A kinetic model for a multicomponent gas // Phys. Fluids A . 1989. V. 1. № 2. P. 380–383.
Andries P., Aoki K., Perthame B. A consistent BGK-type model for gas Mixtures // J. Stat. Phys. 2002. V. 106. № 5. P. 993–1018.
Groppi M., Monica S., Spiga G. // A kinetic ellipsoidal BGK model for a binary gas mixture // Europhys. Lett. 2011. V. 96. № 6. P. 64002.
Brull S. An ellipsoidal statistical model for gas mixtures // Commun. Math. Sci. 2014. V. P. 1–13.
Kosugo S. Model Boltzmann equation for gas mixtures: Construction and numerical comparison // Eur. J. Mech – B Fluids Mechanics B/Fluids. 2009. V. 28. P. 170–184.
Bobylev A.V., Bisi M., Groppi M., Spiga G., Potapenko I.F. A general consistent BGK model for gas mixtures // Kinetic Related Models. 2018. V. 11. № 6. P. 1377–1393.
Haack J.R., Hauck C.D., Murillo M.S. A conservative, entropic multispecies BGK model // J. Stat. Phys. 2017. V. 168. № 4. P. 826–856.
Klingenberg C., Pirner M., Puppo G. A consistent kinetic model for a two component mixture with an application to plasma // Kinetic Related Models. 2017. V. 10. № 2. P. 445–465.
Todorova B., Steijl R. Derivation and numerical comparison of Shakhov and Ellipsoidal Statistical kinetic models for a monoatomic gas mixture // Europ. J. Mech. B/Fluids. 2019. V. 76. P. 390–402.
Коган М.Н. Динамика разреженного газа. М.: Наука, 1967.
Pfeiffer M., Mirza A., Nizenkov P. Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook method for monatomic gas species// Physics of Fluids 2021. V. 33. №. 3. P. 036106.
Kolobov V., Arslanbekov R., Aristov V., Frolova A., Zabelok S. Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement // J. Comput. Phys. 2007. V. 223. P. 589–608.
Черемисин Ф.Г. Консервативный метод вычисления интеграла столкновений Больцмана // Докл. АН 1997. Т. 35. № 1. С. 1–4.
Морозов А.А., Фролова А.А., Титарев В.А. On different kinetic approaches for computing planar gas expansion under pulsed evaporation into vacuum // Physics of Fluids. 2020. V. 32. С. 112005.