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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, Issue 13, Pages 69–73 (Mi vyuru69)  

This article is cited in 6 scientific papers (total in 6 papers)

Mathematical Modelling

Analysis of the Invariance Under the Galilean Transformation of Some Mathematical Models of Multicomponent Media

Yu. M. Kovaleva, V. F. Kuropatenkob

a South Ural State University (Chelyabinsk, Russian Federation)
b Russian Research Institute of Technical Physics, Academician E. I. Zababakhin (Snezhinsk, Russian Federation)

Abstract: The analysis of the invariance under the Galilean transformation of the mathematical model of «frozen» gas suspension is done. It was shown that the equation of the total energy density of the gas phase in the model of «frozen» gas suspension was not invariant under Galilean transformations. This leads to appearance of the total energy density equation of the fictitious source term, which determines the growth of entropy. An additional increase of entropy leads to a violation of the second law of thermodynamics. In this paper a modification of the equation of the total energy density of the gas phase was proposed. The modification consisted in the fact that the right-hand side of the equation of conservation of total energy density was subtracted the work of interfacial forces. The analysis of this equation showed that the equation of the total energy density of the gas phase was invariant under Galilean transformations, and the equation for the entropy production didnít contradict the second law of thermodynamics.

Keywords: mathematical model, invariance, multi-component mixture.

Full text: PDF file (128 kB)
References: PDF file   HTML file
UDC: 532.5
MSC: 76T25
Received: 20.06.2012

Citation: Yu. M. Kovalev, V. F. Kuropatenko, “Analysis of the Invariance Under the Galilean Transformation of Some Mathematical Models of Multicomponent Media”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 13, 69–73

Citation in format AMSBIB
\Bibitem{KovKur12}
\by Yu.~M.~Kovalev, V.~F.~Kuropatenko
\paper Analysis of the Invariance Under the Galilean Transformation of Some Mathematical Models of Multicomponent Media
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2012
\issue 13
\pages 69--73
\mathnet{http://mi.mathnet.ru/vyuru69}


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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. E. S. Shestakovskaya, “Matematicheskoe modelirovanie rasprostraneniya udarnoi volny v geterogennoi srede s khimicheskimi prevrascheniyami v gazovoi faze”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:4 (2013), 128–133  mathnet
    2. Yu. M. Kovalev, E. A. Kovaleva, “Matematicheskii analiz uravnenii sokhraneniya dvukhfaznykh smesei”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:2 (2014), 29–37  mathnet  crossref
    3. Yu. M. Kovalev, “Analiz invariantnosti otnositelno preobrazovaniya Galileya dvukhfaznykh matematicheskikh modelei geterogennykh sred”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:1 (2014), 30–35  mathnet
    4. Yu. M. Kovalev, E. E. Pigasov, “Matematicheskaya model gazovzvesi s khimicheskimi prevrascheniyami v priblizhenii parnykh vzaimodeistvii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:3 (2014), 40–49  mathnet  crossref
    5. Yu. M. Kovalev, “Opredelenie vida sily mezhfaznogo vzaimodeistviya dlya matematicheskoi modeli gazovzvesi s parnymi vzaimodeistviyami”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 23–29  mathnet
    6. A. V. Krasilnikov, V. F. Kuropatenko, “Propagation of a strong discontinuity in a binary mixture of gases”, J. Comp. Eng. Math., 5:3 (2018), 49–60  mathnet  crossref  elib
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