Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ South Ural State Uni...arrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Анализ инвариантности относительно преобразования Галилея некоторых математических моделей многокомпонентных сред

Authors: Kovalev, Yu. M.; Kuropatenko, V. F.;

Анализ инвариантности относительно преобразования Галилея некоторых математических моделей многокомпонентных сред

Abstract

Проведен анализ инвариантности относительно преобразования Галилея математической модели ≪замороженной≫ газовзвеси. Было показано, что уравнение полной удельной энергии газовой фазы в математической модели ≪замороженной≫ газовзвеси не является инвариантным относительно преобразования Галилея. Это приводит к появлению в уравнении полной удельной энергии фиктивного источникового члена, который определяет рост энтропии. Дополнительный рост энтропии ведет к нарушению второго закона термодинамики. В данной работе была предложена модификация уравнения полной удельной энергии газовой фазы. Модификация заключалась в том, что из правой части уравнения сохранения полной удельной энергии вычитается работа межфазных сил. Анализ полученного уравнения показал, что уравнение полной удельной энергии газовой фазы становится инвариантным относительно преобразования Галилея, а уравнение для производства энтропии не противоречит второму закону термодинамики. 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 didn’t contradict the second law of thermodynamics. Юрий Михайлович Ковалев, доктор физико-математических наук, профессор, заведующий кафедрой вычислительной механики сплошных сред, Южно-Уральский государственный университет (НИУ), (г. Челябинск, Российская Федерация), kov@mail.ru. Yu.M. Kovalev, South Ural State University (Chelyabinsk, Russian Federation). Валентин Федорович Куропатенко, доктор физико-математических наук, профессор, главный научный сотрудник Российского федерального ядерного центра – Всероссийского научно-исследовательского института технической физики им. академика Е.И. Забабахина, (г. Снежинск, Российская Федерация), v.f.kuropatenko@rambler.ru. V.F. Kuropatenko, Russian Research Institute of Technical Physics, Academician E.I. Zababakhin (Snezhinsk, Russian Federation)

Country
Russian Federation
Keywords

математическая модель, multi-component mixture, многокомпонентная смесь, invariance, УДК 001.891.573, 533 [УДК 517.958], 001.891.573 [УДК 532.5], инвариантность, mathematical model

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green