Simplified quasi-hydrodynamic model for slow flows of compressible viscous heat conducting gas
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2016), pp. 5-17 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Simplified quasi-hydrodynamic system for slow flows of compressible viscous heat conducting gas is proposed. For it the entropy balance equation is derived and theorem on the increasing of full entropy is proved. Laplace barometric formula is obtained as a consequence of pointed system.
Mots-clés : quasi-hydrodynamic equations
Keywords: slow gas flows, entropy balance equation, barometric formula.
@article{VTPMK_2016_3_a0,
     author = {V. V. Grigoryeva and Yu. V. Sheretov},
     title = {Simplified quasi-hydrodynamic model for slow flows of compressible viscous heat conducting gas},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {5--17},
     year = {2016},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2016_3_a0/}
}
TY  - JOUR
AU  - V. V. Grigoryeva
AU  - Yu. V. Sheretov
TI  - Simplified quasi-hydrodynamic model for slow flows of compressible viscous heat conducting gas
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2016
SP  - 5
EP  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2016_3_a0/
LA  - ru
ID  - VTPMK_2016_3_a0
ER  - 
%0 Journal Article
%A V. V. Grigoryeva
%A Yu. V. Sheretov
%T Simplified quasi-hydrodynamic model for slow flows of compressible viscous heat conducting gas
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2016
%P 5-17
%N 3
%U http://geodesic.mathdoc.fr/item/VTPMK_2016_3_a0/
%G ru
%F VTPMK_2016_3_a0
V. V. Grigoryeva; Yu. V. Sheretov. Simplified quasi-hydrodynamic model for slow flows of compressible viscous heat conducting gas. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2016), pp. 5-17. http://geodesic.mathdoc.fr/item/VTPMK_2016_3_a0/

[1] Loytsyansky L. G., Fluid and Gas Mechanics, “Nauka” Publ., Moscow, 1987, 840 pp. (in Russian) | MR

[2] Sheretov Yu. V., “Quasi–hydrodynamic equations as a model of viscous heat conducting medium flows”, Application of Functional Analysis in the Theory of Approximations, Tver State University, Tver, 1997, 127–155 (in Russian)

[3] Sheretov Yu. V., Mathematical Modeling of Fluid and Gas Flows on the Base of Quasi–hydrodynamic and Quasi–gas–dynamic Equations, Tver State University, Tver, 2000, 235 pp. (in Russian)

[4] Sheretov Yu. V., Continuum Dynamics under Spatiotemporal Averaging, “Regular and Chaotic Dynamics” Publ., Moscow, Izhevsk, 2009, 400 pp. (in Russian)

[5] Sheretov Yu. V., Regularized Hydrodynamic Equations, Tver State University, Tver, 2016, 222 pp. (in Russian)

[6] Grigoryeva V. V., Sheretov Yu. V., “On the exact solutions of full quasi–hydrodynamic equations for stationary flows”, Vestnik TvGU. Seriya: Prikladnaya matematika [Herald of Tver State University. Series: Applied Mathematics], 2016, no. 1(5), 93–101 (in Russian)

[7] Zlotnik A. A., “Parabolicity of a quasi–hydrodynamic system of equations and the stability of its small perturbations”, Mathematical Notes, 83:5–6 (2008), 610–623 | DOI | DOI | MR | Zbl

[8] Zlotnik A. A., Gavrilin V. A., “On the parabolicity criteria of quasi-hydrodynamic system in the case of real gas”, Herald of Moscow Power Engineering Institute, 2009, no. 6, 116–126 (in Russian)

[9] Elizarova T. G., Bulatov O. V., “Numerical simulation of gas flows on the basis of quasi–hydrodynamic equations”, Moscow University Physics Bulletin, 64:6 (2009), 589–593 | DOI | Zbl

[10] Zlotnik A. A., Gavrilin V. A., “On the discretization of one-dimensional quasi–hydrodynamic system of equations for real gas”, Herald of Moscow Power Engineering Institute, 2016, no. 1, 5–14 (in Russian) | MR

[11] Balashov V. A., Savenkov E. B., “Numerical study of a quasi–hydrodynamic system of equations for flow computation at small mach numbers”, Computational Mathematics and Mathematical Physics, 55:10 (2015), 1773–1782 (in Russian) | DOI | MR | Zbl

[12] Balashov V. A., Savenkov E. B., “Direct pore–scale flow simulation using quasi-hydrodynamic equations”, Doklady Physics, 61:4 (2016), 192–194 | DOI | DOI

[13] Klimontovich Yu. L., “On the need for and the possibility of a unified description of kinetic and hydrodynamic processes”, Theoretical and Mathematical Physics, 92:2 (1992), 909–921 | DOI | MR | Zbl

[14] Brenner H., “Fluid mechanics revisited”, Physica A: Statistical Mechanics and its Applications, 370 (2006), 190–224 | DOI

[15] Brenner H., “Fluid mechanics in fluids at rest”, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86:1 (2012), 016307 | DOI | MR

[16] Sambasivam R., Extended Navier–Stokes Equations: Derivations and Applications to Fluid Flow Problems, PhD Thesis, Erlangen, 2013, 217 pp.