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Matem. Mod., 2012, Volume 24, Number 4, Pages 65–79 (Mi mm3259)  

This article is cited in 13 scientific papers (total in 13 papers)

On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force

A. A. Zlotnikab

a NRU Higher Economics School, Department of Higher Mathematics at the Faculty of Economics
b Moscow Power Engineering Institute (Technical University), Department of Mathematical Modeling

Abstract: A short approach is described for constructing barotropic quasi-gasdynamic (QGD) system of equations by means of a special regularization in time of the barotropic Navier–Stokes system of equations. The approach is generalized to the case of the QGD system with general equations of gas state, a body force and a heat source. For the barotropic QGD system with the potential body force, the pointwise energy balance law is derived. The integral energy balance law and global energy bounds are established as corollaries. For the linearized at the equilibrium solution barotropic QGD system with the potential body force, the exponential in time stabilization of solutions to zero is given.

Keywords: quasi-gasdynamic systems of equations, the Navier–Stokes equations, regularization, potential body force, energy balance law, energy bounds, linearization, stabilization.

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Received: 12.09.2011

Citation: A. A. Zlotnik, “On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force”, Matem. Mod., 24:4 (2012), 65–79

Citation in format AMSBIB
\Bibitem{Zlo12}
\by A.~A.~Zlotnik
\paper On construction of quasi-gasdynamic systems of equations and the barotropic system with the potential body force
\jour Matem. Mod.
\yr 2012
\vol 24
\issue 4
\pages 65--79
\mathnet{http://mi.mathnet.ru/mm3259}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3026834}


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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. A. A. Zlotnik, “Prostranstvennaya diskretizatsiya odnomernoi barotropnoi kvazigazodinamicheskoi sistemy uravnenii i uravnenie energeticheskogo balansa”, Matem. modelirovanie, 24:10 (2012), 51–64  mathnet  mathscinet
    2. A. A. Zlotnik, “Spatial discretization of one-dimensional quasi-gasdynamic systems of equations and the entropy and energy balance equations”, Dokl. Math., 86:1 (2012), 464–468  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Sukhomozgii A.A., Sheretov Yu.V., “Testirovanie novogo algoritma rascheta odnomernykh nestatsionarnykh techenii zhidkosti so svobodnoi granitsei”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2012, no. 4, 47–64  mathnet  elib
    4. O. V. Bulatov, “Analytical and numerical Riemann solutions of the Saint Venant equations for forward- and backward-facing step flows”, Comput. Math. Math. Phys., 54:1 (2014), 158–171  mathnet  crossref  crossref  isi  elib  elib
    5. V. A. Balashov, E. B. Savenkov, “Fenomenologicheskii vyvod kvazigidrodinamicheskoi sistemy uravnenii s uchetom ob'emnoi vyazkosti”, Preprinty IPM im. M. V. Keldysha, 2015, 068, 25 pp.  mathnet
    6. A. A. Zlotnik, “On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force”, Comput. Math. Math. Phys., 56:2 (2016), 303–319  mathnet  crossref  crossref  isi  elib
    7. O. V. Bulatov, T. G. Elizarova, “Regularized shallow water equations for numerical simulation of flows with a moving shoreline”, Comput. Math. Math. Phys., 56:4 (2016), 661–679  mathnet  crossref  crossref  mathscinet  isi  elib
    8. V. A. Balashov, A. A. Zlotnik, E. B. Savenkov, “Issledovanie barotropnoi kvazigidrodinamicheskoi modeli dvukhfaznoi smesi s uchetom poverkhnostnykh effektov”, Preprinty IPM im. M. V. Keldysha, 2016, 089, 25 pp.  mathnet  crossref
    9. Zlotnik A. Gavrilin V., “On a Conservative Finite-Difference Method for 1D Shallow Water Flows Based on Regularized Equations”, Mathematical Problems in Meteorological Modelling, Mathematics in Industry, 24, ed. Batkai A. Csomos P. Farago I. Horanyi A. Szepszo G., Springer Int Publishing Ag, 2016, 3–18  crossref  mathscinet  zmath  isi
    10. T. G. Elizarova, A. A. Zlotnik, M. A. Istomina, “O dvumernom chislennom KGD modelirovanii spiralno-vikhrevykh struktur v akkretsionnykh gazovykh diskakh”, Preprinty IPM im. M. V. Keldysha, 2017, 001, 30 pp.  mathnet  crossref
    11. V. Balashov, A. Zlotnik, E. Savenkov, “Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface”, Russ. J. Numer. Anal. Math. Model, 32:6 (2017), 347–358  crossref  mathscinet  zmath  isi  scopus
    12. B. N. Chetverushkin, A. A. Zlotnik, “On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations”, Russ. J. Math. Phys., 24:3 (2017), 299–309  crossref  mathscinet  zmath  isi  scopus
    13. A. A. Zlotnik, B. N. Chetverushkin, “Entropy balance for the one-dimensional hyperbolic quasi-gasdynamic system of equations”, Dokl. Math., 95:3 (2017), 276–281  crossref  crossref  mathscinet  zmath  isi  elib  scopus
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