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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 2, Pages 325–337 (Mi zvmmf4831)  

This article is cited in 32 scientific papers (total in 32 papers)

Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations

A. A. Zlotnikab

a Department of Mathematical Modeling, Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya ul. 14, Moskow, 111250 Russia
b Department of Applied Mathematics, Russian State Social University, ul. W. Pieck 4, Moskow, 129226 Russia

Abstract: Energy equalities are derived for the barotropic quasi-gasdynamic, modified quasi-gasdynamic, and quasi-hydrodynamic systems of equations. Global energy estimates of solutions are obtained. For the second of the systems, necessary and sufficient conditions for nonuniform and uniform Petrovskii parabolicity are derived.

Key words: gas dynamics, quasi-gasdynamic system of equations, energy equality, Petrovskii parabolicity.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:2, 310–321

Bibliographic databases:

UDC: 519.634
Received: 27.07.2009
Revised: 14.08.2009

Citation: A. A. Zlotnik, “Energy equalities and estimates for barotropic quasi-gas-dynamic and quasi-hydrodynamic systems of equations”, Zh. Vychisl. Mat. Mat. Fiz., 50:2 (2010), 325–337; Comput. Math. Math. Phys., 50:2 (2010), 310–321

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Zlotnik, “O kvazigazodinamicheskoi sisteme uravnenii s obschimi uravneniyami sostoyaniya i istochnikom tepla”, Matem. modelirovanie, 22:7 (2010), 53–64  mathnet  mathscinet
    2. Zlotnik A.A., “Linearized stability of equilibrium solutions to the quasi-gasdynamic system of equations”, Dokl. Math., 82:2 (2010), 811–815  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Zlotnik A.A., “Quasi-gasdynamic system of equations with general equations of state”, Dokl. Math., 81:2 (2010), 312–316  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. Sheretov Yu.V., “Ob obschikh tochnykh resheniyakh uravnenii Nave-Stoksa, Eilera i kvazigidrodinamicheskikh uravnenii”, Vestn. Tverskogo gos. un-ta. Ser.: Prikladnaya matematika, 2010, no. 17, 41–58  elib
    5. O. V. Bulatov, T. G. Elizarova, “Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows”, Comput. Math. Math. Phys., 51:1 (2011), 160–173  mathnet  crossref  mathscinet  isi
    6. Zlotnik A., Gavrilin V., “On quasi-gasdynamic system of equations with general equations of state and its application”, Math. Model. Anal., 16:4 (2011), 509–526  crossref  mathscinet  zmath  isi  elib  scopus
    7. Elizarova T.G., Bulatov O.V., “Regularized shallow water equations and a new method of numerical simulation of the open channel flows”, Comput. & Fluids, 46:1 (2011), 206–211  crossref  mathscinet  zmath  isi  scopus
    8. Elizarova T.G., Zlotnik A.A., Nikitina O.V., “Modelirovanie odnomernykh techenii melkoi vody na osnove regulyarizovannykh uravnenii”, Preprinty IPM im. M.V. Keldysha, 2011, no. 33, 1–36  elib
    9. T. G. Elizarova, A. A. Zlotnik, O. V. Nikitina, “Modelirovanie odnomernykh techenii melkoi vody na osnove regulyarizovannykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2011, 033, 36 pp.  mathnet
    10. Zlotnik A.A., “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
    11. A. A. Zlotnik, “O postroenii kvazigazodinamicheskikh sistem uravnenii i barotropnoi sistemy s potentsialnoi massovoi siloi”, Matem. modelirovanie, 24:4 (2012), 65–79  mathnet  mathscinet
    12. A. A. Zlotnik, “Prostranstvennaya diskretizatsiya odnomernoi barotropnoi kvazigazodinamicheskoi sistemy uravnenii i uravnenie energeticheskogo balansa”, Matem. modelirovanie, 24:10 (2012), 51–64  mathnet  mathscinet
    13. Sukhomozgii A.A., Sheretov Yu.V., “Edinstvennost resheniya regulyarizovannykh uravnenii Sen-Venana v lineinom priblizhenii”, Vestn. Tverskogo gos. un-ta. Ser.: Prikladnaya matematika, 2012, no. 1, 5–18  elib
    14. Ducomet B. Zlotnik A., “On a Regularization of the Magnetic Gas Dynamics System of Equations”, Kinet. Relat. Mod., 6:3 (2013), 533–543  crossref  mathscinet  zmath  isi  elib  scopus
    15. T. G. Elizarova, O. V. Bulatov, “Chislennyi algoritm resheniya regulyarizovannykh uravnenii melkoi vody na nestrukturirovannykh setkakh”, Preprinty IPM im. M. V. Keldysha, 2014, 021, 27 pp.  mathnet
    16. Elizarova T.G., Zlotnik A.A., Chetverushkin B.N., “On Quasi-Gasdynamic and Quasi-Hydrodynamic Equations For Binary Gas Mixtures”, Dokl. Math., 90:3 (2014), 719–723  crossref  mathscinet  zmath  isi  elib  scopus
    17. 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
    18. V. A. Balashov, E. B. Savenkov, “Numerical study of a quasi-hydrodynamic system of equations for flow computation at small mach numbers”, Comput. Math. Math. Phys., 55:10 (2015), 1743–1751  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    19. Yu. V. Sheretov, “Edinstvennost klassicheskogo resheniya linearizovannykh kvazigidrodinamicheskikh uravnenii v barotropnom priblizhenii”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2015, no. 1, 137–148  mathnet
    20. 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
    21. 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
    22. 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
    23. M. A. Istomina, T. G. Elizarova, “Kvazigazodinamicheskii algoritm dlya polyarnoi sistemy koordinat i primer chislennogo modelirovaniya neustoichivostei v akkretsionnom diske”, Preprinty IPM im. M. V. Keldysha, 2016, 092, 25 pp.  mathnet  crossref
    24. 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
    25. 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
    26. T. G. Elizarova, D. S. Saburin, “Application of the regularized shallow water equations for numerical simulation of casavie fluctuations in the Azov sea”, Math. Models Comput. Simul., 9:4 (2017), 423–436  mathnet  crossref  elib
    27. Balashov V. Zlotnik A. Savenkov E., “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
    28. Chetverushkin B.N. Zlotnik A.A., “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
    29. Zlotnik A.A., Chetverushkin B.N., “Entropy Balance For the One-Dimensional Hyperbolic Quasi-Gasdynamic System of Equations”, Dokl. Math., 95:3 (2017), 276–281  crossref  mathscinet  zmath  isi  scopus
    30. Saburin D.S. Elizarova T.G., “Modelling the Azov Sea Circulation and Extreme Surges in 2013-2014 Using the Regularized Shallow Water Equations”, Russ. J. Numer. Anal. Math. Model, 33:3 (2018), 173–185  crossref  mathscinet  zmath  isi  scopus
    31. Zlotnik A., “On the Energy Dissipative Spatial Discretization of the Barotropic Quasi-Gasdynamic and Compressible Navier–Stokes Equations in Polar Coordinates”, Russ. J. Numer. Anal. Math. Model, 33:3 (2018), 199–210  crossref  mathscinet  zmath  isi  scopus
    32. Zlotnik A. Lomonosov T., “On Conditions For Weak Conservativeness of Regularized Explicit Finite-Difference Schemes For 1D Barotropic Gas Dynamics Equations”, Differential and Difference Equations With Applications, Springer Proceedings in Mathematics & Statistics, 230, ed. Pinelas S. Caraballo T. Kloeden P. Graef J., Springer, 2018, 635–647  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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