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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 4, Pages 710–729 (Mi zvmmf10565)  

This article is cited in 12 scientific papers (total in 12 papers)

Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations

A. A. Zlotnik

National Research University Higher School of Economics, Moscow, Russia

Abstract: The multidimensional quasi-gasdynamic system written in the form of mass, momentum, and total energy balance equations for a perfect polytropic gas with allowance for a body force and a heat source is considered. A new conservative symmetric spatial discretization of these equations on a nonuniform rectangular grid is constructed (with the basic unknown functions—density, velocity, and temperature—defined on a common grid and with fluxes and viscous stresses defined on staggered grids). Primary attention is given to the analysis of entropy behavior: the discretization is specially constructed so that the total entropy does not decrease. This is achieved via a substantial revision of the standard discretization and applying numerous original features. A simplification of the constructed discretization serves as a conservative discretization with nondecreasing total entropy for the simpler quasi-hydrodynamic system of equations. In the absence of regularizing terms, the results also hold for the Navier–Stokes equations of a viscous compressible heat-conducting gas.

Key words: Navier-Stokes equations for viscous compressible heat-conducting gases, quasi-gasdynamic system of equations, spatial discretization, conservativeness, law of nondecreasing entropy.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00048_а


DOI: https://doi.org/10.7868/S004446691702017X

Full text: PDF file (320 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:4, 706–725

Bibliographic databases:

UDC: 519.634
Received: 09.03.2016

Citation: A. A. Zlotnik, “Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 57:4 (2017), 710–729; Comput. Math. Math. Phys., 57:4 (2017), 706–725

Citation in format AMSBIB
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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. V. A. Balashov, A. A. Zlotnik, E. B. Savenkov, “Chislennyi algoritm dlya rascheta trekhmernykh dvukhfaznykh techenii s poverkhnostnymi effektami v oblastyakh s vokselnoi geometriei”, Preprinty IPM im. M. V. Keldysha, 2017, 091, 28 pp.  mathnet  crossref
    2. A. Zlotnik, “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
    3. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Verifikatsiya odnogo metoda entropiinoi regulyarizatsii razryvnykh skhem Galerkina dlya uravnenii giperbolicheskogo tipa”, Preprinty IPM im. M. V. Keldysha, 2019, 018, 25 pp.  mathnet  crossref  elib
    4. Balashov V., Savenkov E., Zlotnik A., “Numerical Method For 3D Two-Component Isothermal Compressible Flows With Application to Digital Rock Physics”, Russ. J. Numer. Anal. Math. Model, 34:1 (2019), 1–13  crossref  isi
    5. Zlotnik A. Lomonosov T., “Verification of An Entropy Dissipative Qgd-Scheme For the 1D Gas Dynamics Equations”, Math. Model. Anal., 24:2 (2019), 179–194  crossref  isi
    6. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Obespechenie entropiinoi ustoichivosti razryvnogo metoda Galerkina v gazodinamicheskikh zadachakh”, Preprinty IPM im. M. V. Keldysha, 2019, 051, 22 pp.  mathnet  crossref  elib
    7. Yu. A. Kriksin, V. F. Tishkin, “Chislennoe reshenie zadachi Einfeldta na osnove razryvnogo metoda Galerkina”, Preprinty IPM im. M. V. Keldysha, 2019, 090, 22 pp.  mathnet  crossref  elib
    8. S. V. Polyakov, Yu. N. Karamzin, T. A. Kudryashova, V. O. Podryga, D. V. Puzyrkov, N. I. Tarasov, “Mnogomasshtabnoe modelirovanie protsessov ochistki gaza”, Matem. modelirovanie, 31:9 (2019), 54–78  mathnet  crossref  elib
    9. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Razryvnyi metod Galerkina s entropiinym ogranichitelem naklonov dlya uravnenii Eilera”, Matem. modelirovanie, 32:2 (2020), 113–128  mathnet  crossref
    10. Yu. A. Kriksin, V. F. Tishkin, “Entropiino ustoichivyi razryvnyi metod Galerkina dlya uravnenii Eilera, ispolzuyuschii nekonservativnye peremennye”, Matem. modelirovanie, 32:9 (2020), 87–102  mathnet  crossref
    11. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Entropiino ustoichivyi razryvnyi metod Galerkina dlya dvumernykh uravnenii Eilera”, Matem. modelirovanie, 33:2 (2021), 125–140  mathnet  crossref
    12. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Entropiinaya regulyarizatsiya razryvnogo metoda Galerkina v konservativnykh peremennykh dlya dvumernykh uravnenii Eilera”, Matem. modelirovanie, 33:12 (2021), 49–66  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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