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Differential Equations

, Volume 55, Issue 7, pp 976–989 | Cite as

Two-Layer Completely Conservative Difference Schemes for the Gasdynamic Equations in Eulerian Coordinates with Adaptive Solution Regularization

  • Yu. A. PoveshchenkoEmail author
  • V. A. GasilovEmail author
  • V. O. PodrygaEmail author
  • O. R. RehimlyEmail author
  • Yu. S. SharovaEmail author
Numerical Methods
  • 3 Downloads

Abstract

A family of two-layer completely conservative difference schemes with space-profiled weight factors for approximations on a time grid is constructed for the gasdynamic equations in Eulerian coordinates. We propose a construction for regularized mass, momentum, and internal-energy fluxes that effectively removes nonphysical solution oscillations and does not violate the complete conservativeness of the difference schemes in this class.

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References

  1. 1.
    Samarskii, A.A., On conservative difference schemes, in Problemy prikladnoi matematiki i mekhaniki: Sb. statei k 60-letiyu akad. A.A. Dorodnitsyna (Problems of Applied Mathematics and Mechanics: To the 60th Anniversary of Acad. A.A. Dorodnitsyn), Moscow: Nauka, 1971, pp. 129–136.Google Scholar
  2. 2.
    Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1989.Google Scholar
  3. 3.
    Samarskii, A.A. and Mikhailov, A.P., Matematicheskoe modelirovanie: Idei. Metody. Primery (Mathematical Modeling: Ideas, Methods, Examples), Moscow: Fizmatlit, 2005, 2nd ed.zbMATHGoogle Scholar
  4. 4.
    Popov, Yu.P. and Samarskii, A.A., Completely conservative difference schemes, Zh. Vychisl. Mat. Mat. Fiz., 1969, vol. 9, no. 4, pp. 953–958.Google Scholar
  5. 5.
    Samarskii, A.A. and Popov, Yu.P., Raznostnye metody resheniya zadach gazovoi dinamiki (Difference Methods for Solving Gasdynamic Problems), Moscow: Nauka, 1992.Google Scholar
  6. 6.
    Kuz’min, A.V. and Makarov, V.L., On an algorithm for constructing completely conservative difference schemes, Zh. Vychisl. Mat. Mat. Fiz., 1982, vol. 22, no. 1, pp. 123–132.MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kuz’min, A.V., Makarov, V.L., and Meladze, G.V., On a completely conservative difference scheme for the gasdynamic equations in Eulerian variables, Zh. Vychisl. Mat. Mat. Fiz., 1980, vol. 20, no. 1, pp. 171–181.MathSciNetGoogle Scholar
  8. 8.
    Goloviznin, V.M., Krayushkin, I.V., Ryazanov, M.A., and Samarskii, A.A., Two-dimensional completely conservative difference gasdynamic schemes with separated velocities, Prepr. IPM im. M.V. Keldysha Akad. Nauk SSSR, 1983, no. 105.Google Scholar
  9. 9.
    Gasilov, V.A., Goloviznin, V.M., Ryazanov, M.A., Samarskaya, E.A., Sorokovikova, O.S., and Tkachenko, S.I., Two-dimensional completely conservative magnetohydrodynamic schemes in mixed Eulerian-Lagrangian variables, Prepr. IPM im. M.V. Keldysha Akad. Nauk SSSR, 1985, no. 181.Google Scholar
  10. 10.
    Gasilov, V.A., Krukovskii, A.Yu., Otochin, Al.A., and Otochin, An.A., Completely conservative difference scheme in mixed Eulerian-Lagrangian variables for calculating axially symmetric MHD problems, Prepr. VTsMM Akad. Nauk SSSR, 1991, no. 5.Google Scholar
  11. 11.
    Koldoba, A.V., Poveshchenko, Yu.A., and Popov, Yu.P., Two-layer completely conservative difference schemes for the gasdynamic equations in Eulerian variables, Zh. Vychisl. Mat. Mat. Fiz., 1987, vol. 27, no. 5, pp. 779–784.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Koldoba, A.V., Kuznetsov, O.A., Poveshchenko, Yu.A., and Popov, Yu.P., On one approach to the calculation of gasdynamic problems with a variable mass of a quasi-particle, Prepr. IPM im. M.V. Keldysha Akad. Nauk SSSR, 1985, no. 57.Google Scholar
  13. 13.
    Koldoba, A.V. and Poveshchenko, Yu.A., Completely conservative difference schemes for the gasdynamic equations in the presence of sources of mass, Prepr. IPM im. M.V. Keldysha Akad. Nauk SSSR, 1982, no. 160.Google Scholar
  14. 14.
    Poveshchenko, Yu.A., Podryga, V.O., and Sharova, Yu.S., Integrally consistent methods for calculating self-gravitating and magnetohydrodynamic phenomena, Prepr. IPM im. M.V. Keldysha Akad. Nauk SSSR, 2018, no. 160.Google Scholar
  15. 15.
    Samarskii, A.A., Koldoba, A.V., Poveshchenko, Yu.A., Tishkin, V.F., and Favorskii, A.P., Raznostnye skhemy na neregulyarnykh setkakh (Difference Schemes on Nonuniform Grids), Minsk: ZAO Kriterii, 1996.Google Scholar
  16. 16.
    Popov, I.V. and Fryazinov, I.V., Metod adaptivnoi iskusstvennoi vyazkosti chislennogo resheniya uravnenii gazovoi dinamiki (Method of Adaptive Artificial Viscosity for Numerical Solution of the Gasdynamic Equations), Moscow: Krasand, 2015.Google Scholar
  17. 17.
    Landau, L.D. and Lifshits, E.M., Gidrodinamika, T. VI (Hydrodynamics, Vol. VI), Moscow: Nauka, 1986.Google Scholar
  18. 18.
    Morozov, A.I., Vvedenie v plazmodinamiku (Introduction to Plasma Dynamics), Moscow: Fizmatlit, 2006.Google Scholar

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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Moscow Automobile and Road Construction State Technical University (MADI)MoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudnyi, Moscow oblastRussia

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