Kinetic Model and Magnetogasdynamics Equations

  • B. N. Chetverushkin
  • N. D’Ascenzo
  • A. V. Saveliev
  • V. I. Saveliev


An original kinetic model for the molecular velocity distribution function is considered. Based on this model, the equations of ideal magnetogasdynamics (MGD) are derived and an original model for dissipative MGD is obtained. The latter model can be used to construct algorithms easily adaptable to high-performance computer architectures. As an example, results of high-performance computations of astrophysical phenomena are presented, namely, the formation of cosmic jets is modeled.


magnetogasdynamics kinetic models kinetically consistent algorithms high-performance computations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. N. Chetverushkin, “Kinetic models for solving continuum mechanics problems on supercomputers,” Math. Models Comput. Simul. 7 (6), 531–539 (2015).MathSciNetCrossRefGoogle Scholar
  2. 2.
    B. N. Chetverushkin, Kinetic Schemes and Quasi-Gas Dynamic System of Equations (MAKS, Moscow, 2004; CIMNE, Barcelona, 2008).zbMATHGoogle Scholar
  3. 3.
    N. D’Ascenzo, V. I. Saveliev, and B. N. Chetverushkin, “On an algorithm for solving parabolic and elliptic equations,” Comput. Math. Math. Phys. 55 (8), 1290–1297 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    B. N. Chetverushkin, N. D’Ascenzo, A. V. Saveliev, and V. I. Saveliev, “Simulation of astrophysical phenomena on the basis of high-performance computations,” Dokl. Math. 95 (1), 68–71 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    M. N. Kogan, Rarefied Gas Dynamics (Nauka, Moscow, 1967; Plenum, New York, 1969)CrossRefGoogle Scholar
  6. 5a.
    L. Boltzmann, Lectures on Gas Theory (Dover, New York, 1995).Google Scholar
  7. 6.
    L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Nauka, Moscow, 1988; Butterworth-Heinemann, Oxford, 2000).zbMATHGoogle Scholar
  8. 7.
    B. Chetverushkin, N. D’Ascenzo, S. Ishanov, and V. Saveliev, “Hyperbolic type explicit kinetic scheme of magneto gas dynamics for high performance computing systems,” Russ. J. Numer. Anal. Math. Model. 30 (1), 27–36 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 8.
    B. N. Chetverushkin and V. I. Saveliev, Preprint No. 79, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2015).Google Scholar
  10. 9.
    P. J. Dellar, “Lattice kinetic schemes for magnetohydrodynamics,” J. Comput. Phys. 179 (1), 95 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 10.
    K. Xu and X. He, “Lattice Boltzmann method and gas-kinetic BGK scheme in the low-mach number viscous flow simulations,” J. Comput. Phys. 190 (1), 100 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 11.
    J.-P. Croisille, R. Khanfir, and G. Chanteur, “Numerical simulation of the MHD equations by kinetic-type method,” J. Sci. Comput. 10 (1), 81 (1995).CrossRefzbMATHGoogle Scholar
  13. 12.
    A. A. Zlotnik and B. N. Chetverushkin, “Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them,” Comput. Math. Math. Phys. 48 (3), 420–446 (2008).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 13.
    B. N. Chetverushkin, N. D’Ascenzo, A. V. Saveliev, and V. I. Saveliev, “A kinetic model for magnetogasdynamics,” Math. Models Comput. Simul. 9 (5), 544–553 (2017).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 14.
    B. N. Chetverushkin, “Hyperbolic system in magnetogasdynamics,” Mat. Model. (2018) (in press).Google Scholar
  16. 15.
    B. N. Chetverushkin and A. V. Gulin, “Explicit schemes and numerical simulation using ultrahigh-performance computer systems,” Dokl. Math. 86 (2), 681–683 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  17. 16.
    A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1976; Marcel Dekker, New York, 2001).CrossRefzbMATHGoogle Scholar
  18. 17.
    A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Chapman and Hall/CRC, London, 2001; Fizmatlit, Moscow, 2012).zbMATHGoogle Scholar
  19. 18.
    D. V. Bisikalo, A. G. Zhilkin, and A. A. Boyarchuk, Gas Dynamics of Close Binary Stars (Fizmatlit, Moscow, 2013) [in Russian].Google Scholar
  20. 19.
    V. E. Fortov, Physics of High Energy Densities (Fizmatlit, Moscow, 2012) [in Russian].Google Scholar
  21. 20.
    Ya. B. Zel’dovich, S. I. Blinnikov, and N. I. Shakura, Physical Principles of the Structure and Evolution of Stars (Mosk. Gos. Univ., Moscow, 1981) [in Russian].Google Scholar
  22. 21.
    M. A. Abramowicz, G. Björnsson, and J. E. Pringle, Theory of Black Hole Accretion Discs (Cambridge Univ. Press, Cambridge, 1999).Google Scholar
  23. 22.

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • B. N. Chetverushkin
    • 1
  • N. D’Ascenzo
    • 2
  • A. V. Saveliev
    • 3
  • V. I. Saveliev
    • 3
  1. 1.Federal Research Center Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  2. 2.Deutsche ElektronensynchrotronHamburgGermany
  3. 3.Immanuel Kant Baltic Federal UniversityKaliningradRussia

Personalised recommendations