Differential Equations

, Volume 55, Issue 4, pp 575–580 | Cite as

Compact Version of the Quasi-Gasdynamic System for Modeling a Viscous Compressible Gas

  • A. E. LutskiiEmail author
  • B. N. ChetverushkinEmail author
Numerical Methods


We consider a compact version (the CQGD system) of the quasi-gasdynamic system. All algorithms that have been used to approximate the spatial derivatives in the Navier–Stokes equations can also be applied to the CQGD system. At the same time, the use of the CQGD system permits significantly improving the stability of explicit schemes, which is important for ensuring high-performance parallel computations. As examples of the use of algorithms based on the CQGD system, we present the results of computations of a laminar boundary layer on a plate and of a hypersonic laminar separated flow in a compression angle.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chetverushkin, B.N., Kineticheski-soglasovannye skhemy v gazovoi dinamike (Kinetically Consistent Schemes in Gas Dynamics), Moscow: Mosk. Gos. Univ., 1999.Google Scholar
  2. 2.
    Sheretov, Yu.V., Dinamika sploshnykh sred pri prostranstvenno-vremennom osrednenii (Continuum Dynamics under Space-Time Homogenization), Moscow; Izhevsk: Regular and Chaotic Dynamics, 2009.zbMATHGoogle Scholar
  3. 3.
    Chetverushkin, B.N., D’Ascenzo, N., and Savel’ev, V.l., Kinetically consistent magnetogasdynamics equations and their use in supercomputer computations, Dokl. Math., 2014, vol. 90, no. 1, pp. 495–498.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Finite-Difference Schemes), Moscow: Nauka, 1977.Google Scholar
  5. 5.
    Chetverushkin, B.N. and Zlotnic, A.A., On a hyperbolic perturbation of a parabolic initial–boundary value problem, Appl. Math. Lett., 2018, vol. 83, pp. 116–122.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chetverushkin, B.N., Savel’ev, A.V., and Savel’ev, V.l., A quasi-gasdynamic model for the description of magnetogasdynamic phenomena, Comput. Math. Math. Phys., 2018, vol. 58, no. 8, pp. 1384–1394.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gulin, A.V. and Chetverushkin, B.N., Explicit schemes and numerical simulation using ultrahigh-performance computer systems, Dokl. Math., 2012, vol. 446, no. 5, pp. 501–503.zbMATHGoogle Scholar
  8. 8.
    Kudryashov, I.Yu. and Lutskii, A.E., Mathematical simulation of turbulent separated transonic flows around the bodies of revolution, Math. Model., 2011, vol. 23, no. 5, pp. 71–80.zbMATHGoogle Scholar
  9. 9.
    Schlichting, H., Boundary Layer Theory, London: Pergamon, 1955.zbMATHGoogle Scholar
  10. 10.
    Zapryagaev, V.I., Kavun, I.N., and Lipatov, I.I., Supersonic laminar separated flow structure at a ramp for a free-stream Mach number of 6, Progress in Flight Physics, 2013, vol. 5, pp. 349–362.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Federal Research Center Keldysh Institute of Applied Mathematics of the Russian Academy of SciencesMoscowRussia

Personalised recommendations