Complex Conservative Difference Schemes in Modeling of Instabilities and Contact Structures

  • O. A. Azarova


The family of the difference schemes on a minimal stencil is under consideration. Construction of the difference schemes on a minimal stencil is based on the scheme approximation order increasing procedure [1]. This method makes it principally possible to develop the schemes of arbitrary approximation order without extension of the scheme stencil by the use of differential consequences of the initial system of equations. Two-dimensional schemes of similar type for plane and cylinder flow symmetry were presented in [2] - [4]. The schemes on the flow oriented grids for plane, cylinder and spherical flow symmetry supplemented by shock-tracking procedures were presented in [5]. Validation and comparison of calculations with the use of the minimal stencil difference schemes and the other ones was conducted in [5] - [7].


Shear Layer Difference Scheme Drag Reduction Shock Layer Divergent Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Grudnitsky, V.G., Prohorchuk, Y.A.: One Approach to Constructing Difference Schemes with Arbitrary Order of Approximation of Differential Equations in Partial Derivatives. Dokl. AN SSSR 234(6), 1249–1252 (1977)Google Scholar
  2. 2.
    Belotserkovsky, O.M., Grudnitsky, V.G., Prohorchuk, Y.A.: Difference Scheme of the Second Order of Precision on a Minimal Stencil for Hyperbolic Equations. J of Comp. Math. and Math. Phys. 23(1), 119–126 (1983)Google Scholar
  3. 3.
    Grudnitsky, V.G., Podobrjaev, V.N.: On the Interaction of a Shock Wave with a Cylinder Resonator. J. of Comp. Math. and Math. Phys. 23(4), 1008–1011 (1983)Google Scholar
  4. 4.
    Azarova, O.A.: A Minimum-Stencil Difference Scheme for Computing Two-Dimensional Axisymmetric Gas Flows: Examples of Pulsating Flows with Instabilities. J. of Comp. Math. and Math. Phys. 49(4), 734–753 (2009)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Azarova, O.A.: Difference Scheme with Shock Tracking for Calculation of Explosion Flows in Liquids and Gases. Acoustics of Non-uniform Media. Dynamics of Fluid Medium 105, 8–14 (1992)MathSciNetGoogle Scholar
  6. 6.
    Farzan, F., Knight, D., Azarova, O., Kolesnichenko, Y.: Interaction of Microwave Filament and Blunt Body in Supersonic Flow. Paper AIAA-2008-1356, 1–24 (2008)Google Scholar
  7. 7.
    Azarova, O., Knight, D., Kolesnichenko, Y.: Pulsating Stochastic Flows Accompanying Microwave Filament/Supersonic Shock Layer Interaction. Shock Waves (in publishing, 2011)Google Scholar
  8. 8.
    Knight, D.: Survey of Aerodynamic Drag Reduction at High Speed by Energy Deposition. J. of Propulsion and Power 24(6), 1153–1167 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Azarova, O., Knight, D., Kolesnichenko, Y.: Instabilities, Vortices and Structures Characteristics During Interaction of Microwave Filaments with Body in Supersonic Flow. Paper AIAA-2010-1004, 1–16 (2010)Google Scholar
  10. 10.
    Azarova, O.A., Shtemenko, L.S., Shugaev, F.V.: Numerical Modeling of Shock Propagation Through a Turbulent Flow. Computational Fluid Dynamics J. 12(2), 41–45 (2003) (Special Issue) ISSN 0918-6654 Google Scholar
  11. 11.
    Azarova, O.A.: Direct Numerical Simulation of One Type of Compressible Turbulence Interacting with a Shock Wave. J. of Comp. Math. and Math. Phys. 47(11), 1856–1866 (2007)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Artemev, V.I., Bergelson, V.I., Nemchinov, I.V., et al.: Changing the Regime of Supersonic Streamlining Obstacle via Arising the Thin Channel of Low Density. Mechanics of Liquids and Gases 89(5), 146–151 (1989)Google Scholar
  13. 13.
    Richtmyer, R.D.: Taylor Instability in Shock Acceleration of Compressible Fluids. Commun. Pure Appl. Math. 13, 297 (1960)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Meshkov, E.E.: Instability of the Interface of Two Gases Accelerated by a Shock Wave. Fluid Dyn. 4, 101 (1969); Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza 5, 151–158MathSciNetCrossRefGoogle Scholar
  15. 15.
    Azarova, O., Kolesnichenko, Y.: On Details of Flow Structure During the Interaction of an Infinite Rarefied Channel with a Cylinder Shock Layer. In: Proc. 7th Int. Workshop on Magnetoplasma Aerodynamics, Moscow, Institute of High Temperatures, pp. 101–113 (2007)Google Scholar
  16. 16.
    Kolesnichenko, Y.F., Brovkin, V.G., Azarova, O.A., Grudnitsky, V.G., et al.: Microwave Energy Release Regimes for Drag Reduction in Supersonic Flows. Paper AIAA-2002-0353, 1–13 (2002)Google Scholar
  17. 17.
    Giordano, J., Burtschell, Y.: Richtmyer-Meshkov Instability Induced by Shock-Bubble Interaction: Numerical and Analytical Studies with Experimental Validation. Phys. Fluids 18, 036102:1–036102:10 (2006)CrossRefGoogle Scholar
  18. 18.
    Reinaud, J., Joly, L., Chassaing, P.: The Baroclinic Secondary Instability of the Two-Dimensional Shear Layer. Phys. Fluids. 12(10), 2489–2505 (2000)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • O. A. Azarova
    • 1
  1. 1.Dorodnicyn Computing Centre of RASMoscowRussia

Personalised recommendations