Computational Mathematics and Mathematical Physics

, Volume 59, Issue 11, pp 1832–1847 | Cite as

Regularized Equations for Numerical Simulation of Flows of Homogeneous Binary Mixtures of Viscous Compressible Gases

  • T. G. ElizarovaEmail author
  • A. A. ZlotnikEmail author
  • E. V. Shil’nikovEmail author


Regularized equations for binary mixtures of viscous compressible gases (in the absence of chemical reactions) are considered. Two new simpler systems of equations are constructed for the case of a homogeneous mixture, when the velocities and temperatures of the components coincide. In the case of moderately rarefied gases, such a system is obtained by aggregating previously derived general equations for binary mixtures of polyatomic gases. In the case of relatively dense gases, the regularizing terms in these equations are subjected to a further substantial modification. For both cases, balance equations for the total mass, kinetic, and internal energy and new balance equations for total entropy are derived from the constructed equations; additionally, the entropy production is proved to be nonnegative. As an example of successful use of the new equations, the two-dimensional Rayleigh–Taylor instability of relatively dense gas mixtures is numerically simulated in a wide range of Atwood numbers.


homogeneous binary mixture of compressible gases regularized equations entropy balance equation Rayleigh–Taylor instability computer simulation 



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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of SciencesMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Moscow Automobile and Road Construction State Technical University (MADI)MoscowRussia

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