Skip to main content
SpringerLink
Log in

Quasi-Gasdynamic Model and Numerical Algorithm for Describing Mixtures of Different Fluids

  • MATHEMATICAL PHYSICS
  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

An elegant and easy-to-implement numerical algorithm for simulating flows of homogeneous gas mixtures with component temperatures and velocities assumed to be equal is constructed and tested. The algorithm yields monotone density profiles for the components even if their specific heat ratios are widely different. The algorithm can be used to simulate some flows of gas–liquid mixtures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.

REFERENCES

  1. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981).

    Google Scholar 

  2. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover, New York, 2002).

    Google Scholar 

  3. Yu. P. Golovachev, Numerical Simulation of Viscous Gas Flows in Shock Layers (Nauka, Moscow, 1996) [in Russian].

    MATH  Google Scholar 

  4. T. G. Elizarova, Quasi-Gas Dynamic Equations (Nauchnyi Mir, Moscow, 2007; Springer, Berlin, 2009).

  5. T. G. Elizarova, A. A. Zlotnik, and E. V. Shil’nikov, “Regularized equations for numerical simulation of flows of homogeneous binary mixtures of viscous compressible gases,” Comput. Math. Math. Phys. 59 (11), 1832–1847 (2019). https://doi.org/10.1134/S0965542519110058

    Article  MathSciNet  MATH  Google Scholar 

  6. T. G. Elizarova and E. V. Shil’nikov, “Numerical simulation of gas mixtures based on the quasi-gasdynamic approach as applied to the interaction of shock wave with a gas bubble,” Comput. Math. Math. Phys. 61 (1), 118–128 (2021). https://doi.org/10.1134/S096554252101004

    Article  MathSciNet  Google Scholar 

  7. E. V. Shilnikov and T. G. Elizarova, “About one numerical method of compressible multifluid flow modelling in Euler formulation,” in Proceedings of IRF2020: 7th International Conference on Integrity–Reliability–Failure, Ed. by J. F. Silva Gomes and S. A. Meguid (INEGI-FEUP, 2020), pp. 613–622.

  8. I. R. Khaytaliev and E. V. Shilnikov, Preprint No. 52, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2021).

  9. R. Abgrall and S. Karni, “Computations of compressible multifluids,” J. Comput. Phys. 169 (2), 594–623 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  10. J. W. Banks, D. W. Schwendeman, A. K. Karila, and W. D. Henshaw, “A high-resolution Godunov method for compressible multi-material flow on overlapping grids,” J. Comput. Phys. 223 (1), 262–297 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  11. V. E. Borisov and Yu. G. Rykov, “Modified Godunov method for multicomponent flow simulation,” J. Phys.: Conf. Ser. 1250, 012006 (2019). https://doi.org/10.1088/1742-6596/1250/1/012006

  12. V. E. Borisov and Yu. G. Rykov, “Simulation of multicomponent gas flows using the double-flux method,” Math. Models Comput. Simul. 13 (3), 453–465 (2021).

    Article  MathSciNet  Google Scholar 

  13. A. Zlotnik, A. Fedchenko, and T. Lomonosov, “Entropy correct spatial discretizations for 1D regularized systems of equations for gas mixture dynamics,” Symmetry 14, 2171 (2022). https://doi.org/10.3390/sym14102171

    Article  Google Scholar 

  14. github.com/unicfdlab/QGDsolver

  15. M. V. Kraposhin, E. V. Smirnova, T. G. Elizarova, and M. A. Istomina, “Development of a new OpenFOAM solver using regularized gas dynamic equations,” Comput. Fluids 166, 163–175 (2018). https://doi.org/10.1016/j.compfluid.2018.02.010

    Article  MathSciNet  MATH  Google Scholar 

  16. T. G. Elizarova, “Time averaging as an approximate technique for constructing quasi-gasdynamic and quasi-hydrodynamic equations,” Comput. Math. Math. Phys. 51 (11), 1973–1982 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  17. Yu. V. Sheretov, Continuum Dynamics under Spatiotemporal Averaging (Regulyarnaya i Khaoticheskaya Dinamika, Moscow–Izhevsk, 2009) [in Russian].

    Google Scholar 

  18. F. Denner, C.-N. Xiao, and B. G. M. van Wachem, “Pressure-based algorithm for compressible interfacial flows with acoustically-conservative interface discretization,” J. Comput. Phys. 367, 192–234 (2018). https://doi.org/10.1016/j.jcp.2018.04.028

    Article  MathSciNet  MATH  Google Scholar 

  19. K. Kitamura, M.-S. Liou, and C.-H. Chang, “Extension and comparative study of AUSM-family schemes for compressible multiphase flow simulations,” Commun. Comput. Phys. 16 (3), 632–674 (2014). https://doi.org/10.4208/cicp.020813.190214a

    Article  MathSciNet  MATH  Google Scholar 

  20. M.-S. Liou, C. Chang, L. H. Nguyen, and T. G. Theofanous, “How to solve compressible multifluid equations: A simple, robust and accurate method,” AIAA J. 46, 2345–2356 (2007).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    T. G. Elizarova & E. V. Shil’nikov

Authors
  1. T. G. Elizarova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. V. Shil’nikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to T. G. Elizarova or E. V. Shil’nikov.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Elizarova, T.G., Shil’nikov, E.V. Quasi-Gasdynamic Model and Numerical Algorithm for Describing Mixtures of Different Fluids. Comput. Math. and Math. Phys. 63, 1319–1331 (2023). https://doi.org/10.1134/S0965542523070059

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542523070059

Keywords:

Search

Navigation