Skip to main content
Log in

Hyperbolic Model of a One-Velocity Viscous Heat-Conducting Medium

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

A modified, generalized-equilibrium model of a one-velocity heterogeneous medium is presented, which accounts for the viscosity and thermal conductivity of the mixture, as well as for interfractional heat transfer. A characteristic analysis of the model′s equations has been carried out, and their hyperbolicity is shown. A description is given of Godunov′s method with a linearized Riemann solver intended for calculating mixture flows on curvilinear grids, with the use of which a number of problems for a vapor–air mixture has been investigated.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Murrone and H. Guillard, A five equation reduced model for compressible two phase flow problems, J. Comput. Phys., 202, 664–698 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Wackers and B. Koren, A fully conservative model for compressible two-fluid flow, J. Numer. Meth. Fluids, 47, 1337–1343 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  3. J. J. Kreeft and B. Koren, A new formulation of Kapila′s five-equation model for compressible two-fluid flow, and its numerical treatment, J. Comput. Phys., 229, 6220–6242 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  4. V. S. Surov, One-velocity model of a heterogeneous medium, Mat. Modelir., 13, No. 10, 27–42 (2001).

    MathSciNet  MATH  Google Scholar 

  5. V. S. Surov, One-velocity model of a heterogeneous medium with a hyperbolic adiabatic core, Zh. Vych. Mat. Mat. Fiz., 48, No. 6, 1111–1125 (2008).

    MathSciNet  MATH  Google Scholar 

  6. V. S. Surov, Propagation of waves in foams, High Temp., 34, No. 2, 280–287 (1996).

    Google Scholar 

  7. V. S. Surov, Calculation of the interaction of an air shock wave with porous material, Chelyabinsk. Fiz. Mat. Zh., 6, No. 1 (1), 124–134 (1997).

    Google Scholar 

  8. V. S. Surov, Toward calculation of shock-wave processes in bubble liquids, Zh. Tekh. Fiz., 68, No. 11, 12–19 (1998).

    Google Scholar 

  9. R. Saurel, P. Boivin, and O. Lemétayer, A general formulation for cavitating, boiling and evaporating flows, Comp. Fluids, 128, 53–64 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. K. Kapila, D. W. Schwendeman, J. R. Gambino, and W. D. Henshaw, A numerical study of the dynamics of detonation initiated by cavity collapse, Shock Waves, 25, 545–572 (2015).

    Article  Google Scholar 

  11. V. S. Surov, On location of contact surfaces in multifluid hydrodynamics, J. Eng. Phys. Thermophys., 83, No. 3, 549–559 (2010).

    Article  Google Scholar 

  12. V. S. Surov, Self-similar running waves in multicomponent viscous heat-conducting media, J. Eng. Phys. Thermophys., 86, No. 3, 593–603 (2013).

    Article  Google Scholar 

  13. V. S. Surov, Account of interfractional heat-transfer in a hyperbolic model of a one-velocity heterogeneous mixture, J. Eng. Phys. Thermophys., 90, No. 3, 575–585 (2017).

    Article  MathSciNet  Google Scholar 

  14. C. Cattaneo, Sur une forme de l′equation de la chaleur elinant le paradoxe d′une propagation instantance, Cr. Acad. Sci., 247, 431–432 (1958).

    MATH  Google Scholar 

  15. S. K. Godunov, Numerical Solution of Multidimensional Problems of Gas Dynamics [In Russian], Nauka, Moscow (1976).

    Google Scholar 

  16. A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Questions of Numerical Solution of Hyperbolic Systems of Equations [in Russian], 2nd edn., Fizmatlit, Moscow (2012).

    Google Scholar 

  17. E. F. Toro, Riemann solvers with evolved initial condition, Int. J. Numer. Methods Fluids, 52, 433–453 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  18. G. W. Wallis, One-Dimensional Two-Phase Flow [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  19. V. S. Surov, The Godunov method for calculating multidimensional flows of a one-velocity multicomponent mixture, J. Eng. Phys. Thermophys., 89, No. 5, 1227–1240 (2016).

    Article  Google Scholar 

  20. V. S. Surov, On a method of approximate solution of the Riemann problem for a one-velocity flow of a multicomponent mixture, J. Eng. Phys. Thermophys., 83, No. 2, 373–379 (2010).

    Article  Google Scholar 

  21. V. S. Surov, Godunov method for calculating flows of a one-velocity viscous heat-conducting medium, J. Eng. Phys. Thermophys., 88, No. 3, 652–660 (2015).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. S. Surov.

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 92, No. 1, pp. 202–214, January–February, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Surov, V.S. Hyperbolic Model of a One-Velocity Viscous Heat-Conducting Medium. J Eng Phys Thermophy 92, 196–207 (2019). https://doi.org/10.1007/s10891-019-01922-w

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-019-01922-w

Keywords

Navigation