Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On the structure of MHD shock waves in a viscous non-ideal gas


The structure of one-dimensional magnetohydrodynamics (MHD) shock waves is studied using the Navier–Stokes equations for the non-ideal gas phase. The exact solutions are obtained for the flow variables (i.e. particle velocity, temperature, pressure and change-in-entropy) within the shock transition region. The equation of state for a non-ideal gas is considered as given by Landau and Lifshitz. The effects of the non-idealness parameter and coefficient of viscosity of the gas are analysed on the flow variables assuming the magnetic field having only constant axial component. The findings confirm that the thickness of MHD shock front increases with decreasing values of the non-idealness parameter.

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


  1. 1

    Rankine W.J.M.: On the thermodynamic theory of waves of finite longitudinal disturbances. Philos. Trans. R. Soc. Lond. 160, 277–286 (1870)

  2. 2

    Hugoniot P.H.: Memoire sur la propagation du movement dans les corps et plus specialement dans les gaz parfaits. J. Ecole Polytech. Paris 58, 1–125 (1889)

  3. 3

    Mach E.: Uber den Verlauf der FunkenweUen in der Ebene und im Raume. Sitzungsber. A kad. Wiss. Wien 77, 19–38 (1878)

  4. 4

    Van Dyke M.: An Album of Fluid Motion. Parabolic Press, Stanford (1982)

  5. 5

    Zeldovich Ya.B., Raizer Yu.P.: Physics of Shock Waves and High Temperature Hydrodynamics Phenomena. Dover, New York (2002)

  6. 6

    Chang, C.S.W.: On the theory of the thickness of weak shock waves. Department of Engineering Research, University of Michigan. APL/JHU, CM-503 (1948)

  7. 7

    von Mises R.: On the thickness of a steady shock wave. J. Aeron. Sci. 594(17), 551–554 (1650)

  8. 8

    Gilbarg D., Paolucci D.T.: The structure of shock waves in the continuum theory of fluid. J. Rat. Mech. Anal. 2, 617–642 (1953)

  9. 9

    Wu, C.C.: In viscous profiles and numerical methods for shock waves. In: Shearer, M. (ed.) Siam Proceeding Series. SIAM, Philadelpha, pp. 209–236 (1991)

  10. 10

    Yadav H.C., Anand R.K.: Propagation of shock waves in a viscous medium. Phys. Scr. 83, 065402 (2011)

  11. 11

    Anand R.K.: Jump relations across a shock in non-ideal gas flow. Astrophys. Space Sci. 342, 377–388 (2012)

  12. 12

    Freistuehler H., Szmalyan P.: Existence and bifurcation of viscous profile for all intermediate magneto-hydrodynamics shock waves. SIAM J. Math. Anal. 26(1), 112–128 (1995)

  13. 13

    Anand R.K.: Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow. Astrophys. Space Sci. 343, 713–733 (2013)

  14. 14

    Landau L.D., Lifshitz E.M.: Statistical Physics, Course of Theoretical Physics, vol. 5. Pergamon, Oxford (1958)

  15. 15

    Anisimov S.I., Spiner O.M.: Motion of an almost ideal gas in the presence of a strong point explosion. J. Appl. Math. Mech. 36, 883–887 (1972)

Download references

Author information

Correspondence to R. K. Anand.

Additional information

Communicated by Tim Colonius.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Anand, R.K., Yadav, H.C. On the structure of MHD shock waves in a viscous non-ideal gas. Theor. Comput. Fluid Dyn. 28, 369–376 (2014).

Download citation


  • Magnetohydrodynamics (MHD)
  • Viscous shock waves
  • Non-ideal gas
  • Non-idealness parameter
  • Axial magnetic field