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Magnetohydrodynamic shock wave decay

  • Roy M. Gundersen
Original Papers

Summary

A modified hodograph transformation is used to obtain an exact solution of the equations governing the one-dimensional unsteady flow of an ideal, inviscid, perfectly conducting compressible fluid, subjected to a transverse magnetic field. This solution is used to obtain an approximate representation of the path of an initially uniform shock wave which intersects a centered simple wave. In the limit of vanishing magnetic field, the solution reduces exactly to the solution of the corresponding problem for conventional gas dynamics.

Keywords

Magnetic Field Shock Wave Exact Solution Unsteady Flow Transverse Magnetic Field 
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.

Résumé

Une transformation hodographe modifiée est employée pour obtenir une solution exacte des équations relatives aux écoulements unidimensionnels non-stationnaires et non-isentropiques d'un fluide non visqueux idéal, parfaitement conducteur d'électricité et compressible, soumis à l'action d'un champ magnétique transversal. On utilise cette solution pour obtenir une représentation approximative de la trajectoire d'une onde de choc magnétohydrodynamique initialement uniforme, rencontrant une onde simple centrée.

Dans le cas limite d'un champ magnétique nul, la solution se réduit exactement à celle du problème correspondant de la dynamique classique des gaz. C'est là une confirmation de la validité de la théorie.

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References

  1. [1]
    R. Courant and K. Friedrichs,Supersonic Flow and Shock Waves, Interscience Publ., Inc., New York 1948.Google Scholar
  2. [2]
    K. Friedrichs,Formation und decay of shock waves, Comm. Pure Appl. Math.1, 211–245 (1948).Google Scholar
  3. [3]
    P. Germain and R. Gundersen,Sur les écoulements unidimensionnels d'un fluide parfait à entropie faiblement variable, C. R. Acad. Sci. (Paris)241, 925–927 (1955).Google Scholar
  4. [4]
    R. Gundersen,The flow of a compressible fluid with weak entropy changes, J. Fluid Mech.3, 553–581 (1958).Google Scholar
  5. [5]
    R. Gundersen,The non-isentropic perturbation of an arbitrary simple wave, J. Math. Mech.9, 141–146 (1960).Google Scholar
  6. [6]
    R. Burnside and A. Mackie,A problem in shock wave decay, J. Australian Math. Soc.5, 258–272 (1965).Google Scholar
  7. [7]
    R. Gundersen,The non-isentropic perturbation of a centered magnetohydrodynamic simple wave, J. Math. Anal. Appl.6, 86–97 (1963).Google Scholar
  8. [8]
    R. Gundersen,Hydromagnetic simple wave flow in non-uniform ducts, J. Math. Anal. Appl.6, 277–293 (1963).Google Scholar
  9. [9]
    R. Gundersen,Linearized Analysis of One-dimensional Magnetohydrodynamic Flows, Springer-Verlag, Berlin 1964.Google Scholar
  10. [10]
    R. Gundersen,General theory of simple waves in one-dimensional magnetohydrodynamics, J. Mécanique4, 3–19 (1965).Google Scholar
  11. [11]
    R. Gundersen,The decay of a magnetohydrodynamic shock wave, Z. angew. Math. Phys.19, 864–881 (1968).Google Scholar
  12. [12]
    R. Gundersen,The decay of an oblique magnetohydrodynamic shock wave, J. Mécanique11, 579–598 (1972).Google Scholar
  13. [13]
    R. Gundersen,The decay of a magnetohydrodynamic shock wave produced by a piston, AIAA. J.1, 2844–2845 (1963).Google Scholar
  14. [14]
    H. Ardavan-Rhad,The decay of a plane shock wave, J. Fluid Mech.43, 737–751 (1970).Google Scholar

Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Roy M. Gundersen
    • 1
  1. 1.ChicagoUSA

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