Astron. Astrophys. 333, 687-701 (1998)

The structure of radiative shock waves

I. The method of global iterations

Yu. A. Fadeyev ¹ and D. Gillet <sup>2

1</sup> Institute for Astronomy of the Russian Academy of Sciences, Pyatnitskaya 48, 109017 Moscow, Russia (fadeyev@inasan.rssi.ru)
² Observatoire de Haute-Provence - CNRS, F-04870 Saint-Michel l'Observatoire, France (gillet@obs-hp.fr)

Received 4 August 1997 / Accepted 2 January 1998

Abstract

The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations of fluid dynamics, radiation transfer and atomic kinetics. The shock wave model is represented by a flat finite slab with no incoming radiation from external sources at both its boundaries. The self-consistent solution is obtained using the global iteration procedure each step of which involves (1) integration of the fluid dynamics and rate equations for the preshock and postshock regions, consecutively, both solutions being fitted by the Rankine-Hugoniot relations at the discontinuous jump; (2) solution of the radiation transfer equation for the whole slab. The global iteration procedure is shown to converge to the stable solution which allows for the strong coupling of the gas flow and the radiation field produced by this flow. Application of the method is demonstrated for the shock waves with upstream velocities of (i.e. with upstream Mach numbers ) and the hydrogen gas of unperturbed temperature and density .

Key words: shock waves hydrodynamics radiative transfer stars: atmospheres

Contents

• 1. Introduction
• 2. The shock wave model
• 3. The system of ordinary differential equations
• 4. The radiation transfer equation
• 5. The global iteration procedure
• 6. Results of calculations
  • 6.1. The radiative precursor
  • 6.2. The thermalization and recombination zones
  • 6.3. The radiation field
• 7. Conclusion
• Acknowledgements
• References

© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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