Astron. Astrophys. 347, 724-733 (1999)

A new model for deflagration fronts in reactive fluids

M. Reinecke ¹, W. Hillebrandt ¹, J.C. Niemeyer ², R. Klein ³ and A. Gröbl <sup>1

1</sup> Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, D-85740 Garching, Germany
² LASR, Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA
³ Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustrasse 7, D-14195 Berlin-Dahlem, Germany

Received 20 November 1998 / Accepted 19 April 1999

Abstract

We present a new way of modeling deflagration fronts in reactive fluids, the main emphasis being on turbulent thermonuclear deflagration fronts in white dwarfs undergoing a Type Ia supernova explosion. Our approach is based on a level set method which treats the front as a mathematical discontinuity and allows full coupling between the front geometry and the flow field (Smiljanovski et al., 1997). With only minor modifications, this method can also be applied to describe contact discontinuities. Two different implementations are described and their physically correct behaviour for simple testcases is shown. First results of the method applied to the concrete problems of Type Ia supernovae and chemical hydrogen combustion are briefly discussed; a more extensive analysis of our astrophysical simulations is given in Reinecke et al. (1998).

Key words: hydrodynamics nuclear reactions, nucleosynthesis, abundances turbulence methods: numerical stars: supernovae: general

Send offprint requests to: M. Reinecke (martin@mpa-garching.mpg.de)

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Contents

• 1. Introduction
• 2. The level set method
• 3. Implementation
  • 3.1. Passive implementation
    • 3.1.1. G-transport
    • 3.1.2. Re-initialization
    • 3.1.3. Source terms
  • 3.2. Complete implementation
    • 3.2.1. Geometrical quantities
    • 3.2.2. Reconstruction
    • 3.2.3. Transport
    • 3.2.4. Flux-splitting
    • 3.2.5. Source terms
• 4. Numerical tests
  • 4.1. 1D flames
  • 4.2. 2D flames
    • 4.2.1. One circular flame
    • 4.2.2. Two merging circular flames
    • 4.2.3. Perturbed planar flame
  • 4.3. Sensitivity of the reconstruction equations
• 5. Applications
  • 5.1. Type Ia supernovae
  • 5.2. Chemical hydrogen combustion
• 6. Conclusions
• Acknowledgements
• References

© European Southern Observatory (ESO) 1999

Online publication: June 30, 1999
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