Numerical simulation of a point-source initiated flame ball with heat losses

Jacques Audounet; Jean-Michel Roquejoffre; Hélène Rouzaud

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 36, Issue: 2, page 273-291
  • ISSN: 0764-583X

Abstract

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This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.

How to cite

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Audounet, Jacques, Roquejoffre, Jean-Michel, and Rouzaud, Hélène. "Numerical simulation of a point-source initiated flame ball with heat losses." ESAIM: Mathematical Modelling and Numerical Analysis 36.2 (2010): 273-291. <http://eudml.org/doc/194104>.

@article{Audounet2010,
abstract = { This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter. },
author = {Audounet, Jacques, Roquejoffre, Jean-Michel, Rouzaud, Hélène},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Flame ball; integro-differential equation; time discretisation; numerical quenching.; fractional derivative; time discretization; numerical quenching},
language = {eng},
month = {3},
number = {2},
pages = {273-291},
publisher = {EDP Sciences},
title = {Numerical simulation of a point-source initiated flame ball with heat losses},
url = {http://eudml.org/doc/194104},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Audounet, Jacques
AU - Roquejoffre, Jean-Michel
AU - Rouzaud, Hélène
TI - Numerical simulation of a point-source initiated flame ball with heat losses
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 2
SP - 273
EP - 291
AB - This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.
LA - eng
KW - Flame ball; integro-differential equation; time discretisation; numerical quenching.; fractional derivative; time discretization; numerical quenching
UR - http://eudml.org/doc/194104
ER -

References

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  1. J. Audounet, V. Giovangigli and J.-M. Roquejoffre, A threshold phenomenon in the propagation of a point source initiated flame. Phys. D121 (1998) 295-316.  Zbl0938.80003
  2. J. Audounet and J.-M. Roquejoffre, An integral equation describing the propagation of a point source initiated flame: Asymptotics and numerical analysis. Systèmes différentiels fractionnaires: Modèles, Méthodes et Applications, Matignon & Montseny Eds, ESAIM Proc.5 (1998).  
  3. C. Bolley and M. Crouzeix, Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques. RAIRO Anal. Numér.3 (1978) 237-245.  Zbl0392.65042
  4. H. Brunner, A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations. J. Comput. Appl. Math.3 (1982) 213-229.  Zbl0485.65087
  5. J. Buckmaster, G. Joulin and P. Ronney, The structure and stability of nonadiabatic flame balls. Combust. Flame79 (1990) 381-392.  
  6. J. Buckmaster, G. Joulin and P. Ronney, The structure and stability of nonadiabatic flame balls. II. Effects on far-field losses. Combust. Flame84 (1991) 411-422.  
  7. R. Gorenflo and S. Vessella, Abel Integral Equations. Analysis and Applications. Springer-Verlag, Berlin (1991).  Zbl0717.45002
  8. G. Joulin, Point source initiation of lean spherical flames of light reactants: An asymptotic theory. Combust. Sci. Tech.43 (1985) 99-113.  
  9. O.A. Ladyzhenskaya, N.N. Uraltseva and S.N. Solonnikov, Linear and quasilinear equations of parabolic type. Transl. Math. Monogr.23 (1968).  
  10. C. Lubich, Discretized fractional calculus. SIAM J. Math. Anal.3 (1986) 704-719.  Zbl0624.65015
  11. C. Lubich and A. Ostermann, Linearly implicit time discretization of non-linear parabolic equations. IMA J. Numer. Anal.15 (1995) 555-583.  Zbl0834.65092
  12. H. Rouzaud, Dynamique d'un modèle intégro-différentiel de flammes sphériques avec pertes de chaleur. C.R. Acad. Sci. Paris Sér. 1332 (2001) 1083-1086.  

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