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 - Modélisation Mathématique et Analyse Numérique (2002)

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

Abstract

top
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

top

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 - Modélisation Mathématique et Analyse Numérique 36.2 (2002): 273-291. <http://eudml.org/doc/244904>.

@article{Audounet2002,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {flame ball; integro-differential equation; time discretisation; numerical quenching; fractional derivative; time discretization},
language = {eng},
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/244904},
volume = {36},
year = {2002},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2002
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
UR - http://eudml.org/doc/244904
ER -

References

top
  1. [1] J. Audounet, V. Giovangigli and J.-M. Roquejoffre, A threshold phenomenon in the propagation of a point source initiated flame. Phys. D 121 (1998) 295–316. Zbl0938.80003
  2. [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). MR1665560
  3. [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. [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. [5] J. Buckmaster, G. Joulin and P. Ronney, The structure and stability of nonadiabatic flame balls. Combust. Flame 79 (1990) 381–392. 
  6. [6] J. Buckmaster, G. Joulin and P. Ronney, The structure and stability of nonadiabatic flame balls. II. Effects on far-field losses. Combust. Flame 84 (1991) 411–422. 
  7. [7] R. Gorenflo and S. Vessella, Abel Integral Equations. Analysis and Applications. Springer-Verlag, Berlin (1991). Zbl0717.45002MR1095269
  8. [8] G. Joulin, Point source initiation of lean spherical flames of light reactants: An asymptotic theory. Combust. Sci. Tech. 43 (1985) 99–113. 
  9. [9] O.A. Ladyzhenskaya, N.N. Uraltseva and S.N. Solonnikov, Linear and quasilinear equations of parabolic type. Transl. Math. Monogr. 23 (1968). Zbl0174.15403
  10. [10] C. Lubich, Discretized fractional calculus. SIAM J. Math. Anal. 3 (1986) 704–719. Zbl0624.65015
  11. [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. [12] H. Rouzaud, Dynamique d’un modèle intégro-différentiel de flammes sphériques avec pertes de chaleur. C.R. Acad. Sci. Paris Sér. 1 332 (2001) 1083–1086. Zbl0984.45007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.