# 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

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topAudounet, 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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- R. Gorenflo and S. Vessella, Abel Integral Equations. Analysis and Applications. Springer-Verlag, Berlin (1991). Zbl0717.45002
- G. Joulin, Point source initiation of lean spherical flames of light reactants: An asymptotic theory. Combust. Sci. Tech.43 (1985) 99-113.
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- 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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