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.
Mots clés : flame ball, integro-differential equation, time discretisation, numerical quenching
@article{M2AN_2002__36_2_273_0,
author = {Audounet, Jacques and Roquejoffre, Jean-Michel and Rouzaud, H\'el\`ene},
title = {Numerical simulation of a point-source initiated flame ball with heat losses},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {273--291},
publisher = {EDP-Sciences},
volume = {36},
number = {2},
year = {2002},
doi = {10.1051/m2an:2002017},
mrnumber = {1906818},
zbl = {1025.80007},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2002017/}
}
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: Modélisation mathématique et analyse numérique PY - 2002 SP - 273 EP - 291 VL - 36 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2002017/ DO - 10.1051/m2an:2002017 LA - en ID - M2AN_2002__36_2_273_0 ER -
%0 Journal Article %A Audounet, Jacques %A Roquejoffre, Jean-Michel %A Rouzaud, Hélène %T Numerical simulation of a point-source initiated flame ball with heat losses %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 273-291 %V 36 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2002017/ %R 10.1051/m2an:2002017 %G en %F M2AN_2002__36_2_273_0
Audounet, Jacques; Roquejoffre, Jean-Michel; Rouzaud, Hélène. Numerical simulation of a point-source initiated flame ball with heat losses. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 2, pp. 273-291. doi : 10.1051/m2an:2002017. http://www.numdam.org/articles/10.1051/m2an:2002017/
[1] , and, A threshold phenomenon in the propagation of a point source initiated flame. Phys. D 121 (1998) 295-316. | Zbl
[2] and, An integral equation describing the propagation of a point source initiated flame: Asymptotics and numerical analysis 5 (1998). | MR
[3] and, Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques. RAIRO Anal. Numér. 3 (1978) 237-245. | Numdam | Zbl
[4] , A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations. J. Comput. Appl. Math. 3 (1982) 213-229. | Zbl
[5] , and, The structure and stability of nonadiabatic flame balls. Combust. Flame 79 (1990) 381-392.
[6] , and, The structure and stability of nonadiabatic flame balls. II. Effects on far-field losses. Combust. Flame 84 (1991) 411-422.
[7] and, Abel Integral Equations. Analysis and Applications. Springer-Verlag, Berlin (1991). | MR | Zbl
[8] , Point source initiation of lean spherical flames of light reactants: An asymptotic theory. Combust. Sci. Tech. 43 (1985) 99-113.
[9] , and, Linear and quasilinear equations of parabolic type. Transl. Math. Monogr. 23 (1968). | Zbl
[10] , Discretized fractional calculus. SIAM J. Math. Anal. 3 (1986) 704-719. | Zbl
[11] and, Linearly implicit time discretization of non-linear parabolic equations. IMA J. Numer. Anal. 15 (1995) 555-583. | Zbl
[12] , Dynamique d'un modèle intégro-différentiel de flammes sphériques avec pertes de chaleur. C.R. Acad. Sci. Paris Sér. 1 332 (2001) 1083-1086. | Zbl
Cité par Sources :
