A finite element adaptive investigation of curved stable and unstable flame front. (English) Zbl 0687.76071

Summary: We use an adaptive finite element approximation and a semi-implicit temporal integration to produce a numerical scheme intended to handle the difficulties of stiff combustion problems. The numerical analysis of this scheme allows us to adequately choose the numerical parameters involved in the calculations. Some results showing the thermo-diffusive flame front instabilities are presented.


76L05 Shock waves and blast waves in fluid mechanics
76E99 Hydrodynamic stability
76M99 Basic methods in fluid mechanics
80A32 Chemically reacting flows
Full Text: DOI


[1] Hyman, J.M.; Larrouturou, B., On the use of adaptive moving grid methods in combustion problems, (), 222-232
[2] Sivashinsky, G.I., Instabilities, pattern formation and turbulence in flames, Ann. rev. fluid mech., 15, 179-199, (1983) · Zbl 0538.76053
[3] Benkhaldoun, F.; Denet, B.; Larrouturou, B., Numerical investigation of the extinction limit of wrinkled flames, Comb. sci. tech., 64, 187, (1989)
[4] Benkhaldoun, F.; Larrouturou, B., Explicit adaptive calculations of wrinkled flame propagation, Internat. J. numer. methods fluids, 7, 1147-1158, (1987) · Zbl 0645.76075
[5] Benkhaldoun, F.; Larrouturou, B., Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation, Math. mod. and numer. anal., 22, 4, 535-560, (1988) · Zbl 0701.65097
[6] Barenblatt, G.I.; Zeldovich, Y.B.; Istratov, A.G., Prikl. mekh. tekh. fiz., 2, 21, (1962)
[7] Guillard, H.; Larrouturou, B.; Maman, N., Etude numérique des instabilités cellulaires d’un front de flamme par un méthode pseudo-spectrale, INRIA report 721, (1987)
[8] Peters, N., Discussion of test problem A, (), 1-14
[9] Larrouturou, B., Adaptive numerical methods for unsteady flame propagation, (), 415-435, (2)
[10] Larrouturou, B., A conservative adaptive method for unsteady flame propagation, SIAM J. sci. stat. comp., (1989), to appear · Zbl 0676.65129
[11] Ushijima, T., On the uniform convergence for the lumped mass approximation of the heat equation, J. fac. sci. univ. Tokyo, (1977) · Zbl 0379.35032
[12] Oran, E.S.; Boris, J.P., Detailed modelling of combustion systems, Prog. energ. comb. sci., 7, 1-72, (1981)
[13] Lax, P.D.; Richtmyer, R.D., Survey of the stability of linear finite-difference equations, Comm. pure appl. math., 9, (1956) · Zbl 0072.08903
[14] Raviart, P.A., Approximation numérique des phénomènes de diffusion-convection, Ecole d’eté d’analyse numérique EDF-CEA-INRIA, (1979)
[15] Ciarlet, P.G.; Raviart, P.A., Maximum principle and uniform convergence for the finite-element method, Comput. methods appl. mech. engrg., 2, 17-31, (1973) · Zbl 0251.65069
[16] Berestycki, H.; Larrouturou, B., A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model, J. für reine und angewandte Mathematik, 396, 14-40, (1989) · Zbl 0658.35036
[17] Benkhaldoun, F., Etude numérique de modèles mathématiques décrivant la propagation de flammes dans un milieu gazeux bidimensionnel, ()
[18] Williams, F.A., Combustion theory, (1985), Benjamin/Cummings Menlo Park, CA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.