Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation

F. Benkhaldoun; B. Larrouturou

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 4, page 535-560
  • ISSN: 0764-583X

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Benkhaldoun, F., and Larrouturou, B.. "Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.4 (1988): 535-560. <http://eudml.org/doc/193541>.

@article{Benkhaldoun1988,
author = {Benkhaldoun, F., Larrouturou, B.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {thermal-diffusional model; premixed flame propagating; adaptive moving mesh procedure; system of non-linear integro-differential reaction- diffusion equations; convergence; global numerical error},
language = {eng},
number = {4},
pages = {535-560},
publisher = {Dunod},
title = {Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation},
url = {http://eudml.org/doc/193541},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Benkhaldoun, F.
AU - Larrouturou, B.
TI - Numerical analysis of the two-dimensional thermo-diffusive model for flame propagation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 4
SP - 535
EP - 560
LA - eng
KW - thermal-diffusional model; premixed flame propagating; adaptive moving mesh procedure; system of non-linear integro-differential reaction- diffusion equations; convergence; global numerical error
UR - http://eudml.org/doc/193541
ER -

References

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  1. [1] G. I. BARENBLATT, Y. B. ZELDOVICH& A. G. ISTRATOV, Prik. Mekh. Tekh. Fiz., 2, p. 21 (1962). 
  2. [2] F. BENKHALDOUN & B. LARROUTUROU, Explicit adaptive calculations of wrinkled flame propagation, Int. J. Num. Meth. Fluids., Vol. 7, pp. 1147-1158 (1987). Zbl0645.76075
  3. [3] F. BENKHALDOUN& B. LARROUTUROU, A finite-element adaptive investigation of two-dimensional flame front instabilities, to appear. Zbl0687.76071
  4. [4] H. BREZIS, Équations d'évolution non linéaires, to appear. 
  5. [5] J. D. BUCKMASTER & G. S. S. LUDFORD, Theory of laminar flames, Cambridge University Press (1982). Zbl0557.76001MR666866
  6. [6] P. G. CIARLET & P. A. RAVIART, Maximum principle and uniform convergence for the finite-element method, Comp. Meth. Appl. Mech. Eng., 2, pp. 17-31 (1973). Zbl0251.65069MR375802
  7. [7] H. GUILLARD, B. LARROUTUROU & N. MAMAN, Numerical investigation of two-dimensional flame front instabilities using pseudo-spectral methods, to appear. 
  8. [8] B. LARROUTUROU, The equations of one-dimensional unsteady flame propagation, existence and uniqueness, SIAM J. Math. Anal., Vol. 19, N° 1, pp. 32-59 (1988). Zbl0662.35090MR924543
  9. [9] A. PAZY, Semigroups oflinear operators and applications to partial differential equations, Springer Verlag, New York (1983). Zbl0516.47023MR710486
  10. [10] G. I. SIVASHINSKY, Instabilites, pattern formation, and turbulence in flames, Ann. Rev. Fluid Mech., 15, pp. 179-199 (1983). Zbl0538.76053
  11. [11] G. STAMFACCHIA, Equations elliptiques du second ordre à coefficients discontinus, Presses Univ. Montréal, Montréal (1966). Zbl0151.15501MR251373
  12. [12] F. A. WILLIAMS, Combustion theory (second édition), Benjamin Cummings, Menlo Park (1985). 

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