Reactive and reactive-diffusive time scales in stiff reaction-diffusion systems

Dimitris A. Goussis, Mauro Valorani, Francesco Creta, Habib N. Najm

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50 Scopus citations

Abstract

Two different sets of time scales arising in stiff systems of reaction-diffusion PDEs are examined; the first due to the reaction term alone and the second due to the interaction of the reaction and diffusion terms. The fastest time scales of each set are responsible for the development of a low dimensional manifold, the characteristics of which depend on the set of time scales considered. The advantages and disadvantages of employing these two manifolds for the simplification of large and stiff systems of reaction-diffusion PDEs are discussed. It is shown that the two approaches provide a non-stiff simplified system of similar accuracy. The approach based on the reaction time scales allows for a simpler construction of the simplified system, while that based on the reaction/diffusion time scales allows for a simpler time marching scheme.

Original languageBritish English
Pages (from-to)316-326
Number of pages11
JournalProgress in Computational Fluid Dynamics
Volume5
Issue number6
DOIs
StatePublished - 2005

Keywords

  • Asymptotic analysis
  • Chemical kinetics
  • Combustion
  • Intrinsic low-dimensional manifolds
  • Multiple time scales
  • Reaction-diffusion equations
  • Reduction methods
  • Slow manifolds

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