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Singular perturbation analysis for the reduction of complex chemistry in gaseous mixtures using the entropic structure. (Analyse de perturbation singulière pour la réduction de la chimie complexe des mélanges gazeux avec structure entropique.) (English. Abridged French version) Zbl 1115.80320

Summary: In this Note, we investigate the reduction of complex chemistry in gaseous mixtures. We consider an arbitrarily complex network of reversible reactions, the equilibrium constant of which are compatible with thermodynamics, thus providing an entropic structure. We assume that a subset of the reactions is constituted of fast reactions and define a constant and linear projection onto the partial equilibrium manifold compatible with the entropy production. This reduction step is used for the study of a homogeneous reactor at constant density and internal energy where the temperature can encounter strong variations. We prove the global existence of a smooth solution and of an asymptotically stable equilibrium state for both the reduced system and the complete one. A global in time singular perturbation analysis proves that the reduced system on the partial equilibrium manifold approximates the full chemistry system.

MSC:

80A30 Chemical kinetics in thermodynamics and heat transfer
80A32 Chemically reacting flows
34C60 Qualitative investigation and simulation of ordinary differential equation models
35B25 Singular perturbations in context of PDEs
35K57 Reaction-diffusion equations
76V05 Reaction effects in flows
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References:

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