Massot, Marc 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 C. R., Math., Acad. Sci. Paris 335, No. 1, 93-98 (2002). 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 Keywords:homogeneous reactor; constant density; internal energy; existence of a smooth solution; existence of an asymptotically stable equilibrium state; global in time singular perturbation analysis; partial equilibrium manifold PDFBibTeX XMLCite \textit{M. Massot}, C. R., Math., Acad. Sci. Paris 335, No. 1, 93--98 (2002; Zbl 1115.80320) Full Text: DOI References: [1] S. Descombes, M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: singular perturbation and order reduction, Prepublication of the Lab. MAPLY, No. 344 (2002); S. Descombes, M. Massot, Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: singular perturbation and order reduction, Prepublication of the Lab. MAPLY, No. 344 (2002) · Zbl 1060.65105 [2] Duchêne, P.; Rouchon, P., Kinetic scheme reduction via geometric singular perturbation technique, Chemical Engineering Science, 51, 20, 4661-4672 (1996) [3] Giovangigli, V., Multicomponent flow modeling, in: Modeling and Simulation in Science, Engineering & Technology (1999), Birkhäuser Boston: Birkhäuser Boston Boston, MA · Zbl 0956.76003 [4] Giovangigli, V.; Massot, M., Asymptotic stability of equilibrium states for multicomponent reactive flows, Math. Models Methods Appl. Sci., 8, 251-297 (1998) · Zbl 0937.35145 [5] V. Giovangigli, M. Massot, Entropic structure of multicomponent reactive flows with partial equilibrium reduced chemistry, Prepublication of the Lab. MAPLY, No. 326 (2001); V. Giovangigli, M. Massot, Entropic structure of multicomponent reactive flows with partial equilibrium reduced chemistry, Prepublication of the Lab. MAPLY, No. 326 (2001) · Zbl 1047.80006 [6] Lam, S. H.; Goussis, D. A., The csp method for simplifying kinetics, Int. J. Chemical Kinetic, 26 (1994) [7] Maas, U.; Pope, S. B., Simplifying chemical kinetics: intrinsic low dimensional manifold in composition space, Combustion and Flame, 88, 239-264 (1992) [8] Massot, M., Singular perturbation analysis for the reduction of complex chemistry in gaseous mixtures using the entropic structure, Discrete Continuous Dynamical Systems Ser. B, 2, 3, 433-456 (2002) · Zbl 1001.80006 [9] (Smooke, M. D., Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames. Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, Lecture Notes in Phys., 384 (1991), Springer-Verlag) [10] B. Sportisse, Contribution à la modélisation des écoulements réactifs : réduction des modèles de cinétique chimique et simulation de la pollution atmosphérique, Ph.D. thesis, École polytechnique, 1999; B. Sportisse, Contribution à la modélisation des écoulements réactifs : réduction des modèles de cinétique chimique et simulation de la pollution atmosphérique, Ph.D. thesis, École polytechnique, 1999 [11] Tikhonov, A. N.; Vasil’eva, A. B.; Sveshnikov, A. G., Differential Equations (1985), Springer-Verlag · Zbl 0553.34001 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.