Balasuriya, Sanjeeva; Volpert, Vladimir A. Wavespeed analysis: Approximating Arrhenius kinetics with step-function kinetics. (English) Zbl 1152.80003 Combust. Theory Model. 12, No. 4, 643-670 (2008). Summary: The accuracy of using step-function approximations to the Arrhenius exponential in computing the wavespeed in combustion wave propagation is investigated. Gaseous and gasless combustion, and first- and second-order reactions are included in the study. The theoretical analysis is based on Melnikov theory from dynamical systems. The error is shown to be small in most instances. The analytical results are supported with numerical simulations. Cited in 2 Documents MSC: 80A25 Combustion 80A32 Chemically reacting flows 80A30 Chemical kinetics in thermodynamics and heat transfer Keywords:Arrhenius; combustion waves; Melnikov theory; step-function approximation; wavespeed PDFBibTeX XMLCite \textit{S. Balasuriya} and \textit{V. A. Volpert}, Combust. Theory Model. 12, No. 4, 643--670 (2008; Zbl 1152.80003) Full Text: DOI References: [1] Zeldovich Ya. B., The Mathematical Theory of Combustion and Explosion (1985) [2] DOI: 10.1016/0360-1285(88)90006-8 [3] DOI: 10.1007/BF00749022 [4] Aldushin A.P., Sov. Phys. Dokl. 24 pp 29– (1979) [5] DOI: 10.1021/jp962150v [6] DOI: 10.1002/mats.200390028 [7] DOI: 10.1016/S0009-2509(99)00350-4 [8] DOI: 10.1137/050628805 · Zbl 1117.35316 [9] Melnikov V.K., Trans. Moscow Math. Soc. 12 pp 1– (1963) [10] DOI: 10.1137/050640849 · Zbl 1121.80007 [11] Abramowitz M., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1964) · Zbl 0171.38503 [12] Guckenheimer J., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (1983) · Zbl 0515.34001 [13] Wiggins S., Introduction to Applied Nonlinear Dynamical Systems and Chaos (1990) · Zbl 0701.58001 [14] DOI: 10.1512/iumj.1971.21.21017 · Zbl 0246.58015 [15] DOI: 10.1016/S0893-9659(97)00060-8 · Zbl 0890.34019 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.