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arXiv · 1807.02462

Instabilities in a combustion model with two free interfaces

Davide Addona·Claude-Michel Brauner·Luca Lorenzi·Wen Zhang
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Abstract

We study in a strip of $\mathbb R^2$ a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter interface presents an additional difficulty because the non-degeneracy condition is not met. We turn the system to a fully nonlinear problem which is thoroughly investigated. When the width $\ell$ of the strip is sufficiently large, we prove the existence of a critical value $Le_c$ of the Lewis number $Le$, such that the one-dimensional, planar, solution is unstable for $0<Le<Le_c$. Some numerical simulations confirm the analysis.

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Davide Addona, Claude-Michel Brauner, Luca Lorenzi, Wen Zhang. 2018-07-06. Instabilities in a combustion model with two free interfaces. https://arxiv.org/abs/1807.02462

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