Fronts, relaxation oscillations, and period doubling in solid fuel combustion
type: Item
instance of: scholarly article
title: Fronts, relaxation oscillations, and period doubling in solid fuel combustion
zbMATH Open document ID: 0616.65133
DOI: 10.1016/0021-9991(87)90024-6
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
review text: The authors consider a reaction-diffusion system describing gasless, condensed phase or solid fuel combustion, in the framework of finite activation energy. In previous experimental and theoretical results both uniformly and oscillatory propagating planar fronts were observed. A theoretical analysis of the one-dimensional case by the second author and \textit{G. Sivashinsky} [SIAM J. Appl. Math. 35, 465-478 (1978; Zbl 0404.76074)] exhibited a Hopf bifurcation phenomenon. The goal of the present study is to obtain the behavior of the system more globally. To do so, a numerical method is introduced, based on a modification of the standard Chebyshev method in order to reduce the spectral interpolation error by adjusting the collocation points (a fixed number) as the solution evolves in time. In the first part, the mathematical model is discussed. In a second part the adaptive pseudo- spectral method is presented, with details of the implementation. Results are presented to prove the effectiveness of the method and to illustrate the behavior of the solution beyond the neighborhood of the first bifurcation point of the combustion system. As a secondary bifurcation point is exceeded, a period doubling bifurcation is observed.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 3999230
zbMATH Keywords: solid fluid combustion
zbMATH Keywords: adaptative spectral method
zbMATH Keywords: reaction-diffusion system
zbMATH Keywords: gasless, condensed phase or solid fuel combustion
zbMATH Keywords: oscillatory propagating planar fronts
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Chebyshev method
zbMATH Keywords: spectral interpolation error
zbMATH Keywords: collocation
zbMATH Keywords: pseudo-spectral method
zbMATH Keywords: period doubling bifurcation
author: A. Bayliss
author: B. J. Matkowsky
MaRDI profile type: Publication
full work available at URL: 0021-9991(87)90024-6
OpenAlex ID: W2010046566
cites work: Q4199478
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description: scientific article; zbMATH DE number 3999230