Fronts, relaxation oscillations, and period doubling in solid fuel combustion
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.
gasless, condensed phase or solid fuel combustion
scientific article; zbMATH DE number 3999230