High Lewis number combustion wavefronts

John Hornibrook, Sanjeeva Balasuriya and Stephane Lafortune

Abstract

The wavespeed and stability of wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed. The focus is on the singular limit of very large Lewis number, in which fuel diffusivity is small in comparison to that of heat. Many of the established results for the infinite Lewis number are recovered, and an empirical wavespeed formula of excellent accuracy is determined. An Evans function technique is used to verify that the linear operator arising from the linearization about this wavefront solution does not possess any eigenvalues of positive real part, thereby supporting well-established numerical evidence on the stability of the infinite Lewis number front. In the very large (but not infinite) Lewis number instance, a similarly detailed assessment of the wavespeed is obtained. However, the Evans function method shows that such wavefronts are inherently unstable.