High Lewis number combustion wavefronts: a perturbative Melnikove analysis

Abstract

The wavefronts associated with a one-dimensional combustion model with Arrhenius kinetics and no heat loss are analyzed within the high Lewis number perturbative limit. This situation, in which fuel diffusivity is small in comparison to that of heat, is appropriate for highly dense fluids. A formula for the wavespeed is established by a nonstandard application of Melnikov’s method and slow manifold theory from dynamical systems, and compared to numerical results. A simple characterization of the wavespeed correction is obtained: it is proportional to the ratio between the exothermicity parameter and the Lewis number. The perturbation method developed herein is also applicable to more general coupled reaction-diffusion equations with strongly differing diffusivities. The stability of the wavefronts is also tested using a numerical Evans function method.