Linear Stability of One-Dimensional Detonations

Abstract

We examine the one-dimensional stability of plane detonations characterized by one-step Arrhenius kinetics, using numerical techniques. A pseudo-spectral method, specifically a collocation scheme with Tchebychev polynomials, provides an approximation to the unstable discrete spectrum, in addition to permitting the calculation of stability boundaries in parameter space. We show that behavior predicted by Buckmaster and Neves (Physics of Fluids 31 (12) December 1988, pp. 3571–6) using activation energy asymptotics, can occur for physically realistic values of the activation energy. That is, the growth rate of the modes (real part of the eigenvalue) can be a non-monotone function of the frequency (imaginary part). The present work forms part of the Ph.D. thesis of the first author to be submitted to the faculty at the University of Bordeaux.