IUMJ

Title: Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion

Authors: Helge Kristian Jenssen, Gregory Lyng and Mark Williams

Issue: Volume 54 (2005), Issue 1, 1-64

Abstract:

We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-Stokes ($\RNS$) model, and the simpler Zeldovich-von Neumann-D\"oring ($\ZND$) and Chapman-Jouguet (CJ) models. The determinants are functions of frequencies $(\lambda,\eta)$, where $\lambda$ is a complex variable dual to the time variable, and $\eta\in\bR^{d-1}$ is dual to the transverse spatial variables. The zeros of these determinants in $\Re\lambda>0$ correspond to perturbations that grow exponentially with time.