Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion
Published in Indiana University Mathematics Journal , 2005
Recommended citation: Helge Kristian Jenssen, Gregory Lyng, Mark Williams, Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion, Indiana Univ. Math. J. 54 (2005), 1-64. https://dx.doi.org/10.1512/iumj.2005.54.2685
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-Doering (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 $\eta\in\mathbb{R}^{d-1}$ is dual to the transverse spatial variables. The zeros of these determinants in $\Re\lambda>0$ correspond to perturbations that grow exponentially with time.
Recommended citation: Helge Kristian Jenssen, Gregory Lyng, Mark Williams, Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion, Indiana Univ. Math. J. 54 (2005), 1-64.