A geometric singular perturbation analysis of detonation and deflagration waves
Abstract
The existence of steady plane wave solutions of the NavierStokes equations for a reacting gas is analyzed. Under the assumption of an ignition temperature the existence of detonation and deflagration waves close to the corresponding waves of the ZNDmodel is proved in the limit of small viscosity, heat conductivity, and diffusion. The method is constructive, since the classical solutions of the ZNDmodel serve as singular solutions in the context of geometric singular perturbation theory. The singular solutions consist of orbits on which the dynamics are slowdriven by chemical reaction and of orbits on which the dynamics are fastdriven by gasdynamic shocks. The approach is geometric and leads to a clear, complete picture of the existence, structure, and asymptotic behavior of detonation and deflagration waves.
 Publication:

SIAM Journal of Mathematical Analysis
 Pub Date:
 July 1993
 Bibcode:
 1993SJMA...24..968G
 Keywords:

 Computational Fluid Dynamics;
 Deflagration;
 Detonation Waves;
 NavierStokes Equation;
 Perturbation Theory;
 Reacting Flow;
 Asymptotic Properties;
 Chemical Reactions;
 Conductive Heat Transfer;
 Gas Flow;
 Ignition Temperature;
 Traveling Waves;
 Fluid Mechanics and Heat Transfer