Calculation of linear detonation instability. Part one. One-dimensional instability of plane detonation

The detonation stability problem is studied by a normal mode approach which greatly simplifies the calculation of linear instability of detonation in contrast to the Laplace transform procedure used by Erpenbeck. The method of solution, for an arbitrary parameter set, is a classical shooting method. The authors discuss the important issue of the condition on the perturbations applied at the end of the reaction zone, which is shown to be a boundedness condition or an acoustic radiation condition. The method automatically includes the Chapman-Jouguet, case which presents no special numerical difficulty. The method can be automated to easily generate the required information about instability. (Numerically) exact neutral stability boundaries are given, as well as growth rates and eigenfunctions. Representative results are given for this detonation model, and the one-dimensional stability behavior in parameter space is summarized.