Direct numerical calculations of a neutral stability curve for one-dimensional detonations

In this paper we calculate the neutral stability curve for one-dimensional detonation waves based on direct numerical simulations of the Euler equations. We propose multidimensional spectral methods with accurate shock tracking to study the stability of steady Chapman-Jouguet detonations. The numerical methods proposed here can be easily generalized for the simulation of multidimensional detonation waves. The detonations under consideration are for an ideal gas in an irreversible, unimolecular reaction A --> B with finite Arrhenius reaction rate. Critical overdrives f* for various heat releases Q's are computed. The neutral stability curve is obtained and compared with the results of the eigenmode analysis by Erpenbeck [Phys. Fluids, 7 (1964), pp. 684-696].