One-dimensional numerical simulations of idealized detonations

In this paper we use a second-order Godunov scheme to perform one-dimensional time-dependent numerical simulations of an idealized Chapman-Jouguet detonation having an Arrhenius form of reaction rate. The evolution of the longitudinal instability is explored for varying activation temperatures and compared to predictions of a linear stability analysis of the steady detonation. We show that, for large enough activation temperature, the detonation propagates in a series of failures followed by reignition, which can lead to the formation of many large pockets of partly burnt fuel. These results are in disagreement with the previous results of He & Lee, although we find that we can reproduce their results when too coarse a numerical grid is used.