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We analyze the Riemann problem for reacting gas flow, under conditions where detonations and deflagrations can occur. We show that for a given deflagration velocity law, a Riemann solution which involves a deflagration may fail to exist but a Riemann solution involving a detonation may exist instead. We use our results to study an idealized model of transition from deflagration to detonation, using the Glimm (random choice) method. Numerical and asymptotic results are given, which compare well with certain experimental data. The broader usefulness of the results is indicated. One of the most interesting features of our model is the indication it provides that no transition occurs if the flame is laminar, and thus in particular, if the flow is purely one-dimensional.

Riemann Problems for Reacting Gas, with Applications to Transition