The simulation of a reacting mixture of ideal gases is considered. The competition between advection, reac-
tion, and diffusion in an unsteady spatially inhomogeneous geometry often induces phenomena which evolve
on multiple length and time scales. While the continuum model equations are generally well accepted, ana-
lytical solutions are generally not available, and computational solution is difficult due to the plethora of
scales. It is demonstrated that a detailed solution of the model equations is able to capture some of the ob -
servable harmonies in nature; in particular, predictions of oscillating detonations in a hydrogen-air mixture
are able to match well with experiment. Also discussed are reduction strategies for systematically removing
stiffness from reacting systems in the absence of advection and diffusion.
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