AMS Colloquium: Stability of detonation waves

In the study of the stability of detonation waves, it is often common practice to ignore the effects of diffusion and still construct an accurate enough representation of the waves in question. But what happens when these diffusive effects are not neglected, and how do they affect these waves? As part of a collaborative study, Dr. Gregory Lyng of the University of Wyoming Department of Mathematics sought answers to these questions and shared some of his findings at this week’s AMS Colloquium.

Before setting about finding the answers to these questions, however, the first thing Lyng had to consider was how to go about quantifying the effects of these diffusive properties. To accomplish this, numerical Evans-function techniques were chosen as the main model, and the particular set of waves studied were those defined as ‘viscous, strong detonation waves’. This limited the possible wave sets down to only those that modeled the combination of actively reacting gases (i.e. through detonation or explosion) as well as satisfied the Navier-Stokes equations. Once this initial problem setup was complete, it was then possible to implement these numerical tests, collect data, and then analyze the results.

Nothing like what Lyng and the rest of the group had hypothesized, their results indicated that there is a strong connection between increasing activation energies of the detonation and the diffusive effects of the detonation wave and its energy. This correlation exists for each specific subgroup, or ‘family’, of detonation waves possible in the predetermined problem domain. Another interesting aspect of this connection is that when these diffusive effects are taken into account, the normally unstable waves resulting from detonation will actually return to a state of stability. Lyng titled this effect ‘viscous hyperstabilization’, the discovery and properties of which became the main focus of this study, as from here it was hypothesized that, for all nonzero viscosity measurements, this effect would always be present as long as the diffusive effects on the waves are considered.

At this point in time, not much else is known and provable regarding viscous hyperstabilization, but according to Lyng it is very much a ‘fundamental open problem’ referring to the theory behind the methodology. Lyng expressed strong interest in continuing his study into this field, stating that the use of singular perturbation theory coupled with this model may yield very interesting and useable results.