Viscous Hyperstabilization of Detonation Waves in One Space Dimension

Abstract

It is a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such waves, we use numerical Evans-function techniques to study the (spectral) stability of viscous strong detonation waves---particularly traveling-wave solutions of the Navier--Stokes equations modeling a mixture of reacting gases. Our results show a surprising synergy between the high-activation-energy limit typically studied in stability analyses of detonation waves and the presence of small but nonzero diffusive effects. While our calculations do show a modest delay in the onset of instability in agreement with recently reported calculations by direct numerical simulation of the physical equations, our Evans-function-based approach provides additional spectral information. In particular, for each of the families of detonation waves in our computational domain, we find an unexpected kind of hysteresis in the limit of increasing activation energy; that is, our calculations suggest that, whenever diffusive effects are present, there is a return to stability as activation energy is further increased, with unstable eigenvalues returning to the stable complex half-plane.