Theoretical and numerical structure of unstable detonations

Abstract

In this review, we emphasize the recent progress achieved in understanding the behaviour of unstable detonations through the interaction of theoretical, asymp­ totic, and numerical ideas. Theoretical predictions and numerical simulations for unstable one-dimensional detonations are described in detail as an important testing ground for the more complex ideas and phenomena that occur in several space dimensions. The linear and nonlinear theories for unstable detonations are generalized to several space dimensions. A new dedicated numerical method leads to better insight into the physical phenomena of unstable detonations, such as the nature of the turbulence generated in the wake of the front. Simplified models derived through asymptotics and comparisons between theoretical and numerical predictions are stressed throughout this paper.