Review of Multiscale Modeling of Detonation

Issues associated with modeling the multiscale nature of detonation are reviewed, and potential applications to detonation-driven propulsion systems are discussed. It is suggested that a failure of most existing computations to simultaneously capture the intrinsic microscales of the underlying continuum model along with engineering macroscales could in part explain existing discrepancies between numerical predictions and experimental observation. Mathematical and computational strategies for addressing general problems in multiscale physics are first examined, followed by focus on their application to detonation modeling. Results are given for a simple detonation with one-step kinetics, which undergoes a period-doubling transition to chaos; as activation energy is increased, such a system exhibits larger scales than are commonly considered. In contrast, for systems with detailed kinetics, scales finer than are commonly considered are revealed to be present in models typically used for detonation propulsion systems. Some modern computational strategies that have been recently applied to more efficiently capture the multiscale physics of detonation are discussed: intrinsic low-dimensional manifolds for rational filtering of fast chemistry modes, and a wavelet adaptive multilevel representation to filter small-amplitude fine-scale spatial modes. An example that shows the common strategy of relying upon numerical viscosity to filter fine-scale physics induces nonphysical structures downstream of a detonation is given.