Fine scale phenomena in reacting systems: Identification and analysis for their reduction

A robust method for rational reduction of chemically reacting models is developed using a rigorous scale analysis. All the physical scales, spatial and temporal, inherent in reacting systems are accurately identified via eigenvalue analysis. The required temporal scales to assure accuracy in modeling reactive systems and the required spatial discretization to formally capture all detailed continuum physics in the reaction zone are calculated. The interplay between chemistry and transport is addressed via conducting a spectral analysis of reactive flow structure, and the relation between closed reactive systems' dynamics and notions from equilibrium/non-equilibrium thermodynamics is investigated. It revealed that reacting systems' physical scales are coupled, and their dynamics cannot be deduced from classical thermodynamics. The slow invariant manifolds of dynamical systems arising from modeling closed reacting mixtures are constructed. These manifolds describe accurately the reactive systems' slow dynamics. The hydrogen--air reactive mixture described by detailed mass-action kinetics is employed as a paradigm in this work.