A Framework for Adaptive Model Reduction in Chemical Kinetics

Solutions of reaction systems in general, and reactive flows in particular, are computationally very expensive. In general their solutions contain a very large range of scales, which are finite or countably infinite in number depending on wether the system is modeled by ODEs or PDEs. However, to within an arbitrary but fixed accuracy
there are in general vary fast and very slow time scales whose contributions to the dynamics are negligible. We perform a dynamic transformation of the model equations that exploit such asymptotic behaviors. This results in an adaptive reduction of the system to one that is not only substantially smaller, but more importantly non-stiff.
The frozen (slow) and near-equilibrium (fast) modes play crucial roles in defining the active subspace, and thus it is mandatory to account for their contribution. We will present results relevant to illustrative simple test cases and to hydrocarbon kinetics to demonstrate the effectiveness of the method.
In addition to the numerical solution, the new approach provides extra information useful to identify a statical simplification/reduction of the original model equations.