On the Application of Trajectory-based Optimization for Nonlinear Kinetic Model Reduction

The use of increasingly detailed reaction mechanisms for the chemistry description in computational fluid dynamics simulations plays a major role in combustion research. Model reduction adresses the discrepancy between the need to develop detailed high-dimensional multi-scale models (e.g. in chemical kinetics) and the ineffciency of their use in computationally demanding numerical simulations. Many modern model reduction approaches are based on the approximation of slow invariant manifolds of lower dimension than the original system. Pursuing the work of Lebiedz on Minimum Entropy Production Trajectories (MEPT), this work presents a way to approximate slow invariant manifolds based on the optimization of trajectories. This work particularly covers the generalization of the MEPT concept for the construction of invariant manifolds of arbitrary dimension and guides the way for the construction of general relaxation criteria. Especially the minimization of curvature of trajectories - used for model reduction purposes for the first time within the scope of this work - leads to highly encouraging results, where the optimized trajectories are close to the slow invariant manifold. For the derivation of a reliable method for the construction of low-dimensional manifolds to be used in chemical kinetics, this work deals with advanced numerical methods, ideas from thermodynamics and differential geometry