Curvature based criteria for slow invariant manifold computation: from differential geometry to numerical software implementations for model reduction in hydrocarbon combustion

Mathematical models for chemical kinetics are multiple times scale dynamical systems based on ordinary differential equations and can be reduced in order to decrease the dimensionality of the state space and the complexity of their numerical simulation by restriction to the slow flow. Some model order reduction techniques make use of the identification of low-dimensional, so-called slow invariant attracting manifolds. The focus of this work is on a discussion of a general viewpoint using differential geometric concepts in order to deal with slow invariant manifolds within an extended state space aiming to apprehend those manifolds as intrinsic geometric objects with curvature based criteria. In this context, a computational verifiable necessary condition for the slow invariant manifold graph as a reformulation of an invariance property is stated and proven in this work. Besides, an information theoretical viewpoint in a probability theoretical setting is constructed in order to quantify the information loss of a reduced system in comparison to the corresponding full system by using Shannon's entropy notion. Moreover, a software package called AMMSoCK being an acronym for A Manifold Based Model Reduction Software for Chemical Kinetics is presented and a detailed documentation can be found in this work. The software can be used to reduce combustion mechanisms which is demonstrated by means of a hydrogen and a hydrocarbon combustion mechanism. The usage of AMMSoCK as well as the numerical results of those reductions are discussed