On fundamental concepts for model reduction in multiscale combustion models
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
Simulation of chemically reacting flows modeled by dissipative dynamical systems with spectral gaps requires an immense expenditure of time despite the continual advancement of digital computing power. In order to decrease this effort to an acceptable level, model reduction methods aim at a low-dimensional approximation of the underlying model equations. In this context, it is observed that solution trajectories bundle near invariant manifolds of successively lower dimension during time evolution which is caused by the spectral gaps generating multiple time scales. There are two different types of model reduction methods: (i) methods that use spatially homogeneous manifolds as low-dimensional approximation of the chemical reaction and then account for reaction–transport coupling and (ii) methods that identify low-dimensional approximations in terms of manifolds based on the full reaction–transport model. The focus of this work is on a discussion of fundamental and unifying geometric and analytic issues of various approaches to trajectory-based numerical approximation techniques of those spatially homogeneous manifolds that are in practical use for model reduction in chemical kinetics. In this context, two basic concepts are pointed out reducing various model reduction approaches to a common denominator. Both of them are related in a variational boundary value problem viewpoint. Furthermore, a fundamental study of the previously with respect to model reduction little researched unreduced nonlinear reaction–transport model is presented, wherefrom suggestions arise for both the insertion of the spatially homogeneous manifolds into the reaction–transport coupling (i) as well as the approximation of manifolds based on the reaction–transport system (ii).
Subject HeadingsDynamisches System [GND]
Dynamical systems [LCSH]
Manifolds (Mathematics) [LCSH]