TY - JOUR
T1 - Reduced models in chemical kinetics via nonlinear data-mining
AU - Chiavazzo, Eliodoro
AU - Gear, Charles W.
AU - Dsilva, Carmeline J.
AU - Rabin, Neta
AU - Kevrekidis, Ioannis G.
N1 - Publisher Copyright:
© 2014 by the authors.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2014/3/1
Y1 - 2014/3/1
N2 - The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result, reactive flow solvers with detailed chemistry often become intractable even for large clusters of CPUs, especially when dealing with direct numerical simulation (DNS) of turbulent combustion problems. This has motivated the development of several techniques for reducing the complexity of such kinetics models, where, eventually, only a few variables are considered in the development of the simplified model. Unfortunately, no generally applicable a priori recipe for selecting suitable parameterizations of the reduced model is available, and the choice of slow variables often relies upon intuition and experience. We present an automated approach to this task, consisting of three main steps. First, the low dimensional manifold of slow motions is (approximately) sampled by brief simulations of the detailed model, starting from a rich enough ensemble of admissible initial conditions. Second, a global parametrization of the manifold is obtained through the Diffusion Map (DMAP) approach, which has recently emerged as a powerful tool in data analysis/machine learning. Finally, a simplified model is constructed and solved on the fly in terms of the above reduced (slow) variables. Clearly, closing this latter model requires nontrivial interpolation calculations, enabling restriction (mapping from the full ambient space to the reduced one) and lifting (mapping from the reduced space to the ambient one). This is a key step in our approach, and a variety of interpolation schemes are reported and compared. The scope of the proposed procedure is presented and discussed by means of an illustrative combustion example.
AB - The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result, reactive flow solvers with detailed chemistry often become intractable even for large clusters of CPUs, especially when dealing with direct numerical simulation (DNS) of turbulent combustion problems. This has motivated the development of several techniques for reducing the complexity of such kinetics models, where, eventually, only a few variables are considered in the development of the simplified model. Unfortunately, no generally applicable a priori recipe for selecting suitable parameterizations of the reduced model is available, and the choice of slow variables often relies upon intuition and experience. We present an automated approach to this task, consisting of three main steps. First, the low dimensional manifold of slow motions is (approximately) sampled by brief simulations of the detailed model, starting from a rich enough ensemble of admissible initial conditions. Second, a global parametrization of the manifold is obtained through the Diffusion Map (DMAP) approach, which has recently emerged as a powerful tool in data analysis/machine learning. Finally, a simplified model is constructed and solved on the fly in terms of the above reduced (slow) variables. Clearly, closing this latter model requires nontrivial interpolation calculations, enabling restriction (mapping from the full ambient space to the reduced one) and lifting (mapping from the reduced space to the ambient one). This is a key step in our approach, and a variety of interpolation schemes are reported and compared. The scope of the proposed procedure is presented and discussed by means of an illustrative combustion example.
KW - Combustion
KW - Data mining
KW - Model reduction
UR - http://www.scopus.com/inward/record.url?scp=84977818689&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84977818689&partnerID=8YFLogxK
U2 - 10.3390/pr2010112
DO - 10.3390/pr2010112
M3 - Article
AN - SCOPUS:84977818689
VL - 2
SP - 112
EP - 140
JO - Processes
JF - Processes
SN - 2227-9717
IS - 1
ER -