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Reduced Models in Chemical Kinetics via Nonlinear Data-Mining
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Energy Department, Politecnico di Torino, Torino 10129, Italy
Department of Exact Sciences, Afeka Tel-Aviv Academic College of Engineering, Tel-Aviv 69107, Israel
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
* Author to whom correspondence should be addressed.
Received: 23 September 2013; in revised form: 10 December 2013 / Accepted: 19 December 2013 / Published: 23 January 2014
Abstract: 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.
Keywords: model reduction; data mining; combustion
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Chiavazzo, E.; Gear, C.W.; Dsilva, C.J.; Rabin, N.; Kevrekidis, I.G. Reduced Models in Chemical Kinetics via Nonlinear Data-Mining. Processes 2014, 2, 112-140.
Chiavazzo E, Gear CW, Dsilva CJ, Rabin N, Kevrekidis IG. Reduced Models in Chemical Kinetics via Nonlinear Data-Mining. Processes. 2014; 2(1):112-140.
Chiavazzo, Eliodoro; Gear, Charles W.; Dsilva, Carmeline J.; Rabin, Neta; Kevrekidis, Ioannis G. 2014. "Reduced Models in Chemical Kinetics via Nonlinear Data-Mining." Processes 2, no. 1: 112-140.