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Processes 2014, 2(1), 112-140; doi:10.3390/pr2010112

Reduced Models in Chemical Kinetics via Nonlinear Data-Mining

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Received: 23 September 2013 / Revised: 10 December 2013 / Accepted: 19 December 2013 / Published: 23 January 2014
(This article belongs to the Special Issue Feature Papers)
Download PDF [5734 KB, uploaded 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 model reduction; data mining; combustion
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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.

AMA Style

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.

Chicago/Turabian Style

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.

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