Reduced models in chemical kinetics via nonlinear data-mining

Eliodoro Chiavazzo, Charles W. Gear, Carmeline J. Dsilva, Neta Rabin, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

23 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)112-140
Number of pages29
JournalProcesses
Volume2
Issue number1
DOIs
StatePublished - Mar 1 2014

All Science Journal Classification (ASJC) codes

  • Bioengineering
  • Chemical Engineering (miscellaneous)
  • Process Chemistry and Technology

Keywords

  • Combustion
  • Data mining
  • Model reduction

Fingerprint Dive into the research topics of 'Reduced models in chemical kinetics via nonlinear data-mining'. Together they form a unique fingerprint.

  • Cite this

    Chiavazzo, E., Gear, C. W., Dsilva, C. J., Rabin, N., & Kevrekidis, I. G. (2014). Reduced models in chemical kinetics via nonlinear data-mining. Processes, 2(1), 112-140. https://doi.org/10.3390/pr2010112