(613e) Automatic Parameterization and Simplification of Detailed Chemical Kinetics

The solution of detailed models for chemical kinetics often poses severe numerical difficulties mainly due to a large number of degrees of freedom and disparity in the time scales. As a result, reactive flow solvers with detailed chemistry often become intractable even for large clusters of CPUs. This has motivated the development of several approaches for reducing the complexity of such kinetics models, by expressing them in terms of only a few slow variables [1]. However, there are no generally applicable recipes for selecting a good global parameterization of the simplified model, and the choice of slow variables often relies upon intuition and experience. In this work, we provide evidence that a recent nonlinear manifold learning technique (i.e. diffusion maps) [2,3] is a useful tool for systematically extracting a global parameterization of low-dimensional manifolds arising in chemical kinetics such as combustion problems, while less stiff reduced systems can be expressed in terms of those automatically detected slow variables. Advantages and disadvantages of the method will be discussed with the help of illustrative examples, such as the ordinary differential equations describing spatially homogeneous mixture of air and hydrogen.

[1] U. Maas and D. Goussis, in Turbulent Combustion Modeling, vol. 95, T. Echekki and E. Mastorakos, Eds. Springer, 2011, pp. 193--220.

[2] R. Coifman, S. Lafon, A. Lee, M. Maggioni, B. Nadler, F. Warner and S. Zucker, PNAS, vol. 102, pp. 7426, 2005.

[3] R. Coifman, S. Lafon, A. Lee, M. Maggioni, B. Nadler, F. Warner and S. Zucker, PNAS, vol. 102, pp. 7432, 2005.