Fitting a system of odes to detailed kinetic simulations

2 Fitting a system of odes to detailed kinetic simulations 

While fitting parameters of a small system of odes to experimental data lies in the realm of empirical modelling, fitting parameters in a similar way to results of calculations from a detailed kinetic model can be considered as a branch of mechanism reduction. 

The following two-variable empirical model was used by Korobeinikov et al. [216] to give a simple approximation of ignition delay times in shock waves  

Oran et al. [218,219] developed a global parameterized model which describes the chemical induction time as a function of temperature and pressure. Parameters of the induction time function were determined for stoichiometric hydrogen and methane in air mixtures. The parameters were fitted to numerical results obtained from the simulations based on detailed reaction mechanisms. This technique allowed a 22-times faster calculation of the induction time and reduced the simulation time in a onedimensional model by a factor of 7.5. The fitted model was used in two-dimensional shock-wave simulations. 

In a recent article, Revel et al. [224] demonstrated a systematic method for the production of a global mechanism fitted to a detailed mechanism for NO generation in methane flames. The global reactions were deduced on the basis of element flux calculations and pathway analyses. The global mechanism of 10 species and 6 reactions is able to reproduce accurately the ignition delays, temperature profiles, and concentration profiles of major species and NO over a wide range of fuel-to-air ratios and initial temperatures. 

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