Fitting algebraic equations to detailed kinetic simulations

3 Fitting algebraic equations to detailed kinetic simulations 

Chemical kinetic models usually take the form of ordinary differential equations or differential-algebraic equations. Even when reaction phe- 

At a first glance, it is not so obvious that algebraic models can be used for the description of non-stationary kinetic processes where a description of changes in species concentration is required over time. The key lies in the replacement of the kinetic odes by difference equations  

Almost simultaneously, Marsden et al. [227], as discussed in the review by Frenklach [24], developed a different approach for the determination of function F. In their method, the original kinetic model was used in a 

The first stage in the formulation of a repro-model is the generation of suitable data. Usually, several thousand typical data points are considered and a detailed model is used for the calculation of the concentrations as a function of time. The evaluation of a large number of data points requires quite intensive computation, since, large sets of odes must be solved for all conditions. However, this effort has to be expended only once, and when the data have been fitted to polynomials, the repeated kinetic calculations, which are generally carried out during every CFD calculation, are avoided. 

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