Stiffness of Reaction Kinetic Models

The coupling of some chemical modes with relatively fast physical ones may disturb system trajectories from the low-dimensional manifold (Bykov and Maas 2007). Priifert et al. (2014) provide a discussion of the comparison of species lifetimes t,- (see Eq. (6.11)), system timescales based on eigenvalues and two additional timescales called system progress and progress variable timescales for reactive flow models. 

One of the first applications of computers in science was the simulation of the dislocation of weights interconnected with springs. When the springs were not stiff, the simulation was easy and no numerical problems were encountered. However, 

The stiffness of a dynamical system can be characterised via its timescales. Remember that the ratio l/IRe(A,) I is called the /-th timescale of a dynamical system (see Sect. 6.3). The most widely used stiffness index is the reciprocal of the shortest timescale of the system  

A model is called stiff if its characteristic time T is several orders of magnitude (typically 8-12 orders of magnitude) longer than its shortest timescale. Stiffness can be characterised by the following stiffness ratio  

Another possibility is to calculate the ratio of the longest and shortest timescales of the model  

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