Quasi steady state and partial equilibrium approximations: their relation and their validity

The quasi steady state and partial equilibrium approximations are analysed in the context of a system of nonlinear differential equations exhibiting multiscale behaviour. Considering systems in the most general and dimensional form , it is shown that both approximations are limiting cases of leading...

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Vydáno v:Combustion theory and modelling Ročník 16; číslo 5; s. 869 - 926
Hlavní autor: Goussis, Dimitris A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis Group 01.10.2012
Témata:
asymptotics
model reduction
partial equilibrium
singular perturbations
steady state
ISSN:1364-7830, 1741-3559
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Shrnutí:The quasi steady state and partial equilibrium approximations are analysed in the context of a system of nonlinear differential equations exhibiting multiscale behaviour. Considering systems in the most general and dimensional form , it is shown that both approximations are limiting cases of leading-order asymptotics. Algorithmic conditions are established which guarantee that the accuracy and stability delivered by the two approximations are equivalent to those obtained with leading-order asymptotics. It is shown that the quasi steady state approximation is a limiting case of the partial equilibrium approximation. Algorithms are reported for the identification of the variables in quasi steady state and/or of the processes in partial equilibrium.
ISSN:1364-7830
1741-3559
DOI:10.1080/13647830.2012.680502