Method of invariant manifold for chemical kinetics

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). The MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton...

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Bibliographic Details
Published in:Chemical engineering science 2003-11, Vol.58 (21), p.4751-4768
Main Authors: Gorban, Alexander N., Karlin, Iliya V.
Format: Article
Language:English
Subjects:
Entropy
Invariant manifold
Kinetics
Mathematical modeling
Model reduction
Nonlinear dynamics
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Summary:In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). The MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A review of existing alternative methods is extended by a thermodynamically consistent version of the method of intrinsic low-dimensional manifolds. A grid-based version of the MIM is developed, and model extensions of low-dimensional dynamics are described. Generalizations to open systems are suggested. The set of methods covered makes it possible to effectively reduce description in chemical kinetics.
ISSN:0009-2509
1873-4405
DOI:10.1016/j.ces.2002.12.001