Determination of approximate lumping schemes by a singular perturbation method
- Department of Chemistry, Princeton University, Princeton, New Jersey 08540 (United States)
- Department of Computer Science, Agricultural Engineering Faculty, University of Agricultural Science, H-2103 Goedoello, Pater K. u. 1 (Hungary)
A singular perturbation method is employed for the determination of an approximate nonlinear lumped model for a chemical kinetic system described by a set of first order ordinary differential equations with a group of small positive parameters corresponding to different time scales. New variables, called purely fast variables, are introduced and determined. Substituting their explicit expressions into the original kinetic equation system yields a lumped differential equation system containing the independent variable [ital t]. The lumped system can reach any desired accuracy for any initial composition. A further approximation to this lumped system, obtained by omitting transient exponential functions of [ital t], is shown to define the dynamics of the system on a slow invariant manifold. Two simple examples are used to illustrate this approach.
- OSTI ID:
- 6297072
- Journal Information:
- Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 99:5; ISSN JCPSA6; ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
400201* -- Chemical & Physicochemical Properties
661100 -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHEMICAL COMPOSITION
CHEMICAL REACTION KINETICS
DIFFERENTIAL EQUATIONS
EQUATIONS
INVARIANCE PRINCIPLES
KINETIC EQUATIONS
KINETICS
MATHEMATICAL MANIFOLDS
NONLINEAR PROBLEMS
PERTURBATION THEORY
REACTION KINETICS
SINGULARITY