Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics
Eliodoro Chiavazzo 1, Alexander N. Gorban 2, Iliya V. Karlin 1*1 Aerothermochemistry and Combustion Systems Laboratory LAV, ETH Zurich, 8092 Zurich, Switzerland.
2 Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK.
Received 8 November 2006; Accepted (in revised version) 31 January 2007
Available online 30 March 2007
A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold. The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction. We explore a recently introduced Method of Invariant Grids (MIG) for iteratively solving the invariance equation. Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold, Spectral Quasi Equilibrium Manifold, Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold. Slow invariant manifold was also computed using the Computational Singular Perturbation (CSP) method. A comparison between MIG and CSP is also reported.
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PACS: 05.20.Dd, 82.37.-j
Key words: Chemical kinetics, model reduction, invariant manifold, entropy, nonlinear dynamics, mathematical modeling.
Email: firstname.lastname@example.org (E. Chiavazzo), email@example.com (A. N. Gorban), firstname.lastname@example.org (I. V. Karlin)