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Quasi-equilibrium grid algorithm: Geometric construction for model reduction

By Eliodoro Chiavazzo and Iliya V. Karlin

Abstract

The Method of Invariant Grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [1]-[4]. Important role, in that method, is played by the initial grid which, once refined, gives a description of the invariant manifold: the invariant grid. A convenient way to get a first approximation of the SIM is given by the Spectral Quasi Equilibrium Manifold (SQEM) [1]-[2]. In the present paper, a flexible numerical method to construct the discrete analog of a Quasi Equilibrium Manifold, in any dimension, is presented. That object is named Quasi Equilibrium Grid (QEG), while the procedure Quasi Equilibrium Grid Algorithm. Extensions of the QEM notion are also suggested. The QEG is a numerical tool which can be used to find a grid-based approximation for the locus of minima of a convex function under some linear constraints. The method is validated by construction of one and two-dimensional grids for model hydrogen oxidation reaction

Topics: Key words, Chemical kinetics
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.313.1414
Provided by: CiteSeerX
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