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One-dimensional slow invariant manifolds for spatially homogenous reactive systems

J. Chem. Phys. 131, 024118 (2009); doi:10.1063/1.3171613

Published 14 July 2009

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Ashraf N. Al-Khateeb,1 Joseph M. Powers,1,2 Samuel Paolucci,1 Andrew J. Sommese,2 Jeffrey A. Diller,2 Jonathan D. Hauenstein,2 and Joshua D. Mengers1
1Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556-5637, USA
2Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 465556-4618, USA
A reactive system's slow dynamic behavior is approximated well by evolution on manifolds of dimension lower than that of the full composition space. This work addresses the construction of one-dimensional slow invariant manifolds for dynamical systems arising from modeling unsteady spatially homogeneous closed reactive systems. Additionally, the relation between the systems' slow dynamics, described by the constructed manifolds, and thermodynamics is clarified. It is shown that other than identifying the equilibrium state, traditional equilibrium thermodynamic potentials provide no guidance in constructing the systems' actual slow invariant manifolds. The construction technique is based on analyzing the composition space of the reactive system. The system's finite and infinite equilibria are calculated using a homotopy continuation method. The slow invariant manifolds are constructed by calculating attractive heteroclinic orbits which connect appropriate equilibria to the unique stable physical equilibrium point. Application of the method to several realistic reactive systems, including a detailed hydrogen-air kinetics model, reveals that constructing the actual slow invariant manifolds can be computationally efficient and algorithmically easy. ©2009 American Institute of Physics
History: Received 9 March 2009; accepted 17 June 2009; published 14 July 2009
Permalink: http://link.aip.org/link/?JCPSA6/131/024118/1
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KEYWORDS and PACS

Keywords
PACS
  • 82.20.Fd
    Collision theories and trajectory models of chemical kinetics
  • 82.60.-s
    Chemical thermodynamics
  • YEAR: 2009

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ISSN:
0021-9606 (print)   1089-7690 (online)
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