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Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories

  • Dirk Lebiedz
  • Volkmar Reinhardt
  • Jochen Siehr
  • Jonas Unger
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 75)

Abstract

The need for reduced models of chemical kinetics is motivated by the fact that the simulation of reactive flows with detailed chemistry is generally computationally expensive. In dissipative dynamical systems different time scales cause an anisotropically contracting phase flow. Most kinetic model reduction approaches explicitly exploit this and separate the dynamics into fast and slow modes. We propose an implicit approach for the approximation of slow attracting manifolds by computing trajectories as solutions of an optimization problem suggesting a variational principle characterizing trajectories near slow attracting manifolds. The objective functional for the identification of suitable trajectories is supposed to represent the extent of relaxation of chemical forces along the trajectories which is proposed to be minimal on the slow manifold. Corresponding geometric criteria are motivated via fundamental concepts from differential geometry and physics. They are compared to each other through three kinetic reaction mechanisms.

Keywords

Chemical Kinetic Model Reduction Slow Manifold Progress Variable Forward Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

This work was supported by the German Research Foundation (DFG) through the Collaborative Research Center (SFB) 568.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dirk Lebiedz
    • 1
    • 2
  • Volkmar Reinhardt
    • 1
  • Jochen Siehr
    • 1
  • Jonas Unger
    • 2
  1. 1.Interdisciplinary Center for Scientific Computing (IWR)University of HeidelbergHeidelbergGermany
  2. 2.Center for Systems Biology (ZBSA)University of FreiburgFreiburgGermany

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