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Computational Science and High Performance Computing IV pp 233–252Cite as

Hierarchy Analysis and Reduction of Reacting Flow Systems

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Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 115))

Abstract

The qualitative system analysis and model reduction for reacting flows has gained an increasing interest during the last years. Nowadays, simulations based on sophisticated algorithms implemented on powerful workstations turn out to be a prevailing tool of the system analysis. However, modelling of realistic systems of technical importance leads to an extreme growth of mathematical models both in complexity and in dimension, i.e. they become not treatable even by modern computational facilities. Recently, the concept of invariant, slow/fast -, attractive and stable manifolds, which appear in the system state space as a manifestation of a restricted number of degrees of freedom exhibiting by the system, has proven to be an efficient tool of system analysis and model reduction. In the current work questions about the specific low-dimensional manifolds’ identification, the analysis of their properties, their approximation and the application to model reduction of complex reacting flow systems is discussed.

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Author information

Authors and Affiliations

  1. Institute for Technical Thermodynamics, Karlsruhe Institute of Technology, Engelbert-Arndold-Straße 4, Geb. 10.91, 76131, Karlsruhe, Germany

    Viatcheslav Bykov & Ulrich Maas

Authors
  1. Viatcheslav Bykov
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  2. Ulrich Maas
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Editor information

Editors and Affiliations

  1. Aerodynamisches Institut, RWTH Aachen, Wuellnerstr. zw. 5 u. 7, 52062, Aachen, Germany

    Egon Krause

  2. Institute of Computational Technologies of SB RAS, Ac. Lavrentiev Ave. 6, 630090, Novosibirsk, Russia

    Yurii Shokin

  3. High Performance Computing Center Stuttgart, University of Stuttgart, Nobelstrasse 19, 70569, Stuttgart, Germany

    Michael Resch

  4. Section of Applied Mathematics, University of Freiburg, Hermann-Herder-Str. 10, 79104, Freiburg, Germany

    Dietmar Kröner  & Nina Shokina  & 

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Bykov, V., Maas, U. (2011). Hierarchy Analysis and Reduction of Reacting Flow Systems. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_18

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  • DOI: https://doi.org/10.1007/978-3-642-17770-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17769-9

  • Online ISBN: 978-3-642-17770-5

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