Flow, Turbulence and Combustion

, Volume 92, Issue 4, pp 885–902 | Cite as

An Optimization Approach to Kinetic Model Reduction for Combustion Chemistry

  • Dirk Lebiedz
  • Jochen Siehr


Model reduction methods are relevant when the computation time of a full convection–diffusion–reaction simulation based on detailed chemical reaction mechanisms is too large. In this article, we consider a model reduction approach based on optimization of trajectories and its applicability to realistic combustion models. As many model reduction methods, it identifies points on a slow invariant manifold based on time scale separation in the dynamics of the reaction system. The numerical approximation of points on the manifold is achieved by solving a semi-infinite optimization problem, where the dynamics enter the problem as constraints. The proof of existence of a solution for an arbitrarily chosen dimension of the reduced model (slow manifold) is extended to the case of realistic combustion models including thermochemistry by considering the properties of proper maps. The model reduction approach is finally applied to two models based on realistic reaction mechanisms: ozone decomposition as a small test case and syngas combustion as a test case including all features of a detailed combustion mechanism.


Model reduction Slow invariant manifold Chemical kinetics Nonlinear optimization 


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute for Numerical MathematicsUlm UniversityUlmGermany
  2. 2.Interdisciplinary Center for Scientific Computing (IWR)Heidelberg UniversityHeidelbergGermany

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