The size and complexity of multi-scale problems such as those arising in chemical kinetics mechanisms has stimulated the search for methods that reduce the number of species and chemical reactions but retain a desired degree of accuracy. The time-scale characterisation of the multi-scale problem can be carried out on the basis of local information such as the Jacobian matrix of the model problem and its related eigen-system evaluated at one point P of the system trajectory. While the original problem is usually described by ordinary differential equations (ODEs), the reduced order model is described by a reduced number of ODEs and a number of algebraic equations (AEs), that might express one or more physical conservation laws (mass, momentum, energy), or the fact that the long-term dynamics evolves within a so-called Slow Invariant Manifold (SIM). To fully exploit the benefits offered by a reduced order model, it is required that the time scale characterisation of the n-dimensional reduced order model returns an answer consistent and coherent with the time-scale characterisation of the N-dimensional original model. This manuscript discusses a procedure for obtaining the time-scale characterisation of the reduced order model in a manner that is consistent with that of the original problem. While a standard time scale characterisation of the (original) N-dimensional original model can be carried out by evaluating the eigen-system of the (N×N) Jacobian matrix of the vector field that defines the system dynamics, the time-scale characterisation of the n-dimensional reduced order model (with n
Bibliographical noteKAUST Repository Item: Exported on 2022-11-11
Acknowledged KAUST grant number(s): OSR-2019-CCF-1975-35
Acknowledgements: MV acknowledges the support provided by the Italian Ministry of University and Research. This work was supported by KAUST OSR-2019-CCF-1975-35 Subaward Agreement. RMG received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 801505. HNN acknowledges the support provided by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES) Division of Chemical Sciences, Geosciences, and Biosciences. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Energy Engineering and Power Technology
- Physics and Astronomy(all)
- Modeling and Simulation
- Chemical Engineering(all)
- Fuel Technology