par Valorani, Mauro;Malpica Galassi, Riccardo 
;Ciottoli, Pietro Paolo;Najm, Habib H.N.;Paolucci, S.
Référence Combustion theory and modelling, page (1-32)
Publication Publié, 2022-11
;Ciottoli, Pietro Paolo;Najm, Habib H.N.;Paolucci, S.Référence Combustion theory and modelling, page (1-32)
Publication Publié, 2022-11
Article révisé par les pairs
| Résumé : | The size and complexity of multi-scale problems such as those arising in chemicalkinetics mechanisms has stimulated the search for methods that reduce the numberof 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 oflocal information such as the Jacobian matrix of the model problem and its relatedeigen-system evaluated at one pointPof the system trajectory. While the originalproblem is usually described by ordinary differential equations (ODEs), the reducedorder model is described by a reduced number of ODEs and a number of algebraicequations (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-calledSlow Invariant Manifold (SIM). To fully exploit the benefits offered by a reduced ordermodel, it is required that the time scale characterisation of then-dimensional reducedorder model returns an answer consistent and coherent with the time-scale characteri-sation of theN-dimensional original model. This manuscript discusses a procedure forobtaining the time-scale characterisation of the reduced order model in a manner thatis consistent with that of the original problem. While a standard time scale characteri-sation of the (original)N-dimensional original model can be carried out by evaluatingthe eigen-system of the (N×N) Jacobian matrix of the vector field that defines thesystem dynamics, the time-scale characterisation of then-dimensional reduced ordermodel (withn |
