The spectral characterisation of reduced order models in chemical kinetic systems. Issue 7 (10th November 2022)

• Record Type: Journal Article
• Authors: Valorani, Mauro; Malpica Galassi, Riccardo; Ciottoli, Pietro Paolo; Najm, Habib; Paolucci, Samuel
• Is Part Of: Combustion theory and modelling. Volume 26:Issue 7(2022)
• Page Start: 1185
• Page End: 1216
• Publication Date: 2022-11-10
• Subjects: model reduction -- multi-scale problems -- stiff systems -- slow invariant manifolds -- singular perturbation problems; Combustion -- Mathematical models -- Periodicals; 541.361
• DOI: 10.1080/13647830.2022.2136038
• Languages: English
• ISSNs: 1364-7830

Abstract

Abstract : 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 < N ) can be carried out by evaluating the eigen-system of a ( n × n ) constrained Jacobian matrix, J C, of the reduced vector field that accounts for the role of the constraints.