The origin of CEMA and its relation to CSP

Abstract

There currently exist two methods for analysing an explosive mode introduced by chemical kinetics in a reacting process: the Computational Singular Perturbation (CSP) algorithm and the Chemical Explosive Mode Analysis (CEMA). CSP was introduced in 1989 and addressed both dissipative and explosive modes encountered in the multi-scale dynamics that characterize the process, while CEMA was introduced in 2009 and addressed only the explosive modes. It is shown that (i) the algorithmic tools incorporated in CEMA were developed previously on the basis of CSP and (ii) the examination of explosive modes has been the subject of CSP-based works, reported before the introduction of CEMA.

A generalized partially stirred reactor model for turbulent closure

“…The computational singular perturbation (CSP) theory [21] provides additional insights into the role of different time scales identified in the new PaSR model. To this end, the time scale participation index (TPI) [21]:…”

“…Good agreement is found between the model and the filtered quantities at different filter sizes. Tools provided by the computational singular perturbation analysis (CSP) [20], such as the timescale participation index (TPI) [21], are used to assess the contribution of each reaction in the modes originating from the Jacobian decomposition and explain the advances shown by the employment of multiple chemical times against the conventional single scale approach.…”

Computational analysis of the effect of hydrogen peroxide addition on premixed laminar hydrogen/air flames

“…where a i is the (N + 1)-dimensional CSP basis column vector and h i =b i • g(z) is the related amplitude, which is produced using the dual basis row vector b i (b i • a j = δ i j ) [25,27,47]. Interested in leading order accuracy, the CSP basis vectors a i , b i can be approximated by the right (α i ) and left (β i ), respectively, eigenvectors of the Jacobian J of g(z) [31,34,[48][49][50]. Apart from an amplitude, each CSP mode is described by a timescale which is defined as the inverse norm of the associated eigenvalue, i.e., τ i = |λ i | −1 , where [51][52][53].…”

“…Apart from an amplitude, each CSP mode is described by a timescale which is defined as the inverse norm of the associated eigenvalue, i.e., τ i = |λ i | −1 , where [51][52][53]. A CSP mode is characterised as explosive if the associated eigenvalue is positive and dissipative otherwise [50]. Explosive modes are relate to processes that tend to drive the system away from equilibrium.…”

Asymptotic Analysis of Detonation Development at SI Engine Conditions Using Computational Singular Perturbation

“…The details of the CSP method used herein and its algorithmic tools have been discussed elsewhere (see for instance [83][84][85][86][87]), and only a brief summary is provided here. Consider the system of species and temperature equations in the general form of…”