Understanding complex chemical kinetics with computational singular perturbation

Lam, S. H.; Goussis, Dimitris A.

doi:10.1016/s0082-0784(89)80102-x

Cited by 380 publications

(266 citation statements)

References 1 publication

Supporting

Mentioning

238

Contrasting

Unclassified

Order By: Relevance

“…In this article, the focus is on the Computational Singular Perturbation (CSP) method developed by Lam and Goussis [8], [9], [13], [15], [16], [17], [18], [20], [21], [32]. The CSP method, although developed originally for chemical kinetics equations, is generally applicable to multiple-time scale problems.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Analysis of the Computational Singular Perturbation Reduction Method for Chemical Kinetics

2004

View full text Add to dashboard Cite

Summary. This article is concerned with the asymptotic accuracy of the Computational Singular Perturbation (CSP) method developed by Lam and Goussis [The CSP method for simplifying kinetics, Int. J. Chem. Kin. 26 (1994) to reduce the dimensionality of a system of chemical kinetics equations. The method, which is generally applicable to multiple-time scale problems arising in a broad array of scientific disciplines, exploits the presence of disparate time scales to model the dynamics by an evolution equation on a lower-dimensional slow manifold. In this article it is shown that the successive applications of the CSP algorithm generate, order by order, the asymptotic expansion of a slow manifold. The results are illustrated on the Michaelis-Menten-Henri equations of enzyme kinetics. PAC numbers. 82.33.Vx, 87.15.Rn, 82.33.Tb, 02.60.Lj, 02.30.Yy

show abstract

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Analysis of the Computational Singular Perturbation Reduction Method for Chemical Kinetics

2004

View full text Add to dashboard Cite

show abstract

“…[2][3][4]) have been developed and improved continuosly. Examples are the partial-equilibrium- [5] and steady-state approximations [6], the method of rate-controlled constrained equilibrium (RCCE) [7,8], computational singular perturbation (CSP) [9][10][11][12][13][14][15][16], the method of integral or invariant manifolds (MIM) [17][18][19][20], the functional iteration method (FIM) [21][22][23], flamelet generated manifolds (FGM) [24], trajectory-generated manifolds (TGLDM) [25,26], PIC-/ICE-PIC-Methods [27][28][29] and different concepts for reaction-diffusion manifolds (e.g. [30,31]).…”

Section: Introductionmentioning

confidence: 99%

On-demand generation of reduced mechanisms based on hierarchically extended intrinsic low-dimensional manifolds in generalized coordinates

König

Maas

2009

Proceedings of the Combustion Institute

View full text Add to dashboard Cite

A new implementation scheme for reduced mechanisms based on hierarchically generated and extended intrinsic low-dimensional manifolds (ILDMs) created ''on-demand" is presented. The algorithm includes the use of ILDMs in generalized coordinates and a new hierarchical concept for the extension of the ILDMs into the domain of slow chemistry. Problems of pre-calculated ILDM tables are overcome by generating ILDM cells on-demand during the flame calculation, yielding an increased efficiency of the table generation and implementation. In view of a future generation of ILDMs with adaptive dimension based on a local online error control, the presented algorithm includes the possibility to increase the ILDM dimension hierarchically after the stationary solution (solution after 10 4 s) of the first flame calculation with an n c -dimensional ILDM is reached and to re-calculate the result of this first flame calculation using higher-dimensional manifolds with a subsequent error test. The paper presents the generation of hierarchically extended ILDMs in generalized coordinates as well as the on-demand implementation scheme. A sample free flame calculation for the syngas-air system validates the algorithms.

show abstract

“…At present, there are a number of asymptotic tools able to treat the multi-scale system of equations and to expose a 'hidden' hierarchy of the original system of governing equations. An incomplete list includes computational singular perturbation method (Hadjinicolaou & Goussis, 1999;Lam & Goussis, 1988, 1994Valorani & Goussis, 2001), method of integral manifolds (MIM) (Fenichel, 1979;Gol'dshtein & 360 V. BYKOV ET AL. Sobolev, , 1992, and intrinsic low-dimensional manifolds (ILDM) (Maas & Pope, 1992;Rhodes et al, 1999;Kaper & Kaper, 2001).…”

Section: Introductionmentioning

confidence: 99%

On a modified version of ILDM approach: asymptotic analysis based on integral manifolds

Bykov¹,

Goldfarb²,

Gol’dshtein³

et al. 2006

IMA Journal of Applied Mathematics

View full text Add to dashboard Cite

Using the method of integral (invariant) manifolds, the intrinsic low-dimensional manifolds (ILDM) method is analysed. This is a method for identifying invariant manifolds of a system's slow dynamics and has proven to be an efficient tool in modelling of laminar and turbulent combustion. It allows treating multi-scale systems by revealing their hidden hierarchy and decomposing the system dynamics into fast and slow motions. The performed analysis shows that the original ILDM technique can be interpreted as one of the many possible realizations of the general framework, which is based on a special transformation of the original coordinates in the state space. A modification of the ILDM is proposed based on a new definition of the transformation matrix. The proposed numerical procedure is demonstrated on linear examples and highly non-linear test problems of mathematical theory of combustion and demonstrates in some cases better performance with respect to the existing one.

show abstract

Understanding complex chemical kinetics with computational singular perturbation

Cited by 380 publications

References 1 publication

Analysis of the Computational Singular Perturbation Reduction Method for Chemical Kinetics

Analysis of the Computational Singular Perturbation Reduction Method for Chemical Kinetics

On-demand generation of reduced mechanisms based on hierarchically extended intrinsic low-dimensional manifolds in generalized coordinates

On a modified version of ILDM approach: asymptotic analysis based on integral manifolds

Contact Info

Product

Resources

About