2014
DOI: 10.3390/pr2010112
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Reduced Models in Chemical Kinetics via Nonlinear Data-Mining

Abstract: The adoption of detailed mechanisms for chemical kinetics often poses two 1 types of severe challenges: First, the number of degrees of freedom is large; and second, 2 the dynamics is characterized by widely disparate time scales. As a result, reactive flow 3 solvers with detailed chemistry often become intractable even for large clusters of CPUs, 4 especially when dealing with direct numerical simulation (DNS) of turbulent combustion 5 problems. This has motivated the development of several techniques for red… Show more

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Cited by 53 publications
(50 citation statements)
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References 28 publications
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“…here alpha-shapes [19,20], readily implemented in the Matlab package, or more generally, "wrapping" algorithms [21]) we detect the d − 1 dimensional boundary of the region explored ("fathomed") by the available simulation data. [22,23] can also be used for this purpose.…”
Section: Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…here alpha-shapes [19,20], readily implemented in the Matlab package, or more generally, "wrapping" algorithms [21]) we detect the d − 1 dimensional boundary of the region explored ("fathomed") by the available simulation data. [22,23] can also be used for this purpose.…”
Section: Resultsmentioning
confidence: 99%
“…The main assumption upon which our method is based is the same one that underpins most of the model reduction techniques in statistical mechanics: due to time scale separation, the system dynamics is mostly confined on low-dimensional (smooth) manifolds in phase-space [23,[27][28][29]. Our approach squarely aims at exploiting smoothness of the low-dimensional manifolds which, for the gradient systems of interest here, act as the support of the free energy surface governing molecular and other atomistic dynamics.…”
Section: Discussionmentioning
confidence: 99%
“…Defining the 'lifting' and 'restricting' operations is highly problem dependent [44,45,68] and necessarily have to be defined by the user of any generic code. The success or failure of the equationfree methods depend on appropriate 'lifting' and 'restricting' operation; see for example [14]. A key property required from the 'lifting' and 'restricting' operators is that if one 'lifts' and then 'restricts' without time evolving, then the original estimateX i is found [4,33,45].…”
Section: Equation-free Methodsmentioning
confidence: 99%
“…The final two papers of the special issue address the development of such process engineering tools. In the first paper, an automated method for generating reduced order models of complex reaction systems using the approach of diffusion maps is developed and applied to an illustrative turbulent combustion problem [15]. The final paper is focused on the formulation of general iterative controller tuning as a real-time optimization problem and the application of the proposed scheme for tuning model-predictive, general fixed-order and PID controllers for both simulated and experimental systems [16].…”
Section: Process Engineering Methods Developmentmentioning
confidence: 99%