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Flow, Turbulence and Combustion
Published in: Flow, Turbulence and Combustion 4/2018

21-06-2018

Enhancements of the G-Scheme Framework

Authors: Mauro Valorani, Pietro Paolo Ciottoli, Riccardo Malpica Galassi, Samuel Paolucci, Temistocle Grenga, Emanuele Martelli

Published in: Flow, Turbulence and Combustion | Issue 4/2018

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Abstract

The G-Scheme is a well established framework for multi-scale adaptive model reduction, whose effectiveness was demonstrated with reference to a number of test models, together with an identification of the critical areas that were in need of further theoretical and computational refinement. In this communication, we report on how we enhanced the solver performance. Two new features involving (i) the criteria to identify the fast and slow subspace dimensions, and (ii) a criterion to decide if and when the reuse of the CSP Basis is feasible without deteriorating the overall performance of the solver, have been proved able to increase significantly the computational efficiency of the solver without sacrificing its accuracy.
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Footnotes
1
We refer to the collection of mathematical objects involving the Jacobian Jg of g(x), the eigenvectors and the eigenvalues of Jg as the CSP Basis.
 
2
By construction, AB = I
 
3
In the application of the criterion defined by Eq. 4, special care is required to manage the contribution of pairs of complex conjugate eigenvalues and eigenvectors.
 
Literature
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Valorani, M., Paolucci, S.: The G-Scheme: A framework for multi-scale adaptive model reduction. J. Comput. Phys. 228(13), 4665–4701 (2009)MathSciNetCrossRef
2.
Smith, G.P., Golden, D.M., Frenklach, M., Moriarty, N.W., Eiteneer, B., Goldenberg, M., Bowman, C.T., Hanson, R.K., Song, S., Lissianski, V.V., Zhiwei, W.J.Q.: GRI mechanism for Methane/Air, Version 3.0. www.​me.​berkeley.​edu/​gri_​mech/​
3.
Lam, S.H., Goussis, D.A.: The CSP method for simplifying kinetics. Int. J. Chem. Kinet. 26(4), 461–486 (1994)CrossRef
4.
Valorani, M., Paolucci, S., Ciottoli, P.P., Malpica Galassi, R.: Entropy production and timescales. Combust. Theor. Model. 21(1), 137–157 (2017)MathSciNetCrossRef
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Frenklach, M., Wang, H., Goldenberg, M., Smith, G.P., Golden, D.M., Bowman, T., Hanson, R.K., Gardiner, W.C., Lissianski, V.: Gri-Mech – an optimized detailed chemical reaction mechanism for methane combustion. Topical Report GRI-95/0058, Gas Research Institute, Chicago (1995)
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Buda, F., Bounaceur, R., Warth, V., Glaude, P., Fournet, R., Battin-Leclerc, F.: Progress toward a unified detailed kinetic model for the autoignition of alkanes from c4 to c10 between 600 and 1200 k. Combust. Flame 142(1–2), 170–186 (2005)CrossRef
Metadata
Title
Enhancements of the G-Scheme Framework
Authors
Mauro Valorani
Pietro Paolo Ciottoli
Riccardo Malpica Galassi
Samuel Paolucci
Temistocle Grenga
Emanuele Martelli
Publication date
21-06-2018
Publisher
Springer Netherlands
Published in
Flow, Turbulence and Combustion / Issue 4/2018
Print ISSN: 1386-6184
Electronic ISSN: 1573-1987
DOI
https://doi.org/10.1007/s10494-018-9942-2

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