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A CSP and tabulation-based adaptive chemistry model. (English) Zbl 1105.80015

Summary: We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations–hydrogen–air and heptane–air mixtures–to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.

MSC:

80A25 Combustion
80A30 Chemical kinetics in thermodynamics and heat transfer
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

[1] Smith, G. P., Golden, D. M., Frenklach, M., Moriarty, N. W., Eiteneer, B., Goldenberg, M., Bowman, C. T., Hanson, R. K., Song, S., Gardiner, W. C. Jr., Lissianski, V. V. and Qin, A. 1999. Grimech 3.0.www.me.berkeley.edu/gri_mech, Version:3.0, 30 July 1999
[2] Maas, U. and Pope, S. B. Implementation of simplified chemical kinetics based on intrinsic low-dimensional manifolds. Twenty-Fourth Symposium (International) on Combustion. pp.103–112. The Combustion Institute.
[3] DOI: 10.1016/S0010-2180(01)00252-8 · doi:10.1016/S0010-2180(01)00252-8
[4] Lu, T. T. and Law, C. K. Approaches to mechanism reduction for hydrocarbon oxidation: Ethylene. 42nd AIAA Aerospace Sciences Meeting and Exhibit. January5–82004, Reno, NV. Paper number AIAA 2004-1326
[5] DOI: 10.1016/0010-2180(95)00207-3 · doi:10.1016/0010-2180(95)00207-3
[6] Deuflhard P., Towards dynamic dimension reduction in reactive flow problems (1996)
[7] DOI: 10.1016/S0010-2180(03)00045-2 · doi:10.1016/S0010-2180(03)00045-2
[8] Lam S. H., Proceedings of the Combustion Institute 22 pp 931– (1988)
[9] DOI: 10.1002/kin.550260408 · doi:10.1002/kin.550260408
[10] DOI: 10.1016/S0010-2180(98)00132-1 · doi:10.1016/S0010-2180(98)00132-1
[11] DOI: 10.1006/jcph.2001.6709 · Zbl 1037.76045 · doi:10.1006/jcph.2001.6709
[12] DOI: 10.1016/S0010-2180(03)00067-1 · doi:10.1016/S0010-2180(03)00067-1
[13] DOI: 10.1080/713665229 · Zbl 1046.80500 · doi:10.1080/713665229
[14] Tonse S. R., Israel Journal of Chemistry 39 pp 97– (1999) · doi:10.1002/ijch.199900010
[15] DOI: 10.1016/S0082-0784(00)80201-5 · doi:10.1016/S0082-0784(00)80201-5
[16] DOI: 10.1002/kin.10140 · doi:10.1002/kin.10140
[17] DOI: 10.1016/S0167-2789(02)00386-X · Zbl 1036.80007 · doi:10.1016/S0167-2789(02)00386-X
[18] Goussis D. A., On the homogeneous methane–air reaction system (1990)
[19] Lam S. H., Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane–Air Flames 384 (1991)
[20] Levin J. J., Journal of Rational Mechanics and Analysis 3 pp 247– (1954)
[21] DOI: 10.1137/0910062 · Zbl 0677.65075 · doi:10.1137/0910062
[22] Najm H. N., A numerical scheme for modelling reacting flow with detailed chemistry and transport (2003)
[23] DOI: 10.1016/B978-008043944-0/50891-X · doi:10.1016/B978-008043944-0/50891-X
[24] Valorani, M., Goussis, D. A. and Najm, H. N. Using CSP to analyze computed reactive flows. 8th SIAM International Conference On Numerical Combustion. Amelia Island, FL.
[25] Zagaris, A., Kaper, H. G. and Kaper, T. J. Analysis of the CSP reduction method for chemical kinetics. SIAM Conference on Applications of Dynamical Systems. May27–31, Snowbird, Utah. · Zbl 1053.92051
[26] DOI: 10.1006/jcph.1999.6322 · Zbl 0958.76061 · doi:10.1006/jcph.1999.6322
[27] DOI: 10.1088/1364-7830/3/4/306 · doi:10.1088/1364-7830/3/4/306
[28] DOI: 10.1137/S1064827503429168 · Zbl 1061.65090 · doi:10.1137/S1064827503429168
[29] Armstrong, R., Gannon, D., Geist, A., Keahy, K., Kohn, S., McInnes, L., Parker, S. and Smolenski, B. Towards a common component architecture for high performance scientific computing. Proceedings of the 8th International Symposium on High Performance Distributed Computing. Redondo Beach, California
[30] DOI: 10.1002/cpe.651 · Zbl 1008.68528 · doi:10.1002/cpe.651
[31] Anderson E., LAPACK Users’ Guide – Second Edition (1995)
[32] DOI: 10.1016/j.jcp.2005.03.033 · Zbl 1073.65057 · doi:10.1016/j.jcp.2005.03.033
[33] Lefantzi, S., Ray, J. and Najm, H. N. Using the common component architecture to design high performance scientific simulation codes. Proceedings of the International Parallel and Distributed Processing Symposium. Nice, France.
[34] DOI: 10.1504/PCFD.2005.007063 · Zbl 1189.76368 · doi:10.1504/PCFD.2005.007063
[35] Bernholdt D. E., International Journal of High Performance Computing Applications (2005)
[36] DOI: 10.1016/S0377-0427(97)00219-7 · Zbl 0910.65067 · doi:10.1016/S0377-0427(97)00219-7
[37] Lee J. C., Computational Fluid and Solid Mechanics 2005 pp 717– (2005)
[38] DOI: 10.1080/00102209308924120 · doi:10.1080/00102209308924120
[39] DOI: 10.1137/S1064827596303995 · Zbl 0960.65094 · doi:10.1137/S1064827596303995
[40] DOI: 10.1080/00102209108951759 · doi:10.1080/00102209108951759
[41] DOI: 10.1016/j.combustflame.2004.01.011 · doi:10.1016/j.combustflame.2004.01.011
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