Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

Combustion Theory and Modelling

Volumn 16, Issue 3, 2012, Pages 387-418

  Bisetti, Fabrizio ^a  

^a KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

chemical kinetics; exponential methods; integration; Krylov subspace methods; large stiff nonlinear systems; model reduction

Indexed keywords

CHEMICAL KINETIC MECHANISM; CHEMICAL SYSTEMS; COMPUTATIONAL COSTS; ERROR CONTROL; ERROR TOLERANCE; EXPONENTIAL INTEGRATORS; EXPONENTIAL METHODS; GLOBAL ERRORS; HYDROCARBON FUEL; INDIVIDUAL COMPONENTS; JACOBIANS; KRYLOV SUBSPACE; KRYLOV SUBSPACE METHOD; LOCAL MODEL; LOW-DIMENSIONAL SPACES; MATRIX EXPONENTIALS; MATRIX FUNCTIONS; METHANE-AIR; MODEL REDUCTION; NUMBER OF SPECIES; OPTIMAL SELECTION; PREDICTIVE CAPABILITIES; RECENT TRENDS; THIRD-ORDER CONVERGENCE; TIME INTEGRATION; TIME STEP;

ADAPTIVE ALGORITHMS; INTEGRATION; JACOBIAN MATRICES; METHANE; REACTION KINETICS;

KINETICS;

EID: 84859757319     PISSN: 13647830     EISSN: 17413559     Source Type: Journal    
DOI: 10.1080/13647830.2011.631032     Document Type: Article

References (56)

1. Warnatz, J., Maas, U. and Dibble, R. W. 2006. Combustion, Berlin: Springer Verlag.
2. Fox, R. O. 2003. Computational Models for Turbulent Reacting Flows, Cambridge: Cambridge University Press.
3. Correa, S. M. 1993. Turbulence-chemistry interactions in the intermediate regime of premixed combustion. Combust. Flame, 93: 41-60.
4. Poinsot, T. and Veynante, D. 2005. Theoretical and Numerical Combustion, Flourtown, PA: R.T. Edwards.
5. Curran, H.J., Pitz, W.J. and Westbrook, C.K. 2002. UCRL-WEB-204236.
6. Curran, H. J., Gaffuri, P., Pitz, W. J. and Westbrook, C. K. 1998. A comprehensive modeling study of n-heptane oxidation. Combust. Flame, 114: 149-177. Downloaded from https://www-pls.llnl.gov/?url=science_and_technology-chemistry-combustion-iso_octane_version_3. Website version LLNL-MI-421507. Review and release date: December 16, 2009
7. Herbinet, O., Pitz, W. J. and Westbrook, C. K. 2008. Detailed chemical kinetic oxidation mechanism for a biodiesel surrogate. Combust. Flame, 154(3): 507-528.
8. Herbinet, O., Pitz, W. J. and Westbrook, C. K. 2010. Detailed chemical kinetic mechanism for the oxidation of biodiesel fuels blend surrogate. Combust. Flame, 157(5): 893-908.
9. Majda, A. and Sethian, J. J. 1985. The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Technol., 42(3): 185-205.
10. Lam, S. H. 1993. Using CSP to understand complex chemical kinetics. Combust. Sci. Technol., 89(5): 375-404.
11. Lu, T. and Law, C. K. 2009. Toward accommodating realistic fuel chemistry in large-scale computations. Prog. Energ. Combust. Sci., 35(2): 192-215.
12. Byrne, G. D. and Hindmarsh, A. C. 1987. Stiff ODE solvers: a review of current and coming attractions. J. Comput. Phys., 70: 1-62.
13. Hairer, E. and Wanner, G. 2010. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Berlin: Springer.
14. Byrne, G. D. and Hindmarsh, A. C. 1975. A polyalgorithm for the numerical solution of ordinary differential equations. ACM Trans. Math. Software, 1(1): 71-96.
15. Brown, P. N., Byrne, G. D. and Hindmarsh, A. C. 1989. VODE: A variable coefficient ODE solver. SIAM J. Sci. Statist. Comput., 10(5): 1038-1051.
16. Byrne, G. D. and Dean, A. M. 1993. The numerical solution of some kinetics models with VODE and CHEMKIN II. Comput. Chem., 17(3): 297-302.
17. Hochbruck, M. and Ostermann, A. 2010. Exponential integrators. Acta Numerica, 19: 209-286.
18. Tokman, M. 2006. Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods. J. Comput. Phys., 213(2): 748-776.
19. Saad, Y. 1992. Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM J. Num. Anal., 29(1): 209-228.
20. Hochbruck, M. and Lubich, C. 1997. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Num. Anal., 34: 1911-1925.
21. Kosloff, R. 1994. Propagation methods for quantum molecular dynamics. Ann. Rev. Phys. Chem., 45(1): 145-178.
22. Edwards, W. S., Tuckerman, L. S., Friesner, R. A. and Sorensen, D. C. 1994. Krylov methods for the incompressible Navier-Stokes equations. J. Comput. Phys., 110(1): 82-102.
23. Friesner, R. A., Tuckerman, L. S., Dornblaser, B. C. and Russo, T. V. 1989. A method for exponential propagation of large systems of stiff nonlinear differential equations. J. Sci. Comput., 4(4): 327-354.
24. Ratowsky, R. P. and Fleck, J. A. Jr. 1991. Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction. Opt. Lett., 16(11): 787-789.
25. Tokman, M. and Bellan, P. M. 2002. Three-dimensional model of the structure and evolution of coronal mass ejections. Astrophys. J., 567: 1202-1210.
26. Schiesser, W. E. 1991. The Numerical Method of Lines: Integration of Partial Differential Equations, San Diego: Academic Press.
27. Hochbruck, M., Lubich, C. and Selhofer, H. 1998. Exponential integrators for large systems of differential equations. J. Sci. Comput., 19(5): 1552-1574.
28. 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, Z. 1999. http://www.me.berkeley.edu/gri_mech
29. Mueller, M. A., Kim, T. J., Yetter, R. A. and Dryer, F. L. 1999. Flow reactor studies and kinetic modeling of the H2/O2 reaction. Int. J. Chem. Kinet., 31(2): 113-125.
30. Marinov, N. M. 1999. A detailed chemical kinetic model for high temperature ethanol oxidation. Int. J. Chem. Kinet., 31(3): 183-220.
31. Kaiser, E. W., Wallington, T. J., Hurley, M. D., Platz, J., Curran, H. J., Pitz, W. J. and Westbrook, C. K. 2000. Experimental and modeling study of premixed atmospheric-pressure dimethyl ether-air flames. J. Phys. Chem. A, 104(35): 8194-8206.
32. Glaude, P. A., Pitz, W. J. and Thomson, M. J. 2005. Chemical kinetic modeling of dimethyl carbonate in an opposed-flow diffusion flame. Proc. Combust. Inst., 30(1): 1111-1118.
33. Marinov, N. M., Pitz, W. J., Westbrook, C. K., Vincitore, A. M., Castaldi, M. J., Senkan, S. M. and Melius, C. F. 1998. Aromatic and polycyclic aromatic hydrocarbon formation in a laminar premixed n-butane flame. Combust. Flame, 114(1-2): 192-213.
34. Pitz, W. J., Naik, C. V., Mhaolduin, T. N., Westbrook, C. K., Curran, H. J., Orme, J. P. and Simmie, J. M. 2007. Modeling and experimental investigation of methylcyclohexane ignition in a rapid compression machine. Proc. Combust. Inst., 31(1): 267-275.
35. The Mathworks, Inc.,2010. MATLAB® version 7.9.0. Natick, Massachusetts.
36. Kee, R. J., Rupley, F. M. and Miller, J. A. 1989. Chemkin II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics, Livermore, CA: Technical report, SAND-89-8009, Sandia National Laboratories.
37. Descombes, S. and Massot, M. 2004. Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: singular perturbation and order reduction. Numer. Math., 97: 6670-698.
38. Hochbruck, M. and Ostermann, A. 2005. Explicit exponential Runge-Kutta methods for semilinear parabolic problems. SIAM J. Num. Anal., 43(3): 1069-1090.
39. Sidje, R. B. 1998. Expokit. A software package for computing matrix exponentials. ACM Trans. Math. Software, 24: 130-156.
40. Trefethen, L. N. 1999. Computation of pseudospectra. Acta Numerica, 8: 247-295.
41. Moler, C. and Van Loan, C. 2003. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Rev., 45(1): 3-49.
42. Trefethen, L. N., Weideman, J.A. C. and Schmelzer, T. 2006. Talbot quadratures and rational approximations. BIT Numer. Math., 46: 653-670.
43. Gallopoulos, E. and Saad, Y. 1992. Efficient solution of parabolic equations by Krylov approximation methods. SIAM J. Sci. Statist. Comput., 13(5): 1236-1264.
44. Niesen, J. and Wright, W.M. 2011. A Krylov subspace algorithm for evaluating the φ-functions appearing in exponential integrators, ACM Trans. Math. Software. Available at http://arxiv.org/abs/0907.4631.
45. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. and Sorensen, D. 1999. LAPACK Users' Guide, third edition, Philadelphia, PA: Society for Industrial and Applied Mathematics.
46. Higham, N. J. 2009. The scaling and squaring method for the matrix exponential revisited. SIAM Rev., 51: 747-764.
47. Horn, R. A. and Johnson, C. R. 1994. Topics in Matrix Analysis, Cambridge: Cambridge University Press.
48. Lam, S. H. 1985. "Singular perturbation for stiff equations using numerical methods". In Recent Advances in the Aerospace Sciences, Edited by: Casci, C. 3-20. New York: Plenum Press.
49. Henrici, P. 1962. Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices. Numer. Math., 4: 24-40.
50. Golub, G. H. and van Loan, C.F. 1996. Matrix Computations, Baltimore: Johns Hopkins University Press.
51. Lu, T., Yoo, C. S., Chen, J. H. and Law, C. K. 2008. "Analysis of a turbulent lifted hydrogen/air jet flame from direct numerical simulation with computational singular perturbation". In 46th AIAA Aerospace Sciences Meeting and Exhibit, Paper AIAA-2008-1013.
52. Krogh, F. T. 1973. On testing a subroutine for the numerical integration of ordinary differential equations. J. Assoc. Comput. Mach., 20(4): 545-562.
53. Fehlberg, E. 1969. Klassische Runge-Kutta-Formeln fünfter und siebenter Ordnung mit Schrittweiten-Kontrolle. Computing, 4(2): 93-106.
54. Hairer, E., Nørsett, S. P. and Wanner, G. 2010. Solving Ordinary Differential Equations I: Nonstiff Problems, Berlin: Springer.
55. Byrne, G.D. and Thompson, S. VODE_F90 support page, http://www.radford.edu/thompson/vodef90web/, December 2005 release.
56. Gustafsson, K. 1994. Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods. ACM Trans. Math. Software, 20(4): 496-517.