Efficient calculation of intrinsic low-dimensional manifolds for the simplification of chemical kinetics

Computing and Visualization in Science

Volumn 1, Issue 2, 1998, Pages 69-81

  Maas, Ulrich ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

KINETICS;

CHEMICAL REACTION SYSTEMS; CONTINUATION PROCESS; FLOW CONFIGURATIONS; INTRINSIC LOW-DIMENSIONAL MANIFOLDS; LOW-DIMENSIONAL MANIFOLDS; MOLECULAR TRANSPORT; ONE-DIMENSIONAL SYSTEMS; TWO-DIMENSIONAL SYSTEMS;

REACTION KINETICS;

EID: 0001944880     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s007910050007     Document Type: Article

References (38)

1. J. Warnatz. Resolution of gas phase and surface chemistry into elementary reactions. 24th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1992.
2. J. Warnatz, U. Maas, R. W. Dibble. Combustion. Springer-Verlag Berlin Heidelberg New York, 1996.
3. G. Dixon-Lewis, T. Davis, P. H. Gaskell, S. Fukutani, H. Jinno, J. A. Miller, R. J. Kee, M. D. Smooke, N. Peters, E. Effelsberg, J. Warnatz, F. Behrendt. Calculation of the Structure and Extinction Limit of a Methane-Air Counterflow Diffusion Flame in the Forward Stagnation Region of a Porous Cylinder. 20th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1985, p. 1893.
4. J. Warnatz, U. Maas. Calculation of the detailed structure of premixed and non-premixed flame fronts and some applications. In W. F. Ames, editor, IMACS Transactions on Scientific Computing '88, Numerical and Applied Mathematics. J. C. Baltzer AG, Scientific Publishing Co., p. 151, 1989.
5. M. D. Smooke, R. E. Mitchell, D. E. Keyes. Numerical solution of two-dimensional axisymmetric laminar diffusion flames. Comb. Sci. Technol., 67:85, 1989.
6. S. B. Pope. Computations of Turbulent Combustion: Progress and Challenges. 23rd Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1990, p. 591.
7. P. A. Libby, F. A. Williams (eds.). Turbulent Reactive Flows. Springer, New York, 1980.
8. C. Chevalier. Entwicklung eines detaillierten Reaktionsmechanismus zur Modellierung der Verbrennungsprozesse von Kohlenwasserstoffen bei Hoch- und Niedertemperaturbedingungen. PhD thesis, Institut für Technische Verbrennung, Universität Stuttgart, 1993.
9. N. Peters, B. Rogg. Reduced Kinetic Mechanisms for Applications in Combustion Systems. Springer, Berlin, 1993.
10. M. D. Smooke (ed.). Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames. Lecture Notes in Physics 384, Springer, Berlin, Heidelberg, New York, 1991.
11. R. Law, M. Metghalchi, J. C. Keck. Rate-controlled constraint equilibrium calculations of ignition delay times in hydrogen-oxygen mixtures. 22nd Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1988, p. 1705
12. T. Turanyi. Parameterization of reaction mechanisms using orthonormal polynomials. Computers Chem., 18:45-54, 1994.
13. S. H. Lam, D. A. Goussis. Understanding Complex Chemical Kinetics with Computational Singular Perturbation. 22nd Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1988, p. 931.
14. S. H. Lam. Using CSP for complex chemical kinetics. Technical report, Princeton University, USA. Technical Report 1941-MAE, 1992.
15. U. Maas, S. B. Pope. Simplifying chemical kinetics: Intrinsic low- dimensional manifolds in composition space. Combustion and Flame, 88:239-264, 1992.
16. U. Maas, S. B. Pope. Implementation of Simplified Chemical Kinetics Based on Intrinsic Low-Dimensional Manifolds. 24th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1992, p. 101.
17. P. Deuflhard, J. Heroth. Dynamic dimension reduction in ODE models. In F. Keil, W. Mackens, Voß, J. Werther (1996): Scientific Computing in Chemical Engineering, editors, Scientific Computing in Chemical Engineering, pages 29-43. Springer, 1996.
18. P. Deuflhard, J. Heroth, U. Maas. Towards dynamic dimension reduction in reactive flow problems. In J. Warnatz, F. Behrendt, editors, Modelling of Chemical Reaction Systems, Proceedings of an International Workshop, Heidelberg, Germany, July 24 - 26, 1996. Springer, 1996. ISBN 3-932217-00-4.
19. A. S. Tomlin, T. Turanyi, M. J. Pilling. Mathematical tools for the construction, investigation and reduction of combustion mechanisms. In M. J. Pilling, editor, Oxidation Kinetics and Autoignition of Hydrocarbons. Elsevier, in press.
20. U. Maas. Coupling of chemical reaction with flow and molecular transport. Applications of Mathematics, 3:249-266, 1995.
21. U. Maas. Automatische Reduktion von Reaktionsmechanismen zur Simulation reaktiver Strömungen. Habilitation thesis, Institut für Technische Verbrennung, Universität Stuttgart, 1993.
22. U. Maas, S. B. Pope. Laminar Flame Calculations using Simplified Chemical Kinetics Based on Intrinsic Low-Dimensional Manifolds. 25th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1994, p. 1349.
23. H. Niemann, D. Schmidt, U. Maas. An efficient storage scheme for reduced chemical kinetics based on orthogonal polynomials. Journal of Engineering Mathematics, 31:131-142, 1997. (Pubitemid 127506174)
24. D. Schmidt, U. Maas. Analysis of the intrinsic low-dimensional manifolds of strained and unstrained flames. In J. Warnatz, F. Behrendt, editors, Modelling of Chemical Reaction Systems, Proceedings of an International Workshop, Heidelberg, Germany, July 24 - 26, 1996. Springer, 1996. ISBN 3-932217-00-4.
25. R. Seydel. From Equilibrium to Chaos, Practical Bifurcation and Stability Analysis. Elsevier, New York, Amsterdam, London, 1988.
26. E. L. Allgower, K. Georg. Numerical Continuation Methods, volume 13 of Springer Series in Computational Mathematics. Springer, 1990.
27. W. C. Rheinboldt. On the computation of multi-dimensional solution manifolds of parametrized equations. Numerical Mathematics, 53:165- 181, 1988.
28. G. H. Golub, C. F. van Loan. Matrix Computations. The Hopkins University Press, Baltimore, London, 1989.
29. SIAM, Philadelphia. LAPACK User's Guide, 1992.
30. W. C. Rheinboldt, J. V. Burkardt. A locally parametrized continuation process. ACM Trans. Math. Soft., 9:236-246, 1983.
31. P. Deuflhard, B. Fiedler, P. Kunkel. Efficient numerical pathfollowing beyond critical points. SIAM Journal on Numerical Analysis, 24:912- 927, 1987. (Pubitemid 17637143)
32. F. L. Bauer, H. Rutishauser, E. Stiefel. New aspects in numerical quadrature. In Proc. Symp. Appl. Math. AMS 15, pages 199-218, 1963.
33. R. Bulirsch, J. Stoer. Fehlerabschätzungen und Extrapolation. Numer. Math., 6:413-427, 1964.
34. P. Deuflhard. Order and stepsize control in extrapolation methods. Numerical Mathematics, 41:399-422, 1983.
35. P. Deuflhard. A relaxation strategy for the modified newton method. In: Burlisch, Oettliand Stoer, editors, Optimization and Optimal Control. Springer Lecture Notes 477, 1975.
36. U. Nowak, L. Weimann. A family of newton codes for systems of highly nonlinear equations-algorithm, implementation, application. Technical report, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Technical Report TR90-10, 1990.
37. T. Blasenbrey, D. Schmidt, U. Maas. Intrinsic low-dimensional manifolds of strained und unstrained flames. In Proc. 16th International Colloquium on the Dynamics of Explosions and Reactive Systems, Cracow, Poland, pages 329-332, 1997.
38. T. Blasenbrey, D. Schmidt, U. Maas. Publication in preparation, 1997.