Numerical simulation of laminar flames at low Mach number by adaptive finite elements

Combustion Theory and Modelling

Volumn 3, Issue 3, 1999, Pages 503-534

  Becker, R ^a   Braack, M ^a   Rannacher, R ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; FLAME; MACH NUMBER; MATHEMATICAL MODELING;

EID: 0033197597     PISSN: 13647830     EISSN: None     Source Type: Journal    
DOI: 10.1088/1364-7830/3/3/305     Document Type: Article

References (31)

1. Ainsworth M and Oden J T 1997 A posteriori error estimation in finite element analysis Comput. Meth. Appl. Mech. Eng. 142 1-88
2. Baulch D L, Drysdale D D and Horne D G 1986 An assesment of rate data for high temperature systems 14th Symp. Combustion pp 107-18
3. Becker R and Braack M 1999 Comparision of multilevel algorithms on locally refined meshes, unpublished
4. Becker R and Rannacher R 1996 A feed-back approach to error control in finite element methods: basic analysis and examples East-West J. Numer. Math. 4 237-64
5. Bennett B A V and Smooke M D 1998 Local rectangular refinement with application to axisymmetric laminar flames Combustion Theory Modelling 2 221-58
6. Braack M 1998 An adaptive finite element method for reactive flow problems Dissertation Heidelberg University
7. Braack M and Rannacher R 1999 Adaptive Finite Element Methods for Low-Mach-Number Flows with Chemical Reactions 30th Computational Fluid Dynamics (Lecture Series Monographs) ed H Deconinck (Belgium: von Karman Institute)
8. Ciarlet P G 1978 The Finite Element Methods for Elliptic Problems (Amsterdam: North-Holland)
9. de Lange H C and de Goey L P H 1994 Numerical flow modelling in a locally refined grid Int. J. Numer. Meth. Eng. 37 497-515
10. Franca L and Frey S 1992 Stabilized finite element methods: II The incompressible Navier-Stokes equations Comput. Meth. Appl. Mech. Eng. 99 209-33
11. Girault V and Raviart P-A 1986 Finite Elements for Navier Stokes Equations (Berlin: Springer)
12. Hackbusch W 1985 Multi-Grid Methods and Applications (Berlin: Springer)
13. Hughes T J R, Franca L P and Balestra M 1986 A new finite element formulation for computational fluid dynamics: V. Circumvent the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation for the Stokes problem accomodating equal order interpolation Comput. Meth. Appl. Mech. Eng. 59 89-99
14. Johnson C 1987 Numerical Solutions of Partial Differential Equations by the Finite Element Method (Cambridge: Cambridge University Press)
15. Eriksson P H K, Estep D and Johnson C 1995 Introduction to Adaptive Methods for Differential Equations (Acta Numerica vol 28) (Cambridge: Cambridge University Press) pp 105-58
16. Kee R, Rupley F and Miller J 1987 The Chemkin thermodynamic data base Sandia Report SAND87-8215.UC4
17. Kelley C T 1995 Iterative Methods for Linear and Nonlinear Equations (Philadelphia, PA: SIAM)
18. Klaus P 1997 Entwicklung eines detaillierten Reaktionsmechanismus zur Modellierung der Bildung von Stickoxiden in Flammenfronten Dissertation Heidelberg University
19. Majda A 1984 Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (New York: Springer)
20. Miller J A and Craig C T 1989 Prog. Energy Combust. Sci. 15 187
21. Rannacher R 1998 A posteriori error estimation in least-squares stabilized finite element schemes Comput. Meth. Appl. Mech. Eng. 166 99-114 (special issue on advances in stabilised methods in computational mechanics, ed L P Franca)
22. Saad Y 1996 Iterative Methods for Sparse Linear Systems (PWS)
23. Sandboge R 1996 Adaptive finite element methods for reactive flow problems Dissertation Chalmers University of Technology
24. Segatz J, Rannacher R, Wichmann J, Orlemann C, Dreier T and Wolfrum J 1996 Detailed numerical simulation in flow reactors: a new approach in measuring absolute rate constants J. Phys. Chem. 100 9323-33
25. Smooke M D 1991 Numerical Modeling of Laminar Diffusion Flames (Progress in Astronautics and Aeronautics vol 135)
26. Somers L M T and de Goey L P H 1995 A numerical study of a premixed flame on a slit burner Combust. Sci. Technol., Amsterdam 108 121-32
27. Suttmeier F-T 1997 Adaptive finite clement approximation of problems in elasto-plasticity theory Dissertation Heidelberg University
28. Tobiska L and Verfürth R 1996 Analysis of a streamline diffusion finite element method for the Stokes and Navier-Stokes equations SIAM J. Numer. Anal. 33 107-27
29. Warnatz J 1978 Calculation of the structure of laminar flat flames I: flame velocity of freely propagating ozone decomposition flames Ber. Bunsengemeinschaft. Phys. Chem. 82 193-200
30. Warnatz J, Maas U and Dibble R W 1996 Combustion (Berlin: Springer)
31. Wolfrum J 1998 Laser in combustion: from simple models to real devices Plenary Lecture, 27th Int. Symp. on Combustion (Pittsburgh, PA: Combustion Institute)