99
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Bunsen flame simulation by finite elements on adaptively refined, unstructured triangulations

, &
Pages 65-84 | Received 18 Feb 2003, Published online: 16 Aug 2006

References

  • Smooke , M D . 1982 . Solution of burner-stabilized premixed laminar flames by boundary value methods . J. Comput. Phys. , 48 : 72 – 105 .
  • Giovangigli , V and Smooke , M D . 1989 . Adaptive continuation algorithms with application to combustion problems . Appl. Numer. Math. , 5 : 305 – 31 .
  • Coelho P , J and Pereira , J C F . 1993 . Calculation of a confined axisymmetric laminar diffusion flame using a local grid refinement technique . Combust. Sci. Technol. , 92 : 243 – 64 .
  • de Lange , H C and de Goey , L P H . 1994 . Numerical modelling in a locally refined grid . Int. J. Numer. Mech. Eng. , 37 : 497 – 515 .
  • Mallens , R M M , de Lange , H C , van de Ven , C H J and de Goey , L P H . 1995 . Modeling of confined and unconfined laminar premixed flames on slit and tube burners . Combust. Sci. Technol. , 107 : 387 – 401 .
  • Somers L , T and de Goey , L P H . 1995 . A numerical study of a premixed flame on a slit burner . Combust. Sci. Technol. , 108 : 121 – 32 .
  • Bennett B A , V and Smooke , M D . 1998 . Local rectangular refinement with application to axisymmetric laminar flames . Combust. Theory Modelling , 2 : 221 – 58 .
  • Day M , S and Bell , J B . 2000 . Numerical simulation of laminar reacting flows with complex chemistry . Combust. Theory Modelling , 4 : 535 – 56 .
  • 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 .
  • Becker , R and Rannacher , R . 2001 . “ An optimal control approach to a posteriori error estimation in finite element methods ” . In Acta Numerica , Edited by: Iserles , A . Cambridge : Cambridge University Press .
  • Braack , M . 1998 . “ An adaptive finite element method for reactive flow problems ” . In PhD Dissertation , Heidelberg University .
  • Becker , R , Braack , M and Rannacher , R . 1999 . Numerical simulation of laminar flames at low Mach number by adaptive finite elements . Combust. Theory Modelling , 3 : 503 – 34 .
  • Burman , E , Ern , A and Giovangigli , V . 2003 . Adaptive finite element methods for low Mach, steady, laminar combustion . J. Comput. Phys. , 188 : 472 – 92 .
  • Williams , F A . 1985 . Combustion Theory , Reading, MA : Addison-Welsey . 2nd edn
  • Giovangigli , V . 1999 . Multicomponent Flow Modeling , Boston, MA : Birkhäuser .
  • Giovangigli , V and Darabiha , N . 1988 . “ Vector computers and complex chemistry combustion Proc. Conf. Mathematical Modeling in Combustion and Related Topics ” . In NATO Adv. Sci. Inst. Ser. E Edited by: Brauner , C and Schmidt-Lainé , C . Vol. 140 , 491 – 503 .
  • Miller , J , Mitchell , R , Smooke , M and Kee , R J . 1982 . Toward a comprehensive chemical kinetic mechanism for the oxidation of acetylene: comparison of model predictions with results from flame and shock tube experiments . Proc. Combust. Inst. , 19 : 181 – 96 .
  • Ern , A and Giovangigli , V . 1998 . Thermal diffusion effects in hydrogen-air and methane-air flames . Combust. Theory Modelling , 2 : 349 – 72 .
  • Ern , A and Giovangigli , V . 1999 . Impact of detailed multicomponent transport on planar and counterflow hydrogen/air and methane/air flames . Combust. Sci. Technol. , 149 : 157 – 81 .
  • de Charentenay , J and Ern , A . 2002 . Multicomponent transport impact on turbulent premixed H2/O2 flames . Combust. Theory Modelling , 6 : 439 – 62 .
  • Ern , A and Giovangigli , V . 1994 . Multicomponent Transport Algorithms , New Series Monographs vol M 24 , Heidelberg : Springer . Lecture Notes in Physics
  • Ern , A and Giovangigli , V . 1996 . Eglib server with user's manual . http://www.cmap.polytechnique.fr/www.eglib
  • Brooks , A N and Hughes , T J R . 1982 . Streamline upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations . Comput. Methods Appl. Mech. Eng. , 32 : 199 – 259 .
  • Johnson , C , Nävert , U and Pitkäranta , J . 1984 . Finite element methods for linear hyperbolic equations . Comput. Methods Appl. Mech. Eng. , 45 : 285 – 312 .
  • Johnson , C . 1987 . Numerical Solution of Partial Differential Equations by the Finite Element Method , Cambridge : Cambridge University Press .
  • Franca , L P and Frey , S L . 1992 . Stabilized finite element methods: II. The incompressible Navier-Stokes equations . Comput. Methods Appl. Mech. Eng. , 99 : 209 – 33 .
  • 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 .
  • Johnson , C , Schatz , A and Wahlbin , L . 1987 . Crosswind smear and pointwise error in streamline diffusion finite element methods . Math. Comput. , 49 : 25 – 38 .
  • Zienkewicz , O C and Zhu , J Z . 1987 . A simple error estimator and adaptive procedure for practical engineering analysis . Int. J. Numer. Methods Eng. , 24 : 337 – 57 .
  • Burman , E and Hansbo , P . 2003 . Edge stabilization for Galerkin approximations of convection-diffusion-reaction problems . Comput. Methods Appl. Mech. Eng. , at press
  • Rebay , S . 1993 . Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm . J. Comput. Phys. , 106 : 125 – 38 .
  • Clavin , P and Williams , F . 1982 . Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity . J. Fluid Mech. , 116 : 251 – 82 .
  • Burman , E and Ern , A . 2003 . “ Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence ” . In Math. Comput , Switzerland : EPFL . submitted Internal Report 02.2003
  • Burman , E and Hansbo , P . 2003 . Edge stabilization for the generalized Stokes problem: a continuous interior-penalty method . Math. Mod. Numer. Anal. , submitted

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.