Solution of Laminar Combusting Flows Using a Parallel Implicit Adaptive Mesh Refinement Algorithm

  • Scott A. Northrup
  • Clinton P.T. Groth
Conference paper


Numerical methods have become an essential tool for investigating combustion processes. In spite of the advances in solution algorithms and computer hardware, the solution of combusting flows can still place severe demands on available computational resources. In the previous work, Northrup and Groth [1] and Gao and Groth [2] have developed a parallel adaptive mesh refinement (AMR) algorithm that both reduces the overall problem size and the time to calculate a solution for non-premixed laminar and turbulent combusting flows. A preconditioned nonlinear multigrid algorithm with multi-stage semi-implicit time marching scheme as a smoother was used to integrate the governing partial differential equations. Although accurate solutions were obtained, for viscous reacting flows, the approach is non-optimal and in many cases a large number of multigrid cycles and solution residual evaluations were required to obtain steady state solutions.


Parallel Implementation GMRES Method Inexact Newton Method GMRES Algorithm Schwarz Precondition 
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  1. 1.
    Northrup, S. A. and Groth, C. P. T., Paper 2005–0547, AIAA, January 2005.Google Scholar
  2. 2.
    Gao, X. and Groth, C. P. T., Paper 2006-1448, AIAA, January 2006.Google Scholar
  3. 3.
    Groth, C. P. T. and Northrup, S. A., Paper 2005-5333, AIAA, June 2005.Google Scholar
  4. 4.
    Gordon, S. and McBride, B. J., Reference Publication 1311, NASA, 1994.Google Scholar
  5. 5.
    Wilke, C. R., J. Chem. Phys., Vol. 18, 1950, pp. 517–519.CrossRefGoogle Scholar
  6. 6.
    Dixon-Lewis, G., Combustion Chemistry, edited by W. C. Gardiner, Springer-Verlag, New York, 1984, pp. 21–126.Google Scholar
  7. 7.
    Westbrook, C. K. and Dryer, F. L., Combust. Sci. Tech., Vol. 27, 1981, pp. 31.CrossRefGoogle Scholar
  8. 8.
    Weiss, J. M. and Smith, W. A., AIAA J., Vol. 33, No. 11, 1995, pp. 2050–2057.CrossRefGoogle Scholar
  9. 9.
    Barth, T. J., Paper 93-0668, AIAA, January 1993.Google Scholar
  10. 10.
    Roe, P. L., J. Comput. Phys., Vol. 43, 1981, pp. 357–372.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Coirier, W. J. and Powell, K. G., AIAA J., Vol. 34, No. 5, May 1996, pp. 938.CrossRefGoogle Scholar
  12. 12.
    Sachdev, J. S., Groth, C. P. T., and Gottlieb, J. J., Int. J. Comput. Fluid Dyn., Vol. 19, No. 2, 2005, pp. 157–175.CrossRefGoogle Scholar
  13. 13.
    Saad, Y., Iterative Methods for Sparse Linear Systems, PWS, Boston, 1996.zbMATHGoogle Scholar
  14. 14.
    Dembo, R. S., Eisenstat, S. C., and Steihaug, T., SIAM J. Numer. Anal., Vol. 19, No. 2, 1982, pp. 400–408.MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gropp, W. D., Kaushik, D. K., Keyes, D. E., and Smith, B. F., Parallel Computing, Vol. 27, 2001, pp. 337–362.CrossRefGoogle Scholar
  16. 16.
    Knoll, D. A. and Keyes, D. E., J. Comput. Phys., Vol. 193, 2004, pp. 357–397.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Mulder, W. A. and van Leer, B., J. Comput. Phys., Vol. 59, 1985, pp. 232–246.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Aftosmis, M. J., Berger, M. J., Murman, S. M., Paper 2004-1232, AIAA, 2004.Google Scholar
  19. 19.
    Mohammed, R. K., Tanoff, M. A., Smooke, M. D., A. M. Schaffer, A. M., and Long, M. B., 27th Symposium on Combustion, Combustion Institute, Pittsburgh, 1998, pp. 693–702.Google Scholar
  20. 20.
    Day, M. S. and Bell, J. B., Combust. Theory Modelling, Vol. 4, No. 4, 2000, pp. 535–556.CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.University of Toronto Institute for Aerospace StudiesTorontoCanada

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