Skip to main content

A directionally adaptive finite element method for hypersonic thermo-chemical nonequilibrium flows

  • Applications
  • Conference paper
  • First Online:
Fifteenth International Conference on Numerical Methods in Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 490))

Abstract

A segregated, implicit FEM has been described for 2-D hypersonic thermo-chemical nonequilibrium flows on directionally-adapted structured grids. The flow solver is coupled with an adaptive procedure which is based on an edge-based error estimate and an improved mesh movement strategy with no orthogonality constraints. The segregated approach has the advantage of reducing reacting flow problems with a high number of species to a manageable level and offers the possibility of applying the most appropriate numerical scheme for each system of PDEs in order to achieve the best global convergence. The resulting code is first validated on hypersonic, partially-dissociated nitrogen flow where the shock position is correctly reproduced on a coarse mesh. The methodology is also tested for hypersonic air flows and their main features are well predicted on coarse grids. Future work will involve the study of the multi-temperature model and the introduction of the iterative GMRES solver.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Peraire, M. Vahdati, K. Morgan and O. C. Zienkiewicz. J. Comp. Phys., 72:449–466 (1987).

    Article  MATH  ADS  Google Scholar 

  2. M. Fortin, M.-G. Vallet, D. Poirier and W. G. Habashi. AIAA Paper 94-2221 (1994).

    Google Scholar 

  3. D. Ait-Ali-Yahia, W. G. Habashi, A. Tam, M.-G. Vallet and M. Fortin. Int. J. Num. Meth. Fluids, (1996) (in press).

    Google Scholar 

  4. S. Eberhardt and K. Brown, AIAA Paper, 86-0231 (1986).

    Google Scholar 

  5. M. M. Glaz, P. Colella, J. P. Collins and R. E. Ferguson. AIAA Journal, 26:698–705 (1988).

    Article  ADS  Google Scholar 

  6. T. R. A. Bussing and E. M. Murman. AIAA Paper, 85-0331 (1985).

    Google Scholar 

  7. C. Park and S. Yoon. Journal of Spacecraft, 28(1):31–39 (1991).

    Article  ADS  Google Scholar 

  8. R. W. Walters, P. Cinnella, D. C. Slack and D. Halt. AIAA Journal, 30(5):1304–1313 (1992).

    Article  MATH  ADS  Google Scholar 

  9. C. Park, J. Thermo. Heat. Trans., 3(13):233–244 (1989).

    Article  ADS  Google Scholar 

  10. D. Ait-Ali-Yahia, W. G. Habashi et al. Advances in Finite Element Analysis in Fluid Dynamics, Vol. 200, 11–19 (1994).

    Google Scholar 

  11. G. S. Baruzzi, Ph.D. Thesis, Concordia University, Montreal (1995).

    Google Scholar 

  12. R. Löhner, K. Morgan et al. Accuracy Estimates and Adaptive Refinements in Finite Element Computation (1986).

    Google Scholar 

  13. J. T. Oden, T. Strouboulis and Ph. Devloo, Int. J. Num. Meth. Fluids, 7:1211–1228 (1987).

    Article  Google Scholar 

  14. K. Nakahashi and G. S. Deiwert. AIAA Journal, 25(4):513–520 (1987).

    Article  ADS  Google Scholar 

  15. H. G. Hornung. J. of Fluid Mech., 53(1):149–176 (1972).

    Article  MATH  ADS  Google Scholar 

  16. G. V. Candler. AIAA Paper 89-0312 (1989).

    Google Scholar 

  17. R. Abgrall, J.-A. Désidéri, R. Glowinski, M. Mallet and J. Périaux. eds., Hypersonic Flows for Reentry Problems (1991).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Paul Kutler Jolen Flores Jean-Jacques Chattot

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag

About this paper

Cite this paper

Ait-Ali-Yahia, D., Habashi, W.G. (1997). A directionally adaptive finite element method for hypersonic thermo-chemical nonequilibrium flows. In: Kutler, P., Flores, J., Chattot, JJ. (eds) Fifteenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107112

Download citation

  • DOI: https://doi.org/10.1007/BFb0107112

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63054-8

  • Online ISBN: 978-3-540-69120-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics