Skip to main content
SpringerLink
Log in

SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations

  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

In this article, we present our investigation and comparison of the SUPG-stabilized finite element formulations for computation of viscous compressible flows based on the conservation and entropy variables. This article is a sequel to the one on inviscid compressible flows by Le Beau et al. (1992). For the conservation variables formulation, we use the SUPG stabilization technique introduced in Aliabadi and Tezduyar (1992), which is a modified version of the one described in Le Beau et al. (1992). The formulation based on the entropy variables is same as the one introduced in Hughes et al. (1986).

The two formulations are tested on three different problems: adiabatic flat plate at Mach 2.5, Reynolds number 20,000; Mach 3 compression corner at Reynolds number 16,800; and Mach 6 NACA 0012 airfoil at Reynolds number 10,000. In all cases, we show that the results obtained with the two formulations are very close. This observation is the same as the one we had in Le Beau et al. (1992) for inviscid flows.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aliabadi, S. K.; Tezduyar, T. E. (1992): Space-time finite element computation of compressible flows involving moving boundaries and interfaces. University of Minnesota Supercomputer Institute Research Report 92/95, April 1992

  • Brooks, A. N.; Hughes, T. J. R. (1982): Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng. 32, 199–259

    Google Scholar 

  • Carter, J. E. (1972): Numerical solutions of the Navier-Stokes equations for the supersonic laminar flow over a two-dimensional compression corner. NASA Technical Report, NASA TR R-385

  • Donea, J. (1984): A Taylor-Galerkin method for convective transport problems. Int. J. Numer. Meth. Eng. 20, 101–120

    Google Scholar 

  • Hughes, T. J. R.; Brooks, A. N. (1979): A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes, T. J. R. (ed): Finite Element Methods for Convection Dominated Flows, AMD-Vol. 34, pp. 19–35. ASME, New York

    Google Scholar 

  • Hughes, T. J. R.; Tezduyar, T. E. (1984). Finite element methods for first-order hyperbolic systems with particular emphasis in the compressible Euler equations. Comput. Meth. Appl. Mech. & Eng. 45, 217–284

    Google Scholar 

  • Hughes, T. J. R.; Mallet, M.; Franca, L. P. (1986). New finite element methods for compressible Euler and Navier-Stokes equations. In: Glowinski, R.; Lions, J. (eds): Comput. Meth. Appl. Sci. & Eng., pp. 339–360. North Holland: Amsterdam

    Google Scholar 

  • Hung, C. M.; MacCormack, R. W. (1976): Numerical solutions of supersonic and hypersonic laminar compression corner problems. AIAA Journal 14, No. 4, 475–481

    Google Scholar 

  • Le Beau, G. J.; Ray, S. E.; Aliabadi, S. K.; Tezduyar, T. E. (1992): SUPG finite element computation of compressible flows with the conservation and entropy variables formulations. University of Minnesota Supercomputer Institute Research Report 92/26, March 1992

  • Le Beau, G. J.; Tezduyar, T. E. (1991): Finite element computation of compressible flows with the SUPG formulation. In: Dhaubhadel, M. N.; Engelman, M. S.; Reddy, J. N. (eds): Advances in Finite Element Analysis in Fluid Dynamics, FED-Vol. 123, pp. 21–27. ASME, New York

    Google Scholar 

  • Mallet, M. (1985): A finite element method for compressible fluid dynamics. Ph.D. Thesis, Department of Civil Engineering, Stanford University

  • Saad, Y. (1991): A flexible inner-outer preconditioned GMRES algorithm. University of Minnesota Supercomputer Institute Research Report 91/279, November 1991

  • Shakib, F. (1988): Finite element analysis of the compressible Euler and Navier-Stokes equations. Ph.D. Thesis, Department of Mechanical Engineering, Stanford University

  • Tezduyar, T. E.; Hughes, T. J. R. (1982). Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Report prepared under NASA-Ames University Consortium Interchange, No. NCA2-OR745-104

  • Tezduyar, T. E.; Hughes, T. J. R. (1983): Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. Proceedings of AIAA 21st Aerospace Sciences Meeting, Reno, Nevada, January 1983, AIAA Paper, 83-0125

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, Army High Performance Computing Research Center and Minnesota Supercomputer Institute, University of Minnesota, 1200 Washington Avenue South, 55415, Minneapolis, MN, USA

    S. K. Aliabadi, S. E. Ray & T. E. Tezduyar

Authors
  1. S. K. Aliabadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. E. Ray
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. E. Tezduyar
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by T. E. Tezduyar, June 1, 1992

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aliabadi, S.K., Ray, S.E. & Tezduyar, T.E. SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations. Computational Mechanics 11, 300–312 (1993). https://doi.org/10.1007/BF00350089

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00350089

Keywords

Search

Navigation