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Computational Mechanics

, Volume 38, Issue 4–5, pp 469–481 | Cite as

Computation of Inviscid Supersonic Flows Around Cylinders and Spheres with the SUPG Formulation and YZβ Shock-Capturing

  • Tayfun E. Tezduyar
  • Masayoshi Senga
  • Darby Vicker
Original Paper

Abstract

Numerical experiments with inviscid supersonic flows around cylinders and spheres are carried out to evaluate the stabilization and shock-capturing parameters introduced recently for the Streamline–Upwind/Petrov–Galerkin (SUPG) formulation of compressible flows based on conservation variables. The tests with the cylinders are carried out for both structured and unstructured meshes. The new shock-capturing parameters, which we call “YZβ Shock-Capturing”, are compared to earlier SUPG parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for unstructured meshes with triangular and tetrahedral elements. Furthermore, the results obtained with YZβ Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code

Keywords

Supersonic flows Cylinders and spheres SUPG stabilization Stabilization parameter Shock-capturing parameter 

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References

  1. 1.
    Hughes TJR, Brooks AN (1979) A Multi-dimensional Upwind Scheme with no Crosswind Diffusion. In: Hughes TJR (eds). Finite element methods for convection dominated flows, AMD-vol 34. ASME, New York, pp 19–35Google Scholar
  2. 2.
    Brooks AN, Hughes TJR (1982) Streamline Upwind/Petrov–Galerkin Formulations for convection dominated flows with Particular emphasis on the incompressible Navier–Stokes Equations. Comput Methods Appl Mech Eng 32:199–259zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Tezduyar TE, Hughes TJR (1982) Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. NASA Technical Report NASA-CR-204772, NASA, Also available online: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa. gov/19970023187_1997034954.pdfGoogle Scholar
  4. 4.
    Tezduyar TE, Hughes TJR (1983) Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st aerospace sciences meeting, AIAA Paper 83-0125, Reno, NevadaGoogle Scholar
  5. 5.
    Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45:217–284zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hughes TJR, Franca LP, Mallet M (1987) A New Finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Comput Methods Appl Mech Eng 63:97–112zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Le Beau GJ, Tezduyar TE (1991) Finite element computation of compressible flows with the SUPG formulation. In: Advances in finite element analysis in fluid dynamics, FED-vol.123. ASME, New York, pp 21–27Google Scholar
  8. 8.
    Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104:397–422zbMATHCrossRefGoogle Scholar
  9. 9.
    Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59:307–325zbMATHCrossRefGoogle Scholar
  10. 10.
    Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 58:305–328zbMATHMathSciNetGoogle Scholar
  11. 11.
    Shakib F, Hughes TJR, Johan Z (1991) A new finite element formulation for computational fluid dynamics: X. The compressible euler and Navier–Stokes equations. Comput Methods Appl Mech Eng 89:141–219CrossRefMathSciNetGoogle Scholar
  12. 12.
    Tezduyar TE (2001) Adaptive determination of the finite element stabilization parameters. In: Proceedings of the ECCOMAS computational fluid dynamics conference, Swansea, Wales.Google Scholar
  13. 13.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, De Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, volume 3: Fluids, Chapter 17. Wiley, New YorkGoogle Scholar
  15. 15.
    Tezduyar TE (2004) Determination of the stabilization and shock-capturing parameters in SUPG formulation of compressible flows. In: Proceedings of the European Congress on computational methods in applied sciences and engineering, ECCOMAS 2004, Jyvaskyla, FinlandGoogle Scholar
  16. 16.
    Tezduyar TE, Senga M (2005) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng (in press)Google Scholar
  17. 17.
    Tezduyar TE, Senga M (2005) SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing. Comput Fluids (in press)Google Scholar
  18. 18.
    Buning PG, Jespersen DC, Pulliam TH, Klopfer GH, Chan WM, Slotnick JP, Krist SE, Renze KJ (2000) OVERFLOW user’s manual, Version 1.8s, NASA Langley Research Center, Hampton, VirginiaGoogle Scholar
  19. 19.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94:339–351zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces – the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94:353–371zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Aliabadi SK, Tezduyar TE (1995) Parallel fluid dynamics computations in aerospace applications.Int J Numer Methods Fluids 21:783–805zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Saad Y, Schultz M (1986) GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Verlag 2006

Authors and Affiliations

  • Tayfun E. Tezduyar
    • 1
  • Masayoshi Senga
    • 1
  • Darby Vicker
    • 2
  1. 1.Department of Mechanical EngineeringRice University – MS 321HoustonUSA
  2. 2.Applied Aeroscience and CFD Branch NASA Johnson Space CenterHoustonUSA

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