Computational Mechanics

, Volume 11, Issue 5–6, pp 433–451 | Cite as

Finite element multigrid solution of Euler flows past installed aero-engines

  • J. Peraire
  • J. Peiró
  • K. Morgan
Article

Abstract

A finite element based procedure for the solution of the compressible Euler equations on unstructured tetrahedral grids is described. The spatial discretisation is accomplished by means of an approximate variational formulatin, with the explicit addition of a matrix form of artificial viscosity. The solution is advanced in time by means of an explicit multi-stage time stepping procedure. The method is implemented in terms of an edge based representation for the tetrahedral grid. The solution procedure is accelerated by use of a fully unstructured multigrid algorithm. The approach is applied to the simulation of the flow past an installed aero-engine nacelle, at three different free stream conditions. Comparison is made between the numerical predictions and experimental pressure observations.

Keywords

Matrix Form Euler Equation Base Representation Solution Procedure Free Stream 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. Baker, T. J. (1990): Unstructured mesh generation by a generalised Delaunay algorithm. In: AGARD Conference Proceedings No. 464, Applications of Mesh Generation to Complex 3-D Configurations. AGARD, Neuilly Sur Seine. 20.1–20.10Google Scholar
  2. Barth, T. J.; Jespersen, D. C. (1989): The design and application of upwind schemes on unstructured meshes. AIAA Paper 89-0366Google Scholar
  3. Barth, T. J. (1991): Numerical aspects of computing viscous high Reynolds number flows on unstructured meshes. AIAA Paper 91-0721Google Scholar
  4. Bonet, J.; Peraire, J. (1991): An alternate digital tree algorithm for geometric searching and intersection problems. Int. J. Num. Meth. Engng. 31, 1–17Google Scholar
  5. Formaggia, L.; Peraire, J.; Morgan, K.; Peiró, J. (1988): Implementation of a 3D explicit Euler solver on a CRAY computer. In: Proceedings of the 4th International Symposium on Science and Engineering on CRAY Supercomputers. Minneapolis, 45–65Google Scholar
  6. Giles, M. (1987): Energy stability analysis of multi-step methods on unstructured meshes. MIT CFD Laboratory report CFDL-TR-87-1. Cambridge, MassachusettsGoogle Scholar
  7. Jameson, A.; Schmidt, W.; Turkel, E. (1981): Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping. AIAA paper 81-1259Google Scholar
  8. Jameson, A. (1984): Transonic flow calculations. Princeton University Report MAE 1751Google Scholar
  9. Jameson, A.; Baker, T. J.; Weatherill, N. P. (1986): Calculation of inviscid transonic flow over a complete aircraft. AIAA paper 86-0103Google Scholar
  10. Leclercq, M.-P.; Periaux, J.; Stoufflet, B. (1989): Multigrid methods with unstructured meshes. In: Proceedings of the 7th International Conference on Finite Elements in Flow Problems. Huntsville, Alabama. 1113–1118Google Scholar
  11. Löhner, R.; Morgan, K. (1987): Unstructured multigrid methods for elliptic problems. Int. J. Num. Meth. Engng. 24, 101–115Google Scholar
  12. Mavriplis, D. J. (1988): Multigrid solution of the two dimensional Euler equations on unstructured triangular meshes. AIAA J. 26, 824–831Google Scholar
  13. Mavriplis, D. J. (1991): Three dimensional unstructured multigrid for the Euler equations. AIAA Paper 91-1549Google Scholar
  14. Morgan, K.; Peraire, J.; Peiró, J. (1992): Unstructured grid methods for compressible flows. In: AGARD Report No. 787, Special Course on Unstructured Grid Methods for Advection Dominated Flows. AGARD, Neuilly Sur Seine. 5.1–5.39Google Scholar
  15. Numerical Aerodynamic Simulation Program Technical Summaries (1992): March 1990–February 1991, NASA Ames Research CenterGoogle Scholar
  16. Peraire, J.; Morgan, K.; Peiró, J.; Zienkiewicz, O. C. (1987): An adaptive finite element method for high speed flows. AIAA paper 87-0558Google Scholar
  17. Peraire, J.; Morgan, K.; Peiró, J. (1990): Unstructured finite element mesh generation and adaptive procedures for CFD. In: AGARD Conference Proceedings No. 464, Applications of Mesh Generation to Complex 3D Configurations. AGARD, Neuilly Sur Seine. 18.1–18.12Google Scholar
  18. Peraire, J.; Morgan, K.; Vahdati, M.; Peiró, J. (1992): The construction and behaviour of some unstructured grid algorithms for compressible flows. In: Baines, M. J.; Morton, K. W. (ed): Proceedings of the ICFD Conference on Numerical Methods for Fluid Dynamics. Oxford University Press (to appear)Google Scholar
  19. Peraire, J.; Morgan, K.; Peiró, J. (1992): A finite element multigrid solver for the Euler equations. AIAA paper 92-0449Google Scholar
  20. Perez, E. (1985): Finite element and multigrid solution of the two dimensional Euler equations on a non-structured mesh. INRIA report no. 442, INRIA, ParisGoogle Scholar
  21. Pugh, G.; Harris, A. (1981): Establishment of an experimental technique to provide accurate measurement of the installed drag of close-coupled civil nacelle/airframe configurations using a full span model with turbine powered engine simulators. AGARD Conference Proceedings No. 301. AGARD, Neuilly Sur SeineGoogle Scholar
  22. Roe, P. (1981): Approximate Riemann solvers, parameter vectors and difference schemes. J Comput. Phys. 43, 357–372Google Scholar
  23. Smith, R. E. (ed) (1992): Software Systems for Surface Modeling and Grid Generation, NASA Conference Publication 3143Google Scholar
  24. Swanson, R. C.; Turkel, E. (1990): On central difference and upwind schemes. ICASE Report No. 90-44. NASA Langley Research CenterGoogle Scholar
  25. Zienkiewicz, O. C.; Morgan, K. (1983): Finite elements and approximation. New York: WileyGoogle Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • J. Peraire
    • 1
  • J. Peiró
    • 1
  • K. Morgan
    • 2
  1. 1.Department of AeronauticsImperial CollegeLondonUK
  2. 2.Department of Civil EngineeringUniversity CollegeSwanseaUK

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