Skip to main content

A High-Order Discontinuous Galerkin CFD Solver for Turbulent Flows

  • Conference paper
  • First Online:
High Performance Computing in Science and Engineering ’15

Abstract

The Discontinuous Galerkin method is used for the discretisation of the Reynolds-Averaged-Navier-Stokes equations. It is a high-order method in space reducing the amount of cells for calculations compared to standard CFD solvers. We are planning to use the method for two different kind of flow types: highly separated flows and rotor flows. For the first, we implemented a Detached Eddy Simulation method. For rotor flows we started to implement a Chimera grid technique so that we are able to handle moving bodies.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Reed, W., Hill, T.: Triangular mesh methods for the neutron transport equation. Technical Report, Los Alamos Scientific Laboratory (1973)

    Google Scholar 

  2. Cockburn, B., Shu, C.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation law II: general framework. Math. Comput. 52(186), 411–435 (1989)

    MathSciNet  MATH  Google Scholar 

  3. Bassi, F., Rebay, S.: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J. Comput. Phys. 131, 267–279 (1997)

    Article  MathSciNet  Google Scholar 

  4. Bassi, F., Crivellini, A., Rebay, S., Savini, M.: Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and kω turbulence model equations. Comput. Fluids 34, 507–540 (2005)

    Article  Google Scholar 

  5. Lübon, C.: Turbulenzmodellierung und Detached Eddy Simulation mit einem Discontinuous Galerkin Verfahren von hoher Ordnung. PhD thesis, Universität Stuttgart (2009)

    Google Scholar 

  6. Benek, J., Steger, J., Dougherty, F.: A flexible grid embedding technique with application to the Euler equations. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics, July 1983

    Book  Google Scholar 

  7. Galbraith, M., Orkwis, P., Benek, J.: Extending the Discontinuous Galerkin scheme to the Chimera overset method. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics, June 2011

    Book  Google Scholar 

  8. Galbraith, M., Orkwis, P., Benek, J.: Discontinuous Galerkin scheme applied to Chimera overset viscous meshes on curved geometries. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics, June 2012

    Book  Google Scholar 

  9. Spalart, P., Allmaras, S.: A one-equation turbulence model for aerodynamic flows. La Recherche Aerospatiale 1, 5–21 (1994)

    Google Scholar 

  10. Spalart, P., Jou, W.H., Strelets, M., Allmaras, S.: Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Advances in DNS/LES (1997)

    Google Scholar 

  11. Spalart, P., Deck, S., Shur, M., Squires, K., Strelets, M., Travin, A.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20(3), 181–195 (2006)

    Article  Google Scholar 

  12. Bassi, F., Rebay, S., Mariotti, G., Pedinotti, S., Savini, M.: A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows. In: Decuypere, R.G.D. (ed.) 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Antwerpen, Belgium: Technologisch Instituut, pp. 99–108 (1997)

    Google Scholar 

  13. Wurst, M., Keßler, M., Krämer, E.: A high-order discontinuous Galerkin chimera method for laminar and turbulent flows. In: AIAA SciTech. American Institute of Aeronautics and Astronautics, Jan 2015

    MATH  Google Scholar 

  14. Glasby, R., Burgess, N., Anderson, W., Wang, L., Mavriplis, D., Allmaras, S.: Comparison of SU/PG and DG Finite-Element techniques for the compressible Navier-Stokes equations on anisotropic unstructured meshes. In: 51st AIAA Aerospace Sciences Meeting, AIAA 2013–0691 (2013)

    Google Scholar 

  15. Gregory, N., O’Reilly, C.: Low speed aerodynamic characteristics of NACA0012 aerofoil section, including the effects of upper surface roughness simulating hoar frost. Technical Report, Aeronautical Research Council (1970)

    Google Scholar 

  16. Wurst, M., Keßler, M., Krämer, E.: Aerodynamic and acoustic analysis of an extruded airfoil with a trailing edge device using detached eddy simulation with a discontinuous Galerkin method. In: Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics, June 2013

    Book  Google Scholar 

  17. Vogel, J., Eaton, J.: Combined heat transfer and fluid dynamic measurements downstreams of a backward facing step. J. Heat Transf. 107, 922–929 (1985)

    Article  Google Scholar 

  18. Busch, E., Wurst, M., Keßler, M., Kräämer, E.: Computational aeroacoustics with higher order methods. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds.) High Performance Computing in Science and Engineering ’12, pp. 239–253. Springer, Berlin (2013)

    Google Scholar 

  19. Heroux, M.A., Bartlett, R.A., Howle, V.E., Hoekstra, R.J., Hu, J.J., Kolda, T.G., Lehoucq, R.B., Long, K.R., Pawlowski, R.P., Phipps, E.T., Salinger, A.G., Thornquist, H.K., Tuminaro, R.S., Willenbring, J.M., Williams, A., Stanley, K.S.: An overview of the trilinos project. ACM Trans. Math. Softw. 31(3), 397–423 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We greatly acknowledge the provision of supercomputing time and technical support by the High Performance Computing Center Stuttgart (HLRS) for our project DGDES.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Wurst .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Wurst, M., Keßler, M., Krämer, E. (2016). A High-Order Discontinuous Galerkin CFD Solver for Turbulent Flows. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering ’15. Springer, Cham. https://doi.org/10.1007/978-3-319-24633-8_35

Download citation

Publish with us

Policies and ethics