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3D Application of Higher Order Multigrid Algorithms for a RANS-kω DG-Solver

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High Order Nonlinear Numerical Schemes for Evolutionary PDEs

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 99))

Abstract

We present an application of multigrid algorithms to a Discontinuous Galerkin discretization of the 3D Reynolds-averaged Navier–Stokes equations in combination with a kω turbulence model. Based on either lower order discretizations or agglomerated coarse meshes the resulting algorithms can be characterized as p- or h-multigrid, respectively. Linear and nonlinear multigrid algorithms are applied to a 3D numerical test case, namely the VFE-2 delta-wing with rounded leading edge. All presented algorithms are compared to a strongly implicit single grid solver in terms of run time behavior and nonlinear iterations.

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References

  1. 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., Dibelius, G. (eds.) In: 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Antwerpen, 5–7 March 1997, pp. 99–108. Technologisch Instituut (1997)

    Google Scholar 

  2. Bassi, F., Crivellini, A., Rebay, S., Savini, M.: Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and k-ω turbulence model equations. Comput. Fluids 34(4–5), 507–540 (2005)

    Article  MATH  Google Scholar 

  3. Bassi, F., Ghidoni, A., Rebay, S., Tesini, P.: High-order accurate p-multigrid discontinuous Galerkin solution of the Euler equations. Int. J. Numer. Methods Fluids 60, 847–865 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bassi, F., Botti, L., Colombo, A., Di Pietro, D.A., Tesini, P.: On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations. J. Comput. Phys. 231(1), 45–65 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bassi, F., Botti, L., Colombo, A., Rebay, S.: Agglomeration based discontinuous Galerkin discretization of the Euler and Navier-Stokes equations. Comput. Fluids 61, 77–85 (2012)

    Article  MathSciNet  Google Scholar 

  6. Burgess, N.K., Nastase, C.R., Mavriplis, D.J., Martinelli, L.: Efficient solution techniques for discontinuous Galerkin discretizations of the Navier-Stokes equations on hybrid anisotropic meshes. In: 48th AIAA Aerospace Sciences Meeting, AIAA Paper 2010-1448, Orlando (2010)

    Google Scholar 

  7. Fejtek, I.: Summary of code validation results for a multiple element airfoil test case. In: 28th AIAA Fluid Dynamics Conference, AIAA Paper 97-1932, Snowmass Village (1997)

    Google Scholar 

  8. Fidkowski, K.J., Oliver, T.A., Lu, J., Darmofal, D.L.: p-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. J. Comput. Phys. 207(1), 92–113 (2005)

    Google Scholar 

  9. Hartmann, R., Held, J., Leicht, T.: Adjoint-based error estimation and adaptive mesh refinement for the RANS and k-ω turbulence model equations. J. Comput. Phys. 230(11), 4268–4284 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kroll, N.: IDIHOM – European project on industrialization of high-order methods for aeronautical applications. In: ECCOMAS 2012, Wien, Sept 2012

    Google Scholar 

  11. Landmann, B., Kessler, M., Wagner, S., Krämer, E.: A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows. Comput. Fluids 37(4), 427–438 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Luo, H., Baum, J.D., Löhner, R.: A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids. J. Comput. Phys. 227(20), 8875–8893 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Moulitsas, I., Karypis, G.: Multilevel algorithms for generating coarse grids for multigrid methods. In: Proceedings of the 2001 ACM/IEEE Conference on Supercomputing, Denver, p. 45. ACM (2001)

    Google Scholar 

  14. Mulder, W.A., Van Leer, B.: Experiments with implicit upwind methods for the Euler equations. J. Comput. Phys. 59(2), 232–246 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  15. Pelletier, D., Ilinca, F.: Positivity preservation and adaptive solution for the k −ω model of turbulence. AIAA J. 36, 44–50 (1998)

    Article  MATH  Google Scholar 

  16. Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43(2), 357–372 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  17. Trottenberg, U., Oosterlee, C.W., Schüller, A.: Multigrid. Academic, San Diego (2001)

    MATH  Google Scholar 

  18. Wallraff, M., Leicht, T., Lange-Hegermann, M.: Numerical flux functions for Reynolds-averaged Navier-Stokes and k −ω turbulence model computations with a line-preconditioned p-multigrid discontinuous Galerkin solver. Int. J. Numer. Methods Fluids 71(8), 1055–1072 (2012)

    Article  MathSciNet  Google Scholar 

  19. Wilcox, D.C.: Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11), 1299–1310 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  20. Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries, Inc., La Canada (1993)

    Google Scholar 

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Acknowledgements

The authors acknowledge the financial support of both the BMBF joint research project DGHPOPT (Förderkennzeichen: 05M10CLA) and the EC funded IDIHOM project [10].

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Authors and Affiliations

  1. German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, 38108, Braunschweig, Germany

    Marcel Wallraff & Tobias Leicht

Authors
  1. Marcel Wallraff
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  2. Tobias Leicht
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Corresponding author

Correspondence to Marcel Wallraff .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, University of Zurich, Zurich, Switzerland

    Rémi Abgrall

  2. INRIA and Institut Polytechnique de Bordeaux, Institut de Mathématiques de Bordeaux, Talence, France

    Héloïse Beaugendre

  3. INRIA, Institut de Mathématiques de Bordeaux, Talence, France

    Pietro Marco Congedo

  4. INRIA and Institut Polytechnique de Bordeaux, Institut de Mathématiques de Bordeaux, Talence, France

    Cécile Dobrzynski

  5. INRIA, Laboratoire de Mathématiques et de leurs Applications, Pau, France

    Vincent Perrier

  6. INRIA, Institut de Mathématiques de Bordeaux, Talence, France

    Mario Ricchiuto

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Wallraff, M., Leicht, T. (2014). 3D Application of Higher Order Multigrid Algorithms for a RANS-kω DG-Solver. In: Abgrall, R., Beaugendre, H., Congedo, P., Dobrzynski, C., Perrier, V., Ricchiuto, M. (eds) High Order Nonlinear Numerical Schemes for Evolutionary PDEs. Lecture Notes in Computational Science and Engineering, vol 99. Springer, Cham. https://doi.org/10.1007/978-3-319-05455-1_5

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