Abstract
Discontinuous Galerkin methods allow higher-order flow solutions on unstructured or locally refined meshes by increasing the polynomial degree and using curved instead of straight-sided elements. Residual-based adaptation targets at resolving all flow features. In this article, higher-order discontinuous Galerkin methods are combined with residual-based adaptation and applied to a fully turbulent subsonic flow around the second Vortex Flow Experiment (VFE-2) configuration.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bassi, F., Crivellini, A., Ghidoni, A., Rebay, S.: High-order discontinuous Galerkin discretization of transonic turbulent flows. In: 47th AIAA Aerospace Sciences Meeting (2009), AIAA 2009-180
Bassi, F., Crivellini, A., Rebay, S., Savini, M.: Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and k − ω turbulence model equations. Computers & Fluids 34, 507–540 (2005)
Bassi, F., Rebay, S.: A high order discontinuous Galerkin method for compressible turbulent flows. In: Cockburn, B., Karniadakis, G., Shu, C.-W. (eds.) Discontinuous Galerkin Methods. LNCSE, vol. 11, pp. 77–79. Springer (2000)
Giles, M., Süli, E.: Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality. Acta Numerica 11, 145–236 (2002)
Hartmann, R.: Adaptive Finite Element Methods for the Compressible Euler Equations. PhD thesis, University of Heidelberg (2002)
Hartmann, R.: Adaptive discontinuous Galerkin methods with shock-capturing for the compressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids 51(9-10), 1131–1156 (2006)
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) (in press)
Hartmann, R., Held, J., Leicht, T., Prill, F.: Discontinuous Galerkin methods for computational aerodynamics – 3D adaptive flow simulation with the DLR PADGE code. Aerosp. Sci. Technol. 14, 512–519 (2010)
Hartmann, R., Houston, P.: Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations. J. Comput. Phys. 183(2), 508–532 (2002)
Hartmann, R., Houston, P.: Symmetric interior penalty DG methods for the compressible Navier–Stokes equations II: Goal–oriented a posteriori error estimation. Int. J. Num. Anal. Model. 3(2), 141–162 (2006)
Hummel, D., Redeker, G.: A new vortex flow experiment for computer code validation. In: RTO-AVT Symposium on “Vortex Fow and High Angle of Attack”, Loen, Norway, 7.-11.05 (2001)
Ilinca, F., Pelletier, D.: Positivity preservation and adaptive solution for the k − ε model of turbulence. AIAA J. 36(1), 44–50 (1998)
Karniadakis, G., Sherwin, S.: Spectral/hp Finite Element Methods in CFD. Oxford University Press (1999)
Konrath, R., Klein, C., Engler, R., Otter, D.: Analysis of PSP results obtained for the VFE-2 65° delta wing configuration at sub-and transonic speeds. In: 44th AIAA Aerospace Sciences Meeting and Exhibit (2006), AIAA 2006-59-624
Kroll, N.: ADIGMA – A European project on the development of adaptive higher-order variational methods for aerospace applications. In: 47th AIAA Aerospace Sciences Meeting (2009), AIAA 2009-176
Landmann, B., Kessler, M., Wagner, S., Krämer, E.: A parallel discontinuous Galerkin code for the Navier-Stokes equations. In: 44th AIAA Aerospace Sciences Meeting and Exhibit (2006), AIAA 2006-111
Leicht, T., Hartmann, R.: Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations. J. Comput. Phys. 229(19), 7344–7360 (2010)
Schütte, A., Lüdeke, H.: Numerical investigations on the VFE-2 65-degree rounded leading edge delta wing using the unstructured DLR-TAU-Code. In: 46th AIAA Aerospace Sciences Meeting and Exhibit (2009), AIAA 2009-398-883
Šolín, P., Segeth, K., Doležel, I.: Higher-Order Finite Element Methods. Chapman & Hall/CRC (2004)
Wilcox, D.C.: Reassessment of the scale-determining equation for advanced turbulence models. AIAA J. 26(11), 1299–1310 (1988)
Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries, Inc., La Canada (1993)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hartmann, R. (2013). Higher-Order and Adaptive Discontinuous Galerkin Methods Applied to Turbulent Delta Wing Flow. In: Dillmann, A., Heller, G., Kreplin, HP., Nitsche, W., Peltzer, I. (eds) New Results in Numerical and Experimental Fluid Mechanics VIII. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35680-3_59
Download citation
DOI: https://doi.org/10.1007/978-3-642-35680-3_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35679-7
Online ISBN: 978-3-642-35680-3
eBook Packages: EngineeringEngineering (R0)