Skip to main content

2013 | OriginalPaper | Buchkapitel

Discontinuous Galerkin for High Performance Computational Fluid Dynamics

verfasst von : Christoph Altmann, Andrea Beck, Andreas Birkefeld, Gregor Gassner, Florian Hindenlang, Claus-Dieter Munz, Marc Staudenmaier

Erschienen in: High Performance Computing in Science and Engineering ‘12

Verlag: Springer Berlin Heidelberg

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this report we present selected simulations performed on the HLRS clusters. Our simulation framework is based on the discontinuous Galerkin method and consists of four different codes, each of which is developed with a distinct focus. All of those codes are written with a special emphasis on (MPI) based high performance computing. Results of compressible flow simulations such as flow past a sphere, compressible jet flow and isotropic homogeneous turbulence as well as an application of our aeroacoustic framework are reported. All simulations are typically performed on hundreds and thousands of CPU cores.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, 1st Edition, Springer, 2007. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, 1st Edition, Springer, 2007.
2.
Zurück zum Zitat F. Lörcher, Predictor Corrector DG, PhD thesis, University of Stuttgart, (2008). F. Lörcher, Predictor Corrector DG, PhD thesis, University of Stuttgart, (2008).
3.
Zurück zum Zitat F. Lörcher and G. Gassner and C.-D. Munz, A Discontinuous Galerkin Scheme based on a Space-Time Expansion I. Inviscid compressible flow in one space dimension, J. Sci. Comp., Vol. 32, pp. 175–199, (2007).MATHCrossRef F. Lörcher and G. Gassner and C.-D. Munz, A Discontinuous Galerkin Scheme based on a Space-Time Expansion I. Inviscid compressible flow in one space dimension, J. Sci. Comp., Vol. 32, pp. 175–199, (2007).MATHCrossRef
4.
Zurück zum Zitat G. Gassner and F. Lörcher and C.-D. Munz, A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi Dimensions, J. Sci. Comp., Vol. 34, pp. 260–286, (2007).CrossRef G. Gassner and F. Lörcher and C.-D. Munz, A Discontinuous Galerkin Scheme based on a Space-Time Expansion II. Viscous Flow Equations in Multi Dimensions, J. Sci. Comp., Vol. 34, pp. 260–286, (2007).CrossRef
5.
Zurück zum Zitat G. J. Gassner, Frieder Lörcher, Claus-Dieter Munz and Jan S. Hesthaven: ”Polymorphic nodal elements and their application in discontinuous Galerkin methods”. Journal of Computational Physics, Volume 228, Issue 5, 20 March 2009 G. J. Gassner, Frieder Lörcher, Claus-Dieter Munz and Jan S. Hesthaven: ”Polymorphic nodal elements and their application in discontinuous Galerkin methods”. Journal of Computational Physics, Volume 228, Issue 5, 20 March 2009
6.
Zurück zum Zitat F. Lörcher, G. Gassner and C.-D. Munz: ”Arbitrary High Order Accurate Time Integration Schemes for Linear Problems”. European Conference on Computational Fluid Dynamics, ECCOMAS CFD, 2006 F. Lörcher, G. Gassner and C.-D. Munz: ”Arbitrary High Order Accurate Time Integration Schemes for Linear Problems”. European Conference on Computational Fluid Dynamics, ECCOMAS CFD, 2006
7.
Zurück zum Zitat G. Gassner and F. Lörcher and C.-D. Munz, An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations, J. Comput. Phys., Vol. 227, pp. 5649–5670, (2008).MathSciNetMATHCrossRef G. Gassner and F. Lörcher and C.-D. Munz, An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations, J. Comput. Phys., Vol. 227, pp. 5649–5670, (2008).MathSciNetMATHCrossRef
8.
Zurück zum Zitat G. Gassner and M. Dumbser and F. Hindenlang and C.-D. Munz, Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors, J. Comput. Phys., In Press, Corrected Proof, (2010). G. Gassner and M. Dumbser and F. Hindenlang and C.-D. Munz, Explicit one-step time discretizations for discontinuous Galerkin and finite volume schemes based on local predictors, J. Comput. Phys., In Press, Corrected Proof, (2010).
9.
Zurück zum Zitat F. Hindenlang and G. Gassner and T. Bolemann and C.-D. Munz, Unstructured high order grids and their application in Discontinuous Galerkin methods, conference proceedings, V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010, Lisbon,Portugal, (2010). F. Hindenlang and G. Gassner and T. Bolemann and C.-D. Munz, Unstructured high order grids and their application in Discontinuous Galerkin methods, conference proceedings, V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010, Lisbon,Portugal, (2010).
10.
Zurück zum Zitat S. Hickel, Implicit turbulence modeling for large-eddy simulation, PhD thesis, TU Dresden, (2005). S. Hickel, Implicit turbulence modeling for large-eddy simulation, PhD thesis, TU Dresden, (2005).
11.
Zurück zum Zitat M.E. Brachet, Direct simulation of three-dimensional turbulence in the Taylor–Green vortex, Fluid Dynamics Research, Vol. 8, pp. 1–8, (1991).CrossRef M.E. Brachet, Direct simulation of three-dimensional turbulence in the Taylor–Green vortex, Fluid Dynamics Research, Vol. 8, pp. 1–8, (1991).CrossRef
12.
Zurück zum Zitat P.-O. Persson and J. Peraire, Sub-Cell Shock Capturing for Discontinuous Galerkin Methods, Proc. of the 44th AIAA Aerospace Sciences Meeting and Exhibit, (2006). P.-O. Persson and J. Peraire, Sub-Cell Shock Capturing for Discontinuous Galerkin Methods, Proc. of the 44th AIAA Aerospace Sciences Meeting and Exhibit, (2006).
13.
Zurück zum Zitat G. N. Coleman, J. Kim, R. D. Moser, A numerical study of turbulent supersonic isothermal-wall channel flow, J. Fluid Mech, Vol. 305, pp. 159–183, (1995).MATHCrossRef G. N. Coleman, J. Kim, R. D. Moser, A numerical study of turbulent supersonic isothermal-wall channel flow, J. Fluid Mech, Vol. 305, pp. 159–183, (1995).MATHCrossRef
14.
Zurück zum Zitat E. Lenormand, P. Sagaut, L. Ta Phuoc, Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number, Int. J. Numer. Meth. Fluids, Vol. 32, pp. 369–406, (2000).MATHCrossRef E. Lenormand, P. Sagaut, L. Ta Phuoc, Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number, Int. J. Numer. Meth. Fluids, Vol. 32, pp. 369–406, (2000).MATHCrossRef
15.
Zurück zum Zitat A. Birkefeld and C.-D. Munz, A Hybrid Method for CAA, Proc. of the 36. Jahrestagung für Akustik der Deutschen Gesellschaft für Akustik, DAGA, Berlin, (2010). A. Birkefeld and C.-D. Munz, A Hybrid Method for CAA, Proc. of the 36. Jahrestagung für Akustik der Deutschen Gesellschaft für Akustik, DAGA, Berlin, (2010).
16.
Zurück zum Zitat A. Birkefeld and A. Beck and M. Dumbser and C.-D. Munz and D. König and W. Schröder, Advances in the Computational Aeroacoustics with the Discontinuous Galerkin Solver NoisSol, Proc. of the 16th AIAA/CEAS Aeroacoustics Conference (31st AIAA Aeroacoustics Conference), Stockholm, 2010 A. Birkefeld and A. Beck and M. Dumbser and C.-D. Munz and D. König and W. Schröder, Advances in the Computational Aeroacoustics with the Discontinuous Galerkin Solver NoisSol, Proc. of the 16th AIAA/CEAS Aeroacoustics Conference (31st AIAA Aeroacoustics Conference), Stockholm, 2010
17.
Zurück zum Zitat R. Ewert and W. Schröder, Acoustic Perturbation Equations Based on Flow Decomposition via Source Filtering, Journal of Computational Physics, Vol. 188, pp. 365–398, (2003).MathSciNetMATHCrossRef R. Ewert and W. Schröder, Acoustic Perturbation Equations Based on Flow Decomposition via Source Filtering, Journal of Computational Physics, Vol. 188, pp. 365–398, (2003).MathSciNetMATHCrossRef
18.
Zurück zum Zitat Jan W. Delfs and Marcus Bauer and Roland Ewert and Herwig A. and Grogger and Markus Lummer and Thomas G. W. Lauke, Numerical Simulation of Aerodynamic Noise with DLR’s aeroacoustic code PIANO, Deutsches Zentrum für Luft- und Raumfahrt e.V., Institut für Aerodynamik und Strömungstechnik Jan W.  Delfs and Marcus Bauer and Roland Ewert and Herwig A. and Grogger and Markus Lummer and Thomas G. W. Lauke, Numerical Simulation of Aerodynamic Noise with DLR’s aeroacoustic code PIANO, Deutsches Zentrum für Luft- und Raumfahrt e.V., Institut für Aerodynamik und Strömungstechnik
19.
Zurück zum Zitat R. Ewert, Broadband slat noise prediction based on CAA and stochasic sound sources from a fast random particle mesh RPM) method, Computers & Fluids, Vol. 37, pp. 369387, 2008MathSciNetCrossRef R. Ewert, Broadband slat noise prediction based on CAA and stochasic sound sources from a fast random particle mesh RPM) method, Computers & Fluids, Vol. 37, pp. 369387, 2008MathSciNetCrossRef
20.
Zurück zum Zitat S. Orszag, Numerical simulation of the Taylor-Green vortex, Computing Methods in Applied Sciences and Engineering Part 2, Lecture Notes in Computer Science, Vol. 11, pp. 50–64, (1974).MathSciNetCrossRef S. Orszag, Numerical simulation of the Taylor-Green vortex, Computing Methods in Applied Sciences and Engineering Part 2, Lecture Notes in Computer Science, Vol. 11, pp. 50–64, (1974).MathSciNetCrossRef
21.
Zurück zum Zitat D. Fauconnier, Development of a Dynamic Finite Difference Method for Large-Eddy Simulation, PhD thesis, University of Gent, Belgium, (2009). D. Fauconnier, Development of a Dynamic Finite Difference Method for Large-Eddy Simulation, PhD thesis, University of Gent, Belgium, (2009).
22.
Zurück zum Zitat A. Beck, G. Gassner, I. Horenko, R. Klein, C.-D. Munz, Technischer Report im Rahmen des Schwerpunktprogramms 1276 (MetStroem), Lugano, Berlin, Stuttgart, (2011). A. Beck, G. Gassner, I. Horenko, R. Klein, C.-D. Munz, Technischer Report im Rahmen des Schwerpunktprogramms 1276 (MetStroem), Lugano, Berlin, Stuttgart, (2011).
23.
Zurück zum Zitat A.G. Tomboulides and S.A. Orszag, Numerical investigation of transitional and weak turbulent flow past a sphere, J. Fluid Mech., Vol. 416, pp. 45–73, (2000).MathSciNetMATHCrossRef A.G. Tomboulides and S.A. Orszag, Numerical investigation of transitional and weak turbulent flow past a sphere, J. Fluid Mech., Vol. 416, pp. 45–73, (2000).MathSciNetMATHCrossRef
24.
Zurück zum Zitat Bogey, C., Bailly, C. and Juv, D., Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES,Theoretical and Computational Fluid Dynamics,16(4), 273–29, 2003. Bogey, C., Bailly, C. and Juv, D., Noise investigation of a high subsonic, moderate Reynolds number jet using a compressible LES,Theoretical and Computational Fluid Dynamics,16(4), 273–29, 2003.
25.
Zurück zum Zitat J. Dierke, C. Appel, J. Siebert, M. Bauer, M. Siefert and R. Ewert, 3D Computation of Broadband Slat Noise from Swept and Unswept High-Lift Wing Sections, Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, Portland, AIAA paper 2011–2905 (2011). J. Dierke, C. Appel, J. Siebert, M. Bauer, M. Siefert and R. Ewert, 3D Computation of Broadband Slat Noise from Swept and Unswept High-Lift Wing Sections, Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, Portland, AIAA paper 2011–2905 (2011).
26.
Zurück zum Zitat D. P. Lockard and M. M. Choudhari, Noise Radiation from a Leading-Edge Slat, AIAA paper 2009–3101 (2009). D. P. Lockard and M. M. Choudhari, Noise Radiation from a Leading-Edge Slat, AIAA paper 2009–3101 (2009).
27.
Zurück zum Zitat G.J. Gassner and A.D.Beck, On the accuracy of high-order discretizations for underresolved turbulence simulations, Theoretical and Computational Fluid Dynamics, DOI 10.1007/s00162-011-0253-7 G.J. Gassner and A.D.Beck, On the accuracy of high-order discretizations for underresolved turbulence simulations, Theoretical and Computational Fluid Dynamics, DOI 10.1007/s00162-011-0253-7
Metadaten
Titel
Discontinuous Galerkin for High Performance Computational Fluid Dynamics
verfasst von
Christoph Altmann
Andrea Beck
Andreas Birkefeld
Gregor Gassner
Florian Hindenlang
Claus-Dieter Munz
Marc Staudenmaier
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-33374-3_18

Premium Partner