Skip to main content
SpringerLink
Log in

Numerische Methoden

  • Chapter
  • First Online:
Hucho - Aerodynamik des Automobils

Part of the book series: ATZ/MTZ-Fachbuch ((ATZMTZ))

  • 1425 Accesses

Zusammenfassung

Vor allem in der Frühphase der Automobilentwicklung sind meist keine realen Fahrzeuge, sondern nur Teile- oder Plastilinversuchsträger verfügbar. Dennoch müssen eine Reihe miteinander konkurrierender Designentwürfe technisch bewertet werden, bspw. hinsichtlich ihrer aerodynamischen und aeroakustischen Eigenschaften. Dabei besteht Bedarf an sehr genauer Kenntnis der auftretenden Strömungsphänomene, Schallerzeugungs- und -übertragungsmechanismen, denn diese gilt es im Fortgang der Entwicklung zu beherrschen. Für Auslegung, Entwicklung und Optimierung werden hierzu, neben dem über viele Jahrzehnte unverzichtbaren Windkanalversuch, auch eine Vielzahl unterschiedlicher numerischer Simulationen eingesetzt. Die wesentlichen Motive, die den Einsatz von numerischen Methoden rechtfertigen, sind:

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 299.99
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

Notes

  1. 1.

    Computational Fluid Dynamics.

  2. 2.

    www.top500.org.

  3. 3.

    Bspw. MPI = Message Passing Interface.

  4. 4.

    Reynolds Averaged Navier Stokes.

  5. 5.

    Aus dieser Eigenschaft resultiert in den RANS-Gleichungen lediglich ein Störterm. Bei der Hinführung auf die LES-Methode in Abschn. 15.1.4.2 ist diese Eigenschaft wegen des kontinuierlichen Kolmogorov-Spektrums nicht gegeben, infolgedessen entstehen dort in den Grobstrukturgleichungen weitere Störterme.

  6. 6.

    Hierbei wird allerdings nicht die Turbulenz selbst, sondern die Reynolds-Spannungen modelliert.

  7. 7.

    Zitiert bei Ahmed [11].

  8. 8.

    Engl.: Design of Experiment.

  9. 9.

    Das λ2-Kriterium ist eine weitere Möglichkeit, Wirbelstrukturen zu identifizieren, ähnlich dem in Abb. 4.28 verwendeten Q-Kriterium.

Literatur

  1. Kuthada, T.: CFD and Wind Tunnel: Competitive Tools or Supplementary Use? 4th FKFS Conference, Stuttgart (2007)

    Google Scholar 

  2. Jungmann, J.: Eine experimentell validierte Methodik zur numerischen Simulation und Analyse des aerodynamischen und fahrdynamischen Verhaltens von Personenkraftwagen bei realitätsnaher, querdynamischer Fahrzeuganregung. Dissertation, Technische Universität Darmstadt (2020)

    Google Scholar 

  3. Jungmann, J., Schütz, T., Jakirlic, S., Tropea, C.: Flow past a DrivAer body in a scale model wind tunnel: computational study by reference to a complementary experiment. iMech International Conference on Vehicle Aerodynamics 2016 – Aerodynamics by Design; September 21st – 22nd, Coventry/England (2016)

    Google Scholar 

  4. Hardy, J., Pomeau, Y., de Pazzis, O.: Time evolution of two-dimensional model system. I. Invariant states and time correlation functions. J. Math. Phys. 14, 1746–1759 (1973)

    Article  MathSciNet  Google Scholar 

  5. Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-gas automata for the Navier-Stokes equation. Phys. Rev. Lett. 56, 1505–1508 (1986)

    Article  Google Scholar 

  6. Chen, H.: Volumetric formulation of the Lattice Boltzmann method for fluid dynamics. Phys. Rev. E. 58 (1998)

    Google Scholar 

  7. Chen, H., Teixeira, C., Molvig, K.: Digital Physics® approach to computational fluid dynamics: Some basic theoretical features. Int. J. Mod. Phys. C. 9(4) (1997)

    Google Scholar 

  8. Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511–525 (1954)

    Article  MATH  Google Scholar 

  9. Teixeira: Incorporating turbulence models into the Lattice-Boltzmann method. Int. J. Mod. Phy. C. 9(8) (1998)

    Google Scholar 

  10. Theissen, P.: Unsteady Vehicle Aerodynamics in Gusty Crosswind, Dissertation TU München, Lehrstuhl für Aerodynamik und Strömungsmechanik (2012)

    Google Scholar 

  11. Theissen, P., Wojciak J., Demuth R., Adams N.A., Indinger T.: Unsteady aerodynamic phenomena under time-dependent flow conditions for different vehicle shapes. In Proceedings of 8th International Vehicle Aerodynamics Conference (2010)

    Google Scholar 

  12. Schäufele, S.: Validierung der neuen Windkanäle im Aerodynamischen Versuchszentrum der BMW Group und Analyse der Übertragbarkeit der Ergebnisse. Dissertation KIT Karlsruhe (2010)

    Google Scholar 

  13. Kandasamy, S., Duncan, B., Gau, H., Maroy, F., Belanger, A., Grün, N., Schäufele, S.: Aerodynamic Performance Assessment of BMW Validation Models using Computational Fluid Dynamics. SAE-Paper 2012-01-0297. Society of Automotive Engineers (SAE), Warrendale (2012)

    Google Scholar 

  14. Kandasamy, S., Duncan, B., Gau, H., Maroy, F., Belanger, A., Grün, N., Schäufele, S.: Impact of Wheel Rotation on Aerodynamic Drag and Lift. FKFS Symposium, Stuttgart (2012)

    Google Scholar 

  15. Schlichting, H., Gersten, K.: Grenzschichttheorie, 10 Aufl.. Springer, Berlin/Heidelberg (2006)

    Google Scholar 

  16. Kolmogorov, A.N.: Izw Akad Nauk SSSR. Ser. Phys. 6, 56 (1942)

    Google Scholar 

  17. Ferziger, J.H., Peric, M.: Numerische Strömungsmechanik. Springer, Berlin/Heidelberg (2008). ISBN: 13 978-3-540-68228-8

    Google Scholar 

  18. Menter, F.: Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows, AIAA Paper 93-2906 (1993)

    Google Scholar 

  19. Versteeg, H.K., Malalasekera, W.: An Introduction to Computational Fluid Dynamics: The Finite Volume Method. 2. Aufl. Prentice Hall (2007). ISBN-13 978-0131274983

    Google Scholar 

  20. Oertel, H., Laurien, E.: Numerische Strömungsmechanik. Grundgleichungen – Lösungsmethoden – Softwarebeispiele, 2 Aufl.. Vieweg, Wiesbaden (2003). isbn:3-528-03936-1

    Book  Google Scholar 

  21. Schwarze, R.: CFD-Modellierung: Grundlagen und Anwendungen bei Strömungsprozessen. Springer, Berlin/Heidelberg (2013). ISBN: 13 978-3-642-24378-3

    Google Scholar 

  22. Launder, B.E., Sharma, B.I.: Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transf. 1(2), 131–138 (1974)

    Article  Google Scholar 

  23. Wäschle, A.: Numerische und experimentelle Untersuchung des Einflusses von drehenden Rädern auf die Fahrzeugaerodynamik. Dissertation, Universität Stuttgart (2006)

    Google Scholar 

  24. Smagorinsky, J.: General circulation experiments with the primitive equations. I: The basic experiment. Mon. Weather Rev. 91, 99–152 (1963)

    Article  Google Scholar 

  25. Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  26. Fröhlich, J., von Terzi, D.: Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44(5), 349–377 (2008)

    Article  Google Scholar 

  27. Davidson, L.: Large eddy simulations: how to evaluate resolution. Int. J. Heat Fluid Flow. 30(5), 1016–1025 (2009)

    Article  Google Scholar 

  28. Ferziger, J.H.: Large eddy simulation. In: Gatski, T.B., Hussaini, M.Y., Lumley, J.L. (Hrsg.) Simulation and Modelling of Turbulent Flows, ICASE/LaRC Series in Comp. Sci. and Eng., S. 109–154. Oxford University Press, New York (1996)

    Google Scholar 

  29. Jakirlic, S., Kutej, L., Unterlechner, P., Tropea, C.: Critical assessment of some popular scale-resolving turbulence models for vehicle aerodynamics. SAE Int. J. Passeng. Cars Mech. Syst. 10, 235–250 (2017)

    Article  Google Scholar 

  30. Spalart, P.R.: Strategies for turbulence modelling and simulations. Eng. Turbul. Model. Exp. 4, 3–17 (1999) Elsevier Science Ltd

    Article  Google Scholar 

  31. Fröhlich, J.: Large Eddy Simulation turbulenter Strömungen. Teubner (2006)

    Google Scholar 

  32. Werner, H.: Grobstruktursimulation der turbulenten Strömung über eine querliegende Rippe in einem Plattenkanal bei hoher Reynolds-Zahl. Dissertation, TU München (1991)

    Google Scholar 

  33. Beaudan, P., Moin, P.: Numerical experiments on the flow past a circular cylinder at sub-critical Reynolds number. Technical Report. TF-62. Stanford University (1994)

    Google Scholar 

  34. Dawi, A.H., Akkermans, R.A.D.: Spurious noise in direct noise computation with a finite volume method for automotive applications. Int. J. Heat Fluid Flow. 72, 243–256 (2018)

    Article  Google Scholar 

  35. Tabor, G.R., Baba-Ahmadi, M.H.: Inlet conditions for large eddy simulation: a review. Comput. Fluids. 39(4), 553–567 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  36. Larsson, J., Kawai, S., Bodart, J., Bermejo-Moreno, I.: Large eddy simulation with modeled wall-stress: recent progress and future directions. Bull. JSME. 3(1) (2016)

    Google Scholar 

  37. Balaras, E., Benocci, C., Piomelli, U.: Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34(6), 1111–1119 (1996)

    Article  MATH  Google Scholar 

  38. Templeton, J.A., Wang, M., Moin, P.: A predictive wall model for large-eddy simulation based on optimal control. Techn. Phys. Fluids. 20 (2008)

    Google Scholar 

  39. Bodart, J.; Larsson, J.: Sensor-based computation of transitional flows using wall-modeled large eddy simulation. In Annu. Res. Briefs, S. 229–240. Center for Turbulence Research (2012)

    Google Scholar 

  40. Spalart, P.R., Jou, W.H., Strelets, M., Allmaras, S.R.: Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach, 1st AFOSR Int. Conf. on DNS/LES, Aug. 4-8, 1997, Ruston, LA. In: Liu, C., Liu, Z. (Hrsg.) Advances in DNS/LES. Greyden Press, Columbus (1997)

    Google Scholar 

  41. Gritskevich, M., Garbaruk, A., Schütze, J., Menter, F.: Development of DDES and IDDES formulations for the k-ω shear stress transport model. Flow, Turbul. Combust. 88, 432–449 (2012)

    Article  MATH  Google Scholar 

  42. Spalding, D.B.: A single formula for the „law of the wall“. J. Appl. Mech. 28, 455–458 (1961)

    Article  MATH  Google Scholar 

  43. Spalart, P.R., Streett, C.: Young-Person’s Guide to Detached-Eddy Simulation Grids (2001)

    Google Scholar 

  44. Ashton, N., Revell, A., Poletto, R.: Grey-area mitigation for the ahmed car body using embedded DDES. Progress in Hybrid RANS-LES Modelling, 119–129 (2015)

    Google Scholar 

  45. Spalart, P.R., 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, 181–195 (2006)

    Article  MATH  Google Scholar 

  46. Ashton, N.: Recalibrating delayed Detached-Eddy Simulation to eliminate modelled-stress depletion, 23rd AIAA Computational Fluid Dynamics Conference, June (2017)

    Google Scholar 

  47. Fuchs, M., Mockett, C., Sesterhenn, J., Thiele, F.: The grey-area improved σ-DDES approach: formulation review and application to complex test cases. In: Progress in Hybrid RANS-LES Modelling. Springer International Publishing, New York (2020)

    Google Scholar 

  48. Shur, M., Spalart, P., Strelets, M., Travin, A.: A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Int. J. Heat Fluid Flow. 29(6), 1638–1649 (2008)

    Article  Google Scholar 

  49. Girimaji, S., Abdol-Hamid, K.: Partially-Averaged Navier-Stokes Model for Turbulence: Implementation and Validation. AIAA paper 2005-0502, 43rd AIAA Aerospace Sciences Meeting and Exhibit (2005)

    Google Scholar 

  50. Basara, B., Krajnović, S., Girimaji, S.: PANS vs. LES for computations of the flow around a 3D bluff body. In: Proc. of ERCOFTAC 7th Int. Symp. – ETMM7, Lymassol, Cyprus, vol. 2/3, pp. 548–554 (2008)

    Google Scholar 

  51. Speziale, C.: Turbulence modeling for time-dependent RANS and VLES: a review. AIAA J. 36(2), 173–184 (1998)

    Article  MATH  Google Scholar 

  52. Fasel, H., Seidel, J., Wernz, S.: A methodology for simulations of complex turbulent flows. ASME. J. Fluids Eng. 124(4), 933–942 (2002)

    Article  Google Scholar 

  53. Ahmed, S.R., Ramm, G., Faltin, G.: Some Salient Features of the Time-Averaged Ground Vehicle Wake. SAE-Paper 840300. Society of Automotive Engineers (SAE), Warrendale (1984)

    Google Scholar 

  54. Lienhart, H., Becker, S.: Flow and Turbulent Structure in the Wake of a Simplified Car Model. SAE-Paper 2003-01-0656 (2003)

    Google Scholar 

  55. Lienhart, H., Stoots, C., Becker, S.: Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed model). DGLR Fach Symp. der AG STAB, Stuttgart University (2000)

    Google Scholar 

  56. Rao, A., Minelli, G., Basara, B., Krajnović, S.: On the two flow states in the wake of a hatchback Ahmed body. J. Wind Eng. Ind. Aerodyn. 173, 262–278 (2018)

    Article  Google Scholar 

  57. Kitoh, K., Chatani, S., Oshima, N., Nakashima, T., Sebben, S.: Large Eddy Simulation on the Underbody Flow of the Vehicle with Semi-Complex Underbody Configuration. SAE-paper 2007-01-0103. Society of Automotive Engineers (SAE), Warrendale (2007)

    Google Scholar 

  58. Islam, M., Decker, F., de Villiers, E., Jackson, A., Gines, J., Grahs, T., Gitt-Gehrke, A., Comas i Font, J.: Application of Detached-Eddy Simulation for Automotive Aerodynamics Development. SAE-Paper 2009-01-0333. Society of Automotive Engineers (SAE), Warrendale (2009)

    Google Scholar 

  59. Schütz, T.: Fortschritt der CFD-Validierung in der Entwicklung der Kraftfahrzeugaerodynamik bei Audi. 11. Internationales Stuttgarter Symposium (2011)

    Google Scholar 

  60. Blacha, T., Islam, M.: The Aerodynamic Development of the New Audi Q5. SAE Int. J. Passeng. Cars – Mech. Syst. 10(2), S. 638–648. Society of Automotive Engineers (SAE), Warrendale (2017)

    Google Scholar 

  61. Hosseini, S.M., Vinuesa, R., Schlatter, P., Hanifi, A., Henningson, D.S.: Direct numerical simulation of the flow around a wing section at moderate Reynolds number. Int. J. Heat Fluid Flow. 61, 117–128 (2016)

    Article  Google Scholar 

  62. Moser, R.D., Lee, M.: Direct numerical simulation of turbulent channel flow up to Re = 5200. J. Fluid Mech. 774, 395–415 (2015). https://doi.org/10.1017/jfm.2015.268. Cambridge University Press

    Article  Google Scholar 

  63. Tsuboi, K., Shirayama, S., Oana, M., Kuwahara, K.: Computational study of the effect of base slant. In: Marino, C. (Hrsg.) Supercomputer Applications in Automotive Research and Engineering Development, S. 257–272. Cray Research Inc. book, Minneapolis (1988)

    Google Scholar 

  64. Morel, T.: The effect of base slant on the flow pattern and drag of three-dimensional bodies with blunt ends. In: Sovran, G., Morel, T., Mason, W.T. (Hrsg.) Aerodynamic drag mechanisms of bluff bodies and road vehicles, S. 191–226. Plenum Press, New York (1978)

    Chapter  Google Scholar 

  65. Bearman, P.W.: Bluff body flows applicable to vehicle aerodynamics. In: Morel, T., Dalton, C. (Hrsg.) Aerodynamics of Transportation. ASME-CSME Conference, New York, Niagara Falls, 1–11 (1979)

    Google Scholar 

  66. Kataoka, T., China, H., Nakagawa, K., Yoshida, M.: Numerical Simulation of Road Vehicle Aerodynamics and Effect of Aerodynamic Devices. SAE-Paper 910597. Society of Automotive Engineers (SAE), Warrendale (1991)

    Google Scholar 

  67. Lumley, J.: Turbulence modeling. 3rd International Conference, Innovation and Reliability in in Automotive Design and Testing, Florence, Italy, 8–10 April, 1381–1392 (1992)

    Google Scholar 

  68. Ahmed, S.R.: Numerical Flow Simulation in Road Vehicle Aerodynamics. Euromotor Short Course „Using Aerodynamics to Improve the Properties of Cars“. FKFS, Stuttgart (1998)

    Google Scholar 

  69. Hess, J.L., Smith, A.M.O.: Calculation of Potential Flow About Arbitrary Bodies. Prog. Aeron. Sci. 8, 1–138 (1967) Pergamon Press, New York

    Article  MATH  Google Scholar 

  70. Ahmed, S.R., Hucho, W.-H.: The Calculation of the Flow Field Past a Van with the Aid of a Panel Method. SAE-Paper 770390. Society of Automotive Engineers (SAE), Warrendale (1977)

    Google Scholar 

  71. Grün, N.: Simulating External Vehicle Aerodynamics with CARFLOW. SAE-Paper 980679 (1996)

    Google Scholar 

  72. Cousteix, J.: Analyse théorique et moyens de Prévision de la Couche Limite turbulente tridimensionnelle. ONERA Publication No. 157 (1974)

    Google Scholar 

  73. Grün, N.: Strömungsfeldangepasste Oberflächenkoordinaten zur Berechnung dreidimensionaler Grenzschichten Fortschrittberichte Reihe 7, Nr. 187. VDI, Düsseldorf (1991)

    Google Scholar 

  74. Tesch, G.: Kühlluftführungs- und Lüfterkonzepte am PKW bei typischen Bauraumbeschränkungen. Dissertation TU München. Dr. Hut, München (2011)

    Google Scholar 

  75. Link, A.: Analyse, Messung und Optimierung des aerodynamischen Ventilationswiderstands von Pkw-Rädern. Dissertation Universität Stuttgart. Springer Fachmedien, Wiesbaden (2018). ISBN: 978-3-658-22285-7

    Google Scholar 

  76. Tesch, G., Modlinger, F.: Die Aerodynamikfelge von BMW – Einfluss und Gestaltung von Rädern zur Minimierung von Fahrwiderständen. Tagung: Fahrzeug-Aerodynamik – Neue Chancen und Perspektiven für die Kraftfahrzeugaerodynamik durch CO2-Gesetzgebung und Energiewende. Haus der Technik, München (2012)

    Google Scholar 

  77. Peric, M., Schreck, E., Muzaferija, S.: Die Methode der überlappenden Rechengitter und deren Anwendung in der Fahrzeugaerodynamik. 10. Tagung Fahrzeugaerodynamik. Haus der Technik, München (2012)

    Google Scholar 

  78. Ferziger, J.H., Peric, M.: Computational Methods for Fluid Dynamics, 3. Aufl. Springer, Berlin/Heidelberg (2010). ISBN: 13 978-3540420743

    Google Scholar 

  79. Ham, F., Mattsson, K., Iaccarino, G.: Accurate and stable Finite volume operators for unstructured flow solvers. Center for Turbulence Research. Annual Research Briefs (2006)

    Google Scholar 

  80. Jansen, K.: A stabilized finite element method for computing turbulence. Comp. Meth. Appl. Mech. Eng. 174, 299–317 (1999)

    Article  MATH  Google Scholar 

  81. Frank, H., Munz, C.: Large eddy simulation of tonal noise at a side-view mirror using a high order discontinuous Galerkin method. 22nd AIAA/CEAS Aeroacoustics Conference. AIAA paper 2016-2847 (2016)

    Google Scholar 

  82. Schwarz, H. R.; Köckler, N.: Numerische Mathematik, Springer Vieweg, Wiesbaden 2009.

    Google Scholar 

  83. Biswas, R., Strawn, R.: Tetrahedral and hexahedral mesh adaptation for CFD problems. Appl. Numer. Math. 26(1-2), 135–151 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  84. Schwertfirm, F., Kreuzinger, J., Peller, N., Hartmann, M.: Validation of a hybrid simulation method for flow. 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference) (2012)

    Google Scholar 

  85. Schütz, T.: Aerodynamische Effizienz von Fahrwerkskomponenten bei zukünftigen Fahrzeugen. VDI Tagung „Reifen – Fahrwerk – Fahrbahn“. Hannover (2017)

    Google Scholar 

  86. Flurl, B.: Ein modulares Verfahren zur Simulation von Mehrfeldproblemen in Strömungsmaschinen. Dissertation, Technische Universität München (2011)

    Google Scholar 

  87. Yeoh, G.H., Tu, J.: Computational Techniques for Multi-Phase Flows. Chapt. 3, Elsevier Ltd (2009)

    Google Scholar 

  88. Meister, A.: Numerik linearer Gleichungssysteme – Eine Einführung in moderne Verfahren. Mit MATLAB®-Implementierungen von C. Vömel (2015)

    Google Scholar 

  89. Gerlinger, P.: Numerische Verbrennungssimulation – Effiziente numerische Simulation turbulenter Verbrennung. Springer, Berlin/Heidelberg (2005)

    Google Scholar 

  90. Stüben, K.: A review of algebraic multigrid. J. Comput. Appl. Math. 128(1–2), 281–309 (2001)., issn 0377-0427

    Article  MathSciNet  MATH  Google Scholar 

  91. Adams, N.: Exascale-computing challenges and opportunities in aerodynamic simulations. 10. Tagung Fahrzeugaerodynamik. Haus der Technik, München (2012)

    Google Scholar 

  92. Behnsch, M.: Die Optimierung des Luftwiderstands in der Fahrzeugaerodynamik unter Anwendung der Adjungiertenmethode. Dissertation, Technische Universität Darmstadt (2021)

    Google Scholar 

  93. Höfer, C., Dupslaff, M.: Aerodynamic Optimization in the Early Development Phase. 13. Tagung Fahrzeugaerodynamik, Haus der Technik, München (2018)

    Google Scholar 

  94. Thévenin, D., Janiga, G. (Hrsg.): Optimization and Computational Fluid Dynamics. Springer, Berlin/eidelberg (2008). https://doi.org/10.1007/978-3-540-72153-6

    Book  MATH  Google Scholar 

  95. Cavazzuti, M.: Optimization Methods – From Theory to Scientific Design and Technological Aspects in Mechanics. Springer, Berlin/Heidelberg (2013). https://doi.org/10.1007/978-3-642-31187-1

    Book  MATH  Google Scholar 

  96. Othmer, C.: Adjoint methods for car aerodynamics. J. Math. Ind. 4, 6 (2014). https://doi.org/10.1186/2190-5983-4-6

    Article  MathSciNet  Google Scholar 

  97. Wagner, A., Lindener, N.: Die Aerodynamik des neuen Audi Q5. In: Schol, O. (Hrsg.) Der neue Audi Q5 – Entwicklung und Technik. Springer Vieweg, Wiesbaden (2008). isbn:978-3-8348-0604-8

    Google Scholar 

  98. Blumrich, R.: Vehicle aeroacoustics – today and future developments. 5th Int. Styrian Noise, Vibration & Harshness Congress „Optimising NVH in future vehicles“ Graz, 4th–6th, June (2008)

    Google Scholar 

  99. Lighthill, M.J.: On sound generated aerodynamically – I. General theory. London Proc. R. Soc. A211 (1951)

    Google Scholar 

  100. Lighthill, M.J.: On sound generated aerodynamically – II. Turbulence as a source of sound. London Proc. R. Soc. 222 (1951)

    Google Scholar 

  101. Maestrello, L.: Use of turbulent model to calculate the vibration and radiation responses of a panel, with practical suggestions for reducing sound level. J. Sound Vib. 5(3), 13–38 (1967)

    Article  Google Scholar 

  102. Blumrich, R., Hazir, A.: Berechnung der Fahrzeugaeroakustik – Methoden und Beispiele. 3. Seminar „Mess- und Analysetechnik in der Fahrzeugakustik“, 11.–12.10.2011, Stuttgart (2011)

    Google Scholar 

  103. Duncan, D. R.: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, New York, Chap. 2.2.3 (1999)

    Google Scholar 

  104. Blumrich, R.: Berechnungsmethoden für die Aeroakustik von Fahrzeugen, ATZ/MTZ-KONFERENZ AKUSTIK – Akustik zukünftiger Fahrzeuge, Stuttgart, 17.–18.05 (2006)

    Google Scholar 

  105. Bailly, C., Lafon, P., Candel, S.: A stochastic approach to compute noise generation and radiation of free turbulent flows. AIAA 95-092 (1995)

    Google Scholar 

  106. Béchara, W., Bailly, C., Lafon, P., Candel, S.: Stochastic approach to noise modelling for free turbulent flows. AIAA J. 32(4), 455–463 (1994)

    Article  MATH  Google Scholar 

  107. Glegg, S., Devenport, W.: Aeroacoustics of Low Mach Number Flows – Fundamentals, Analysis, and Measurement, 1. Aufl.. Academic Press, Elsevier, Amsterdam (2017). ISBN 978-0-1280-96512

    Google Scholar 

  108. Curle, N.: The influence of solid boundaries upon aerodynamic sound. Proc. Roy. Soc. 231(A), 505–514 (1955) London

    MathSciNet  MATH  Google Scholar 

  109. Ffowcs Williams, J.E., Hawkings, D.L.: Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. Roy. Soc. 264(A), 321–342 (1969). London

    MATH  Google Scholar 

  110. Lilley, G.M.: On the noise from air jets. In: Noise Mechanisms, AGARD CP 131, 13.1–13.12 (1973)

    Google Scholar 

  111. Howe, M.S.: Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  112. Möhring, W.: On vortex sound at low Mach number. J. Fluid Mech. 85, 685–691 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  113. Goldstein, M.E.: Aeroacoustics. McGraw-Hill Book Company, New York (1976)

    MATH  Google Scholar 

  114. Farassat, F., Myers, M.K.: Extension of Kirchhoff’s formula to radiation from moving surfaces. J. Sound Vib. 123(3), 451–460 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  115. Blumrich, R., Heimann, D.: A linearized eulerian sound propagation model for studies of complex meteorological effects. J. Acoust. Soc. Am. 112(2), 446–455 (2002)

    Article  Google Scholar 

  116. Ewert, R., Schröder, W.: Acoustic perturbation equation based on flow decomposition via source filtering. J. Comput. Phys. 188, 365–398 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  117. Jacqmot, J., Detandt, Y., Lielens, G., Copiello, D.: Vibro-aero-acoustic simulation of side mirror wind noise and strategies to evaluate pressure contributions. Proceedings of ISMA 2016, Leuven 19-21 September (2016)

    Google Scholar 

  118. Hartmann, M., Ocker, J., Lemke, T., Mutzke, A., Schwarz, V., Tokuno, H., Toppinga, R., Unterlechner, P., Wickern, G.: Wind Noise Caused by the A-Pillar and the Side Mirror Flow of a Generic Vehicle Model. In: Tagungsband 18th AIAA/CEAS Aeroacoustics Conference, Colorado Springs (USA), 04.-06. Juni (2012)

    Google Scholar 

  119. Fahy, F.: Sound and Structural Vibration. Academic Press, London (1985)

    Google Scholar 

  120. Banerjee, P.K., Butterfield, R.: Boundary Element Methods in Engineering Science. McGraw-Hill Book Company, New York (1981)

    MATH  Google Scholar 

  121. Lyon, R.: Statistical Energy Analysis of Dynamical Systems. MIT Press, Cambridge, MA (1975)

    Google Scholar 

  122. Astley, R.J.: Infinite elements. Kap. 7. In: Marburg, S., Nolte, B. (Hrsg.) Computational Acoustics of Noise Propagation in Fluids – Finite and Boundary Element Methods. Springer, Berlin (2008)

    Google Scholar 

  123. Agnantiaris, J.P., Polyzos, D., Beskos, D.E.: Three-dimensional structural vibration analysis by the Dual Reciprocity BEM. Comput. Mech. 21(4/5), 372–381 (1998)

    Article  MATH  Google Scholar 

  124. Heuer, R., Irschik, H., Ziegler, F.: A BEM-formulation of nonlinear plate vibrations. In: Kuhn, G., et al. (Hrsg.) Proc. IUTAM/IACM-Symp. on Discretization Methods in Structural Mechanics, S. 341–351. Springer, Berlin (1990)

    Chapter  Google Scholar 

  125. Hazir, A., Blumrich, R., Crouse, B., Freed, D.: Wind Noise Transmission into Convertibles by Fluid Structure Interaction, in: Aeroacoustics Research in Europe: The CEAS-ASC Report on 2008 Highlights. J. Sound Vib. 328, 213–242 (2009)

    Article  Google Scholar 

  126. Desmet, W., Sas, P., Vandepitte, D.: Performance of a wave based prediction technique for 3D coupled vibro-acoustic analysis. In: Proceedings of EuroNoise98, München, Vol. 3 (1998)

    Google Scholar 

  127. van Hal, B., Vanmaele, C., Silar, P., Priebsch, H.-H.: Hybrid Finite Element – Wave Based Method for Steady-State Acoustic Analysis. In: Proceedings of ISMA, September (2004)

    Google Scholar 

  128. Blumrich, R., Crouse, B., Freed, D., Hazir, A., Balasubramanian, G.: Untersuchung der Kopplungseffekte Innenraum-Kofferraum beim Schiebedachwummern anhand eines SAE-Modells. In: Tagungsband der DAGA ‚07, 19. bis 22. März 2007 in Stuttgart. Deutsche Gesellschaft für Akustik e.V., Berlin (2007). ISBN:978-3-9808659-3-7

    Google Scholar 

  129. Crouse, B., Senthooran, S., Balasubramanian, G., Freed, D.: Computational Aeroacoustics Investigation of Automobile Sunroof Buffeting. SAE-paper 2007-01-2403. Society of Automotive Engineers (SAE), Warrendale (2007)

    Google Scholar 

  130. Read, A., Mendonca, F., Scharm, C., Tournour, M.: Optimal Sunroof Buffeting Predictions with Compressibility and Surface Impedance Effects – American Institute of Aeronautics and Astraunotics Paper 2005-2859, S.1–13 (2005)

    Google Scholar 

  131. Seibert, W.; Ehlen, M.; Sovani, S.: Simulation of Transient Aerodyanamics-Predicting Buffeting, Roaring and Whistling using CFD – 5th MIRA International Vehicle Aerodynamics Conference, Heritage Motor Center Warwick, October (2004)

    Google Scholar 

  132. Senthooran, S., Crouse, B., Balasubramanian, G., Freed, D., Shin, S.R., Ih, K.-D.: Effect of surface mounted microphones on automobile side glass pressure fluctuations. Proceedings of 7th MIRA International Vehicle Aerodynamics Conference, Coventry 22.–23.10.2008 (2008)

    Google Scholar 

  133. Moron, P., Powell, R., Freed, D., Perot, F., Crouse, B., Neuhierl, B., Ullrich, F., Höll, M., Waibl, A., Fertl, C.: A CFD/SEA Approach for Prediction of Vehicle Interior Noise due to Wind Noise, SAE Technical Paper 2009-01-2203 (2009)

    Google Scholar 

  134. Pérot, F., Wada, K., Norisada, K., Kitada, M., Hirayama, S., Sakai, M., Imahigasi, S., Sasaki, N.: HVAC blower aero-acoustics predictions based on the lattice Boltzmann method. AJK 2011 Conference, Hamamatsu, Japan, July (2011)

    Google Scholar 

  135. Pérot, F., Kim, M.S., Freed, D.M., Dongkon, L., Ih, K.D., Lee, M.H.: Direct aeroacoustics prediction of ducts and vents noise. AIAA paper 2010-3724, 14th AIAA/CEAS Aeroacoustics Conference, Stockhom, June (2010)

    Google Scholar 

  136. Gollub, M., Semmler, C., Wiedemann, J., Gnannt, D.: Annoyance reduction of the cooling fan noise. ATZ worldwide, Ausgabe 121 07/08 (2019)

    Google Scholar 

  137. Crouse, B., Freed, D., Senthooran, S., Ullrich, F., Fertl, C.: Numerical Investigation of Underbody Aeroacoustic Noise of Automobiles SAE-Paper 2007-01-2400. Society of Automotive Engineers (SAE), Warrendale (2007)

    Google Scholar 

  138. Moron, P., Hazir, A., Crouse, B., Powell, R., Neuhierl, B., Wiedemann, J.: Hybrid Technique for Underbody Noise Transmission of Wind Noise. SAE-Paper No. 2011-01-1700 (2011)

    Google Scholar 

  139. Senthooran, S., Duncan, B., Freed, D., Hendriana, D., Powell, R., Nalevanko, J.: Design of Roof-Rack Crossbars for Production Automobiles to Reduce Howl Noise using a Lattice Boltzmann Scheme. SAE-Paper 2007-01-2398 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AUDI AG, Ingolstadt, Deutschland

    Thomas Blacha & Fabian Rösler

  2. FKFS/IFS Universität Stuttgart, Stuttgart, Deutschland

    Reinhard Blumrich

  3. Wang, Deutschland

    Norbert Grün

  4. Motorrad Werksprojekte, BMW AG, Berlin, Deutschland

    Thomas Schütz

Authors
  1. Thomas Blacha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reinhard Blumrich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Norbert Grün
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fabian Rösler
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Thomas Schütz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Schütz .

Editor information

Editors and Affiliations

  1. Motorrad Werksprojekte, BMW AG, Berlin, Deutschland

    Thomas Schütz

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Blacha, T., Blumrich, R., Grün, N., Rösler, F., Schütz, T. (2023). Numerische Methoden. In: Schütz, T. (eds) Hucho - Aerodynamik des Automobils. ATZ/MTZ-Fachbuch. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-35833-4_15

Download citation

Publish with us

Policies and ethics

Search

Navigation