Multiple Scale Considerations for Sound Generation in Low Mach Number Flow

  • R. Fortenbach
  • E. Frénod
  • R. Klein
  • C. D. Munz
  • E. Sonnendrücker
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM) book series (NNFM, volume 82)


The calculation of sound generated by fluid flow at low Mach numbers formulates a multiple scale problem due to the very different space and energy scales involved. This leads to a difficult task for the construction of numerical methods which capture sound generation and propagation as well. In this paper, a multiple scale asymptotic analysis in space and in time is used to approach this problem. The analysis results in perturbation equations with source terms describing the sound propagation and generation. Furthermore this has some consequences for direct numerical simulations of flow and acoustics which are captured in numerical results for a co-rotating vortex pair. A multiple time scale asymptotic analysis covering the problem of high frequency acoustic waves is performed for a model equation and convergence results are given in one space dimension.


Mach Number Acoustic Wave Euler Equation Sound Generation Incompressible Limit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • R. Fortenbach
    • 1
  • E. Frénod
    • 2
  • R. Klein
    • 3
  • C. D. Munz
    • 1
  • E. Sonnendrücker
    • 4
  1. 1.Institut für Aero- und GasdynamikUniversität StuttgartStuttgartGermany
  2. 2.Laboratoire de Mathématiques et Applications des MathématiquesUniversité de Bretagne SudVannes CedexFrance
  3. 3.Fachbereich Mathematik und InformatikFreie Universität BerlinBerlinGermany
  4. 4.Institut de Recherche Mathématique AvancéeUniversité Louis PasteurStrasbourg CedexFrance

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