Czechoslovak Journal of Physics

, Volume 55, Issue 6, pp 673–680 | Cite as

Description of Finite-amplitude Standing Acoustic Waves Using Convection-diffusion Equations

  • M. Cervenka
  • M. Bednarik
Article

Abstract

This paper deals with problems of finite-amplitude standing waves in acoustical resonators of variable cross-section. Set of two one-dimensional partial differential equations in the third approximation, formulated in conservative form, is derived from the fundamental equations of gas dynamics. The model equations which takes into account external driving force, gas dynamic nonlinearities and thermoviscous dissipation are solved numerically in time domain using a central scheme developed for convection-diffusion equations integration. In this paper numerical results for closed air-filled acoustic resonators are presented.

Key words

nonlinear standing waves acoustical resonator convection-diffusion equation numerical solution 

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References

  1. [1]
    Yu.A. Illinski, B. Lipkens, T.S. Lucas, T.W. Van Doren, and E. Zabolotskaya: J. Acoust. Soc. Am. 104 (1998) 2664.CrossRefGoogle Scholar
  2. [2]
    M.F. Hamilton, Y.A. Ilinskii, and E.A. Zabolotskaya: J. Acoust. Soc. Am. 110 (2001) 109.CrossRefGoogle Scholar
  3. [3]
    F.D. Gaitan and A.A. Atchley: J. Acoust. Soc. Am. 93 (1993) 2489.Google Scholar
  4. [4]
    P.-T. Huang and J.G. Brisson: J. Acoust. Soc. Am. 102 (1997) 3256.CrossRefGoogle Scholar
  5. [5]
    E.V. Gusev: J. Acoust. Soc. Am. 103 (1998) 3717.CrossRefGoogle Scholar
  6. [6]
    V.G. Andreev, V.E. Gusev, A.A. Karabutov, O.V. Rudenko, and O.A. Sapozhnikov: Sov. Phys. Acoust. 31 (1985) 162.Google Scholar
  7. [7]
    R.R. Erickson and B.T. Zinn: J. Acoust. Soc. Am. 113 (2003) 1863.CrossRefPubMedGoogle Scholar
  8. [8]
    A. Kurganov and E. Tadmor: J. Comput. Phys 160 (2000) 241.CrossRefGoogle Scholar
  9. [9]
    A. Kurganov and G. Petrova: Numerische Math. 88 (2001) 683.Google Scholar
  10. [10]
    S. Makarov and M. Ochmann: Acustica 82 (1996) 579.Google Scholar
  11. [11]
    O.V. Rudenko and S.I. Soluyan: Theoretical foundations of nonlinear acoustics, Consultants Bureau, New York, 1977.Google Scholar
  12. [12]
    M.F. Hamilton and D.T. Blackstock: Nonlinear Acoustic, Academic Press, San Diego, 1998.Google Scholar
  13. [13]
    R. Brepta, L. Pust, and F. Turek: Mechanical vibrations, Sobotles, Prague, 1994 (in Czech).Google Scholar

Copyright information

© Institute of Physics, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • M. Cervenka
    • 1
  • M. Bednarik
    • 1
  1. 1.Dpt. of Physics, Faculty of Electrical EngineeringCzech Technical University in Prague, Technicka 2Praha 6Czech Republic

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