Acoustic shock wave propagation in a heterogeneous medium: A numerical simulation beyond the parabolic approximation

Journal of the Acoustical Society of America

Volumn 130, Issue 1, 2011, Pages 20-32

  Dagrau, Franck ^a,b   Rénier, Mathieu ^a   Marchiano, Régis ^a   Coulouvrat, François ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b DASSAULT AVIATION   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC SHOCK WAVES; ACOUSTICAL LENS; ANALYTICAL SOLUTIONS; DISPERSION EQUATIONS; EVANESCENT WAVE; HETEROGENEOUS EFFECTS; HETEROGENEOUS MEDIUM; LOSSLESS MEDIUM; NON-LINEAR ACOUSTICS; NONLINEAR TERMS; NUMERICAL CONVERGENCE; PARABOLIC APPROXIMATION; PHYSICAL ANALYSIS; SECOND-ORDER PARABOLIC APPROXIMATION; SHOCK-FITTING; SPECTRAL DOMAINS; VALIDATION TEST; WAVE FOCUSING;

COMPUTER SIMULATION; CONTROL NONLINEARITIES; CONVERGENCE OF NUMERICAL METHODS; DIFFRACTION; SHOCK WAVES; WAVES;

ACOUSTIC WAVE PROPAGATION;

ACOUSTICS; ALGORITHM; ARTICLE; COMPUTER SIMULATION; FOURIER ANALYSIS; MATHEMATICAL COMPUTING; MOTION; NONLINEAR SYSTEM; PRESSURE; RADIATION; RADIATION SCATTERING; REPRODUCIBILITY; THEORETICAL MODEL; TIME;

ACOUSTICS; ALGORITHMS; COMPUTER SIMULATION; FOURIER ANALYSIS; HIGH-ENERGY SHOCK WAVES; MODELS, THEORETICAL; MOTION; NONLINEAR DYNAMICS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PRESSURE; REPRODUCIBILITY OF RESULTS; SCATTERING, RADIATION; TIME FACTORS;

EID: 79960692612     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.3583549     Document Type: Article

References (60)

1. D. J. Maglieri and K. J. Plotkin Sonic boom., Aeroacoustics of Flight Vehicles, edited by, H. H. Hubbard, (Acoustical Society of America, New York, 1995), vol. 1, pp. 519-561
2. A. McAlpine and M. J. Fisher, On the prediction of buzz-saw noise in aero-engine inlet ducts., J. Sound Vibrat. 248, 123-149 (2001). 10.1006/jsvi.2001.3770 (Pubitemid 33105860)
3. K. L. Gee, V. W. Sparrow, M. M. James, J. M. Downing, C. M. Hobbs, T. B. Gabrielson, and A. A. Atchley, The role of nonlinear effects in the propagation of noise from high-power jet aircraft., J. Acoust. Soc. Am. 123, 4082-4093 (2008). 10.1121/1.2903871 (Pubitemid 351810144)
4. J. N. Ambrosiano, D. Plante, B. E. McDonald, and W. A. Kuperman, Nonlinear propagation in an ocean waveguide., J. Acoust. Soc. Am. 87, 1473-1481 (1990). 10.1121/1.399444 (Pubitemid 20254954)
5. K. Castor, P. Gerstoft, Ph. Roux, W. A. Kuperman, and B. E. McDonald, Long-range propagation of finite-amplitude acoustic waves in an ocean waveguide., J. Acoust. Soc. Am. 78, 672-681 (2004).
6. M. R. Bailey, V. A. Khokhlova, O. A. Sapozhnikov, S. G. Kargl, and L. A. Crum, Physical mechanisms of the therapeutic effect of ultrasound-a review., Acoust. Phys. 49, 369-388 (2003). 10.1134/1.1591291 (Pubitemid 37056472)
7. F. A. Duck, Nonlinear acoustics in diagnostic ultrasound., Ultrasound Med. Biol. 28, 1-18 (2002). 10.1016/S0301-5629(01)00463-X (Pubitemid 34202297)
8. A. J. Coleman and J. E. Saunders, A review of the physical properties and biological effects of the high amplitude acoustic fields used in extra-corporeal lithotripsy., Ultrasonics 31, 75-89 (1993). 10.1016/0041- 624X(93)90037-Z (Pubitemid 23640744)
9. M. Delius, History of shock wave lithotripsy., Nonlinear Acoustics at the Turn of the Millenium, Proc. 15th Int. Symposium on Nonlinear Acoustics 1999, edited by, W. Lauterborn, and, T. Kurz, (AIP, Melville, NY, 1999), pp. 23-32.
10. M. S. Canney, M. R. Bailey, L. A. Crum, V. A. Khokhlova, and O. A. Sapozhnikov, Acoustic characterization of high intensity focused ultrasound fields: A combined measurement and modeling approach. J. Acoust. Soc. Am. 124, 2406-2420 (2008). 10.1121/1.2967836
11. E. A. Zabolotskaya and R. V. Khokhlov, Quasi-plane waves in the non-linear acoustics of confined beams., Sov. Phys. Acoust. 15, 35-40 (1969).
12. V. P. Kuznetsov, Equations of nonlinear acoustics., Sov. Phys. Acoust. 16, 467-470 (1970).
13. B. K. Novikov, O. V. Rudenko, and V. I. Timoshenko, Nonlinear Underwater Acoustics. Acoustical Society of America (Translation Books, New York, 1987), pp. 109-118.
14. M. A. Averkiou and R. O. Cleveland. Modeling of an electrohydraulic lithotripter with the KZK equation., J. Acoust. Soc. Am. 106, 102-112 (1999). 10.1121/1.427039 (Pubitemid 29323640)
15. A. Bouakaz, E. Closset, and D. Cathignol, Harmonic ultrasonic field of medical phased arrays: Simulations and experiments., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 (6), 730-735 (2003). 10.1109/TUFFC.2003.1209563
16. V. F. Humphrey, Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging., Ultrasonics 38, 267-272 (2000). 10.1016/S0041-624X(99)00122-5 (Pubitemid 30592566)
17. X. Yang and R. O. Cleveland, Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging., J. Acoust. Soc. Am. 117, 113-123 (2004). 10.1121/1.1828671 (Pubitemid 40130138)
18. R. Marchiano, F. Coulouvrat, and J.-L. Thomas, Nonlinear focusing of acoustic shock waves at a caustic cusp., J. Acoust. Soc. Am. 117, 566-577 (2005). 10.1121/1.1841551 (Pubitemid 40223418)
19. A. A. Piacsek, Atmospheric turbulence conditions leading to focused and folded sonic boom wave fronts., J. Acoust. Soc. Am. 111, 520-529 (2002). 10.1121/1.1377631 (Pubitemid 34113263)
20. S. Baskar, F. Coulouvrat, and R. Marchiano, Nonlinear reflection of grazing acoustical shock waves: unsteady transition from von Neumann to Mach to Snell-Descartes reflections., J. Fluid Mech. 575, 27-55 (2007). 10.1017/S0022112006003752 (Pubitemid 46404084)
21. M. Brio and J. K. Hunter, Mach reflection for the two-dimensional Burgers' equation., Phys. D 60, 194-207 (1992). 10.1016/0167-2789(92)90236-G
22. R. Marchiano, F. Coulouvrat, and J.-L. Thomas, Numerical investigation of the properties of nonlinear acoustical vortices through weakly heterogeneous media., Phys. Rev. E, 77: 016605 (1-11), (2008). 10.1103/PhysRevE.77.016605 (Pubitemid 351169680)
23. Ph. Blanc-Benon, B. Lipkens, L. L. Dallois, M. F. Hamilton, and D. T. Blackstock, Propagation of finite amplitude sound through turbulence: Modeling with geometrical acoustics and the parabolic approximation., J. Acoust. Soc. Am. 111, 487-498 (2002). 10.1121/1.1404378 (Pubitemid 34113260)
24. Y. Jing and R. O. Cleveland, Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media., J. Acoust. Soc. Am. 122, 1352-1364 (2007). 10.1121/1.2767420 (Pubitemid 47560501)
25. M. V. Aver'yanov, V. A. Khokhlova, O. A. Sapozhnikov, Ph. Blanc-Benon, and R. O. Cleveland, Parabolic equation for nonlinear acoustic wave propagation in homogeneous moving media., Acoust. Phys. 52, 623-632 (2006). 10.1134/S1063771006060017 (Pubitemid 44833292)
26. M. F. Hamilton and D. T. Blackstock, Nonlinear Acoustics (Academic Press, San Diego, 1988), pp. 309-341.
27. W. F. Ames, Numerical Methods for Partial Differential Equations (Academic Press, San Diego, 1977), pp. 307-310.
28. N. S. Bakhvalov, Ya. M. Zhileikin, E. A. Zabolotskaya, and R. V. Khokhlov, Nonlinear propagation of a sound beam in a nondissipative medium., Sov. Phys. Acoust. 22, 272-274 (1976).
29. V. A. Khokhlova, A. E. Ponomarev, M. A. Averkiou, and L. A. Crum, Nonlinear pulsed ultrasound beams radiated by a rectangular focused diagnostic transducers., Acoust. Phys. 53, 481-489 (2006). 10.1134/S1063771006040178 (Pubitemid 44048552)
30. Y. S. Lee and M. F. Hamilton, Time-domain modeling of pulsed finite-amplitude sound beams., J. Acoust. Soc. Am. 97, 906-917 (1995). 10.1121/1.412135
31. S. I. Aanonsen, T. Barkve, J. Naze Tjtta, and S. Tjtta, Distortion and harmonic generation in the nearfield of a finite amplitude sound beam., J. Acoust. Soc. Am. 75, 749-768 (1984). 10.1121/1.390585
32. R. J. Leveque. Numerical Methods for Conservation Laws (Birkhauser, Basel, 1992), pp. 114-157.
33. F. Coulouvrat, A quasi exact shock fitting algorithm for general nonlinear progressive waves., Wave Motion 49, 97-107 (2009). 10.1016/j.wavemoti.2008.09.002
34. T. D. Mast, Fresnel approximations for acoustics fields of rectangularly symmetric sources. J. Acoust. Soc. Am. 121, 3311-3322 (2007). 10.1121/1.2726252 (Pubitemid 46872090)
35. F. Coulouvrat, Nonlinear parabolic wave equation in ray coordinates for high frequency acoustical propagation in a inhomogeneous and high speed moving fluid., Wave Motion 45, 804-820 (2008). 10.1016/j.wavemoti.2008.02.002
36. J. F. Claerbout, Fundamentals of Geophysical Data Processing (McGraw-Hill, New York, 1976), pp. 194-207.
37. B. E. McDonald, High-angle formulation for the nonlinear progressive-wave equation model., Wave Motion 31, 165-171 (2000). 10.1016/S0165-2125(99)00044-X
38. L. Ganjehi, Ondes de choc acoustiques en milieu hétérogne, des ultrasons au bang sonique (Acousical shock waves in heterogeneous media: From ultrasonic waves to sonic boom), Ph.D. dissertation, Université Pierre et Marie Curie, Paris, 2008.
39. Th. Auger and F. Coulouvrat, Numerical simulation of sonic boom focusing. AIAA J. 40, 1726-1734 (2002). 10.2514/2.1877 (Pubitemid 35019517)
40. F. Coulouvrat, Sonic boom in the shadow zone: A geometrical theory of diffraction., J. Acoust. Soc. Am. 111, 499-508 (2002). 10.1121/1.1371973 (Pubitemid 34113261)
41. P. Boulanger, R. Raspet, and H. E. Bass, Sonic boom propagation through realistic turbulence., J. Acoust. Soc. Am. 98, 3412-3417 (1995). 10.1121/1.413792
42. M. K. Kelly, R. Raspet, and H. E. Bass, Scattering of sonic booms by anisotropic turbules., J. Acoust. Soc. Am. 107, 3059-3064 (2000). 10.1121/1.429334 (Pubitemid 30397000)
43. T. Christopher and K. J. Parker, New approaches to nonlinear diffractive field propagation., J. Acoust. Soc. Am. 90, 488-499 (1991). 10.1121/1.401274
44. J. Tavakkoli, D. Cathignol, R. Souchon, and O. A. Sapozhnikov, Modeling of pulsed finite-amplitude focused sound beams in time domain., J. Acoust. Soc. Am. 104, 2061-2072 (1998). 10.1121/1.423720 (Pubitemid 28463100)
45. V. A. Khokhlova, R. Souchon, J. Tavakkoli, O. A. Sapozhnikov, and D. Cathignol, Numerical modeling of finite-amplitude sound beams: Shock formation in the near field of a cw plane piston source., J. Acoust. Soc. Am. 110, 95-108 (2001). 10.1121/1.1369097 (Pubitemid 32642552)
46. R. J. Zemp, J. Tavakkoli, and R. S. Cobbold, Modeling of nonlinear ultrasound propagation in tissue from array transducers., J. Acoust. Soc. Am. 113, 139-152 (2003). 10.1121/1.1528926 (Pubitemid 36105668)
47. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New-York, 1968), pp. 45-50.
48. G. Taraldsen, Derivation of a generalized Westervelt equation for nonlinear medical ultrasound., J. Acoust. Soc. Am. 109, 1329-1333 (2001). 10.1121/1.1344157 (Pubitemid 32275176)
49. F. Dagrau, Simulation de la propagation du bang sonique: de la CFD l'acoustique non linéaire (Numerical simulation of the sonic boom propagation: From CFD to nonlinear acoustics), Ph.D. dissertation, Université Pierre et Marie Curie, Paris, 2009.
50. G. Cohen, Higher-Order Numerical Methods for Transient Wave Equations (Springer Verlag, Berlin, 2002), pp. 307-330.
51. F. Collino, Perfectly matched absorbing layers for the paraxial equations., J. Comp. Phys. 131, 164-180 (1997). 10.1006/jcph.1996.5594 (Pubitemid 127341388)
52. W. D. Hayes, R. C. Haefeli, and H. E. Kulsrud, Sonic boom propagation in a stratified atmosphere with computer program, Technical Report, NASA CR-1299 (1969).
53. L. Landau, On shock waves at large distances from the place of their origin., J. Phys. USSR 9, 496-500 (1945).
54. J. M. Burgers, Further statistical problems connected with the solution of a simple nonlinear partial differential equation., Proc. Kon. Nederlandse Akad. van Wet., Ser. B 57, 159-169 (1954).
55. P. M. Morse, Vibration and Sound (McGraw-Hill, New York, 1948), pp. 347-350.
56. F. Coulouvrat, Focusing of weak acoustic shock waves at a caustic cusp., Wave Motion 32, 233-245 (2000). 10.1016/S0165-2125(00)00045-7
57. J.-P. Guiraud, Acoustique géométrique, bruit balistique des avions supersoniques et focalisation (Geometrical acoustics, ballistic noise of supersonic aircraft and focusing)., J. Mécan. 4, 215-267 (1965).
58. A. D. Pierce, Acoustics: An Introduction to its Physical Principles and Applications (Acoustical Society of America, New York, 1989), pp. 460-469.
59. P. L. Marston, Geometrical and catastrophe optics methods in scattering., High Frequency and Pulse Scattering. Physical Acoustics, edited by, A. D. Pierce, and, R. N. Thurston, (Academic Press, San Diego, 1992), Vol. XXI, pages 1-234
60. A. D. Pierce and D. J. Maglieri, Effects of atmospheric irregularities on sonic-boom propagation., J. Acoust. Soc. Am. 51, 702-721 (1972). 10.1121/1.1912904