Modeling weakly nonlinear acoustic wave propagation

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 60, Issue 4, 2007, Pages 473-495

  Christov, Ivan ^a,d   Christov, C I ^b   Jordan, P M ^c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^c NAVAL RESEARCH LABORATORY   (United States)

^d Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; COMPRESSIBLE FLOW; EULER EQUATIONS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

INVISCID KUZNETSOV EQUATION; LIGHTHILL-WESTERVELT EQUATION; WEAKLY NONLINEAR EQUATION;

ACOUSTIC WAVE PROPAGATION;

EID: 36349032333     PISSN: 00335614     EISSN: 14643855     Source Type: Journal    
DOI: 10.1093/qjmam/hbm017     Document Type: Article

References (45)

1. P. A. Thompson, Compressible-Fluid Dynamics (McGraw Hill, New York 1972).
2. L. I. Sedov, Mechanics of Continuous Media (World Scientific, River Edge, NJ 1997), Chapter 8.
3. K. Naugolnykh and L. Ostrovsky, Nonlinear Wave Processes in Acoustics (Cambridge University Press, New York 1998), Chapter 1.
4. M. F. Hamilton and C. L. Morfey, Model equations, Nonlinear Acoustics: Theory and Applications (ed. M. F. Hamilton & D. T. Blackstock; Academic Press, New York 1997) 41-63.
5. S. Makarov and M. Ochmann, Nonlinear and thermoviscous phenomena in acoustics, Part I, Acoustica 82 (1996) 579-606.
6. S. Makarov and M. Ochmann, Nonlinear and thermoviscous phenomena in acoustics, Part II, ibid. 83 (1997) 197-222.
7. S. Makarov and M. Ochmann, Nonlinear and thermoviscous phenomena in acoustics, Part III, ibid. 83 (1997) 827-846.
8. V. P. Kuznetsov, Equations of nonlinear acoustics, Sov. Phys. Acoust. 16 (1971) 467-470.
9. P. J. Westervelt, Parametric acoustic array, J. Acoust. Soc. Amer. 35 (1963) 535-537.
10. I. Christov, P. M. Jordan and C. I. Christov, Nonlinear acoustic propagation in homentropic perfect gases: A numerical study, Phys. Lett. A 353 (2006) 273-280.
11. I. Christov, C. I. Christov and P. M. Jordan, Cumulative nonlinear effects in acoustic wave propagation, Comput. Model. Engng Sci. 17 (2007) 47-54.
12. E. R. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics (Springer, Berlin 1999).
13. R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems (Cambridge University Press, New York 2002).
14. Y. Kagawa, T. Tsuchiya, T. Yamabuchi, H. Kawabe and T. Fuji, Finite element simulation of non-linear sound wave propagation, J. Sound Vib. 154 (1992) 125-145.
15. T. Tsuchiya and Y. Kagawa, A simulation study on nonlinear sound propagation by a finite element approach, J. Acoust. Soc. Jpn (E) 13 (1992) 223-230.
16. P. M. Jordan and C. I. Christov, A simple finite-difference scheme for modeling the finite-time blow-up of acoustic acceleration waves, J. Sound Vib. 281 (2005) 1207-1216.
17. Y. Inoue and T. Yano, Propagation of strongly nonlinear plane N waves, J. Fluid Mech. 341 (1997) 59-76.
18. T. R. Fogarty and R. J. LeVeque, High-resolution finite-volume methods for acoustic waves in periodic and random media, J. Acoust. Soc. Amer. 106 (1999) 17-28.
19. P. J. Chen, Growth and decay of waves in solids, Handbuch der Physik Vol. VIa/3 (ed. S. Flügge & C. Truesdell; Springer, Berlin 1973) 303-402.
20. B. D. Coleman and M. E. Gurtin, Growth and decay of discontinuities in fluids with internal state variables, Phys. Fluids 10 (1967) 1454-1458.
21. Y. B. Fu and N. H. Scott, The transition from acceleration wave to shock wave, Int. J. Engng Sci. 29 (1991) 617-624.
22. T. Y. Thomas, The growth and decay of sonic discontinuities in ideal gases, J. Math. Mech. 6 (1957) 455-469.
23. A. R. Elcrat, On the propagation of sonic discontinuities in the unsteady flow of a perfect gas, Int. J. Engng Sci. 15 (1977) 29-34.
24. P. M. Jordan and B. Straughan, Acoustic acceleration waves in homentropic Green and Naghdi gases, Proc. R. Soc. A 462 (2006) 3601-3611.
25. M. F. McCarthy, Singular surfaces and waves, Continuum Physics, Vol. II (ed. A. C. Eringen; Academic Press, London 1975) 449-521.
26. K. A. Lindsay and B. Straughan, Acceleration waves and second sound in a perfect fluid, Arch. Ration. Mech. Anal. 68 (1978) 53-87.
27. B. Straughan, Nonlinear waves in a general magnetic fluid, J. Appl. Math. Phys. 37 (1986) 274-279.
28. G. Saccomandi, Acceleration waves in a thermo-microstretch fluid, Int. J. Non-Linear Mech. 29 (1994) 809-817.
29. M. Ostoja-Starzewski and J. Trȩbicki, On the growth and decay of acceleration waves in random media, Proc. R. Soc. A 455 (1999) 2577-2614.
30. R. Quintanilla and B. Straughan, A note on discontinuity waves in type III thermoelasticity, ibid. 460 (2004) 1169-1175.
31. P. M. Jordan, Growth and decay of acoustic acceleration waves in Darcy-type porous media, ibid. 461 (2005) 2749-2766.
32. A. Morro, Jump relations and discontinuity waves in conductors with memory, Math. Comput. Model. 43 (2006) 138-149.
33. M. Ciarletta and B. Straughan, Thermo-poroacoustic acceleration waves in elastic materials with voids, J. Math. Anal. Appl. 333 (2007) 142-150.
34. J. Jaisaardsuetrong and B. Straughan, Thermal waves in a rigid heat conductor, Phys. Lett. A 366 (2007) 433-436.
35. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey and D. E. Knuth, On the Lambert W function, Adv. Comput. Math. 5 (1996) 329-359.
36. R. T. Beyer, The parameter B/A, Nonlinear Acoustics (ed. M. F. Hamilton & D. T. Blackstock; Academic Press, New York 1997) 25-39.
37. H. Ockendon and J. R. Ockendon, Nonlinearity in fluid resonances, Meccanica 36 (2001) 297-321.
38. D. G. Crighton, Model equations of nonlinear acoustics, Ann. Rev. Fluid Mech. 11 (1979) 11-33.
39. M. J. Lighthill, On sound generated aerodynamically. I. General theory, Proc. R. Soc. A 211 (1952) 564-587.
40. H. C. Woodsum and P. J. Westervelt, A general theory for the scattering of sound by sound, J. Sound Vib. 76 (1981) 179-186.
41. G. B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York 1974).
42. H. Lin and A. J. Szeri, Shock formation in the presence of entropy gradients, J. Fluid Mech. 431 (2001) 161-188.
43. A. Harten, P. D. Lax and B. van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev. 25 (1983) 35-61.
44. C. Truesdell and K. R. Rajagopal, An Introduction to the Mechanics of Fluids (Birkhäuser, Boston 2000), Chapter 11.
45. D. R. Bland, Wave Theory and Applications (Oxford University Press, Oxford 1988).