Direction-Independent Algorithm for Simulating Nonlinear Pressure Waves
Publication: Journal of Engineering Mechanics
Volume 143, Issue 4
Abstract
This study formulates a frequency-domain computational scheme for simulating nonlinear wave propagation in a homogeneous medium governed by the Westervelt equation. The need for such numerical treatment arises in both engineering and medical imaging applications, where finite-amplitude pressure waves trigger nonlinear effects that may critically affect the sensory data. The primary advantage of the proposed approach over commonly used approximations, which account for nonlinear effects via the Burgers’ equation, lies in its ability to handle nonlinearities due to arbitrarily inclined incident waves, which becomes especially important for focused sound beams with large apertures, i.e., wide ranges of inclination angles. The proposed direction-independent algorithm has a direct mathematical connection with the Westervelt equation, as opposed to the Burger’s equation (that relies on the plane-wave hypothesis), and has computational efficiency that is comparable to that of the traditional approach. The developments are illustrated by numerical examples that verify the method against an analytical solution and highlight the significance of accurately modeling nonlinear waves.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aanonsen, S., Barkve, T., Tjøtta, J., and Tjøtta, S. (1984). “Distortion and harmonic generation in the nearfield of a finite amplitude sound beam.” J. Acoust. Soc. Am., 75(3), 749–768.
Averkiou, M., and Cleveland, R. (1999). “Modeling of an electrohydraulic lithotripter with the KZK equation.” J. Acoust. Soc. Am., 106(1), 102–112.
Christopher, P., and Parker, K. (1991). “New approaches to nonlinear diffractive field propagation.” J. Acoust. Soc. Am., 90(1), 488–499.
Ciampa, F., Scarselli, G., Pickering, S., and Meo, M. (2015). “Nonlinear elastic wave tomography for the imaging of corrosion damage.” Ultrasonics, 62, 147–155.
Cleveland, R., Hamilton, M., and Blackstock, D. (1996). “Time-domain modeling of finite-amplitude sound in relaxing fluids.” J. Acoust. Soc. Am., 99(6), 3312–3318.
Dontsov, E., and Guzina, B. (2013a). “On the KZK-type equation for modulated ultrasound fields.” Wave Motion, 50(4), 763–775.
Dontsov, E., and Guzina, B. B. (2013b). “Dual-time approach to the numerical simulation of modulated nonlinear ultrasound fields.” Acta Acustica United Acustica, 99(5), 777–791.
Fatemi, M., and Greenleaf, J. (1999). “Vibro-acoustography: An imaging modality based on ultrasound-stimulated acoustic emission.” Proc. Natl. Acad. Sci., 96(12), 6603–6608.
Hamilton, M., and Blackstock, D. (1998). Nonlinear acoustics, Academic Press, San Diego.
Huijssen, J., and Verweij, M. D. (2010). “An iterative method for the computation of nonlinear, wide-angle, pulsed acoustic fields of medical diagnostic transducers.” J. Acoust. Soc. Am., 127(1), 33–44.
Johnson, P., Zinszner, B., Rasolofosaon, P., Cohen-Tenoudji, F., and Abeele, K. V. D. (2004). “Dynamic measurements of the nonlinear elastic parameter in rock under varying conditions.” J. Geophys. Res., 109(B2), 1–12.
Khokhlova, V., Bailey, M., Reed, J., Cunitz, B., Kaczkowski, P., and Crum, L. (2006). “Effects of nonlinear propagation, cavitation, and boiling in lesion formation by high intensity focused ultrasound in a gel phantom.” J. Acoust. Soc. Am., 119(3), 1834–1848.
Palmeri, M., Sharma, A., Bouchard, R., Nightingale, R., and Nightingale, K. (2005). “A finite-element method model of soft tissue response to impulsive acoustic radiation force.” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 52(10), 1699–1712.
Papadakis, E. (1999). Ultrasonic instruments and devices: Reference for modern instrumentation, techniques, and technology, Academic Press, New York.
Pieczonka, L., Klepka, A., Staszewski, W., and Uhl, T. (2014). “Nonlinear acoustic imaging of structural damages in laminated composites.” EWSHM—7th European Workshop on Structural Health Monitoring, Nantes, France, World Scientific, Singapore.
Sapozhnikov, O., Maxwell, A., MacConaghy, B., and Bailey, M. (2007). “A mechanistic analysis of stone fracture in lithotripsy.” J. Acoust. Soc. Am., 121(2), 1190–1202.
Sarvazyan, A., Rudenko, O., Swanson, S., Fowlkes, J., and Emelianov, S. (1998). “Shear wave elasticity imaging: A new ultrasonic technology of medical diagnostics.” Ultras. Med. Biol., 24(9), 1419–1435.
Soneson, J. E., and Myers, M. R. (2010). “Thresholds for nonlinear effects in high- intensity focused ultrasound propagation and tissue heating.” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 57(11), 2450–2459.
Tavakkoli, J., Cathignol, D., Souchon, R., and Sapozhnikov, O. (1998). “Modeling of pulsed finite-amplitude focused sound beams in time domain.” J. Acoust. Soc. Am., 104(4), 2061–2072.
van Dongen, K., Demi, L., and Verweij, M. (2012). “Numerical schemes for the iterative nonlinear contrast source method.” J. Acoust. Soc. Am., 132(3), 1918.
Zabolotskaya, E., and Khokhlov, R. (1969). “Quasi-plane waves in the nonlinear acoustics of confined beams.” Sov. Phys. Acoust., 15(1), 35–40.
Information & Authors
Information
Published In
Copyright
©2017 American Society of Civil Engineers.
History
Received: Apr 25, 2016
Accepted: Sep 15, 2016
Published online: Jan 27, 2017
Published in print: Apr 1, 2017
Discussion open until: Jun 27, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.