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A novel numerical solution to the diffraction term in the KZK nonlinear wave equation

Content Provider	IEEE Xplore Digital Library
Author	Hajihasani, M. Farjami, Y. Gharibzadeh, S. Tavakkoli, J.
Copyright Year	2009
Description	Author affiliation: Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran (Hajihasani, M.; Farjami, Y.; Gharibzadeh, S.) \|\| Department of Physics, Ryerson University, Toronto, Ontario, Canada (Tavakkoli, J.)
Abstract	Nonlinear ultrasound modeling is finding an increasing number of applications in both medical and industrial areas where due to high pressure amplitudes the effects of nonlinear propagation are no longer negligible. Taking nonlinear effects into account makes the ultrasound beam analysis more accurate in these applications. One of the most widely used nonlinear models for propagation of 3D diffractive sound beams in dissipative media is the KZK (Khokhlov, Kuznetsov, Zabolotskaya) parabolic nonlinear wave equation. Various numerical algorithms have been developed to solve the KZK equation. Generally, these algorithms fall into one of three main categories: frequency domain, time domain and combined time-frequency domain. The intrinsic parabolic approximation in the KZK equation imposes a limiting accuracy on the solution to the diffraction term of the KZK equation, particularly for field points in near field or in far off-axis regions. In this work we developed a novel generalized time domain numerical algorithm to solve the diffraction term of the KZK equation. The algorithm solves the Laplacian operator of the KZK equation in 3D Cartesian coordinates using a novel finite difference technique. This leads to a more accurate solution to the diffraction term in the KZK equation without compromising calculational efficiency. The outcome is a new numerical algorithm to solve the KZK equation with higher accuracy and increased efficiency compared to current algorithms.
Starting Page	1
Ending Page	9
File Size	1342707
Page Count	9
File Format	PDF
ISBN	9781424464302
e-ISBN	9781424464296
DOI	10.1109/UIA.2009.5404032
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-03-23
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Laplace equations Nonlinear equations Partial differential equations Acoustic propagation KZK nonlinear wave equation Time frequency analysis Frequency domain analysis Laplacian operator Ultrasonic imaging Diffraction Difference equations Numerical solution Acoustic diffraction Finite difference methods
Content Type	Text
Resource Type	Article

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