Document Type : Full Research Paper


1 M.Sc Graduated, School of Electrical Engineering, Sharif University of Technology

2 Assistant Professor, School of Computer Engineering, University of Qom

3 Assistance Professor, School of Electrical Engineering, Sharif University of Technology

4 Assistant Professor, School of Physics, Ryerson University



Increasing number of diagnostic and therapeutic applications of finite amplitude ultrasound in medicine and biology has motivated researchers toward more accurate modeling and more efficient simulation of nonlinear ultrasound regime. 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 the three main categories: frequency domain, time domain and combined time-frequency domain. The intrinsic parabolic approximation in the KZK equation imposes limiting accuracy in the solution to the diffraction term of the KZK equation particularly for field points close to the source or in far off-axis region. 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 the 3D Cartesian coordinates using novel 5-point Implicit Backward Finite Difference (IBFD) and 5-point Crank-Nicolson Finite Difference (CNFD) techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in a more accurate solution to the diffraction term in the KZK equation. Comparison between results obtained with the new algorithm and the previously-published data for rectangular ultrasound sources is presented.


Main Subjects

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