12 April 2005 Numerical methods for axisymmetric and 3D nonlinear beams
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Time domain algorithms that solve the Khokhlov--Zabolotzskaya--Kuznetsov (KZK) equation are described and implemented. This equation represents the propagation of finite amplitude sound beams in a homogenous thermoviscous fluid for axisymmetric and fully three dimensional geometries. In the numerical solution each of the terms is considered separately and the numerical methods are compared with known solutions. First and second order operator splitting are used to combine the separate terms in the KZK equation and their convergence is examined.
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Gianmarco F. Pinton, Gianmarco F. Pinton, Gregg E. Trahey, Gregg E. Trahey, } "Numerical methods for axisymmetric and 3D nonlinear beams", Proc. SPIE 5750, Medical Imaging 2005: Ultrasonic Imaging and Signal Processing, (12 April 2005); doi: 10.1117/12.595910; https://doi.org/10.1117/12.595910

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