Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

Abstract

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed.

Computation of nonlinear ultrasound fields using a linearized contrast source method

“…[33][34][35][36][37] Some other methods also employ the benefits of using the wavevector domain. However, unlike the INCS method, these methods either are not really omnidirectional [38][39][40][41] or require a dense sampling in the nonlinear case, 42 and none of these methods has a mechanism of iteratively improving the solution.…”

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“…A similar argument was made in a recent study. 13 Accordingly, the final approximated solution can be written as…”

A wave-vector-frequency-domain method for linear/nonlinear wave modeling in heterogeneous media

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