Modeling of pulsed finite-amplitude focused sound beams in time domain

Abstract

A time-domain numerical model is presented for simulating the finite-amplitude focused acoustic pulse propagation in a dissipative and nonlinear medium with a symmetrical source geometry. In this method, the main effects responsible in finite-amplitude wave propagation, i.e., diffraction, nonlinearity, and absorption, are taken into account. These effects are treated independently using the method of fractional steps with a second-order operator-splitting algorithm. In this method, the acoustic beam propagates, plane-by-plane, from the surface of a highly focused radiator up to its focus. The results of calculations in an ideal (linear and nondissipative) medium show the validity of the model for simulating the effect of diffraction in highly focused pulse propagation. For real media, very good agreement was obtained in the shape of the theoretical and experimental pressure-time waveforms. A discrepancy in the amplitudes was observed with a maximum of around 20%, which can be explained by existing sources of error in our measurements and on the assumptions inherent in our theoretical model. The model has certain advantages over other time-domain methods previously reported in that it: (1) allows for arbitrary absorption and dispersion, and (2) makes use of full diffraction formulation. The latter point is particularly important for studying intense sources with high focusing gains.

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

“…Although a number of temporal frequencydomain nonlinear algorithms have been reported, 17,18 the present approach is unique in that it also solves the nonlinear term in the spatial frequency domain. In this way, the interaction of waves in all directions (all wave vectors) are included automatically in the solution, not only in one direction of propagation k z as in previously used KZK or onedirection Westervelt equation models, 5,6 which is expected to be advantageous for strongly focused transducers or sources with broadband spatial spectra.…”

“…While most available forward nonlinear wave approaches assume the main nonlinear distortion in the direction normal to the source plane, 5,6 only a few works in the literature have proposed methods that are "omni-directional" in terms of the nonlinear acoustic field. 16 This ability to consider nonlinear distortion in a direction other than normal to the source plane is especially advantageous when a strongly focused or steered transducer is to be modeled.…”

“…Subsequently, a variety of Burgers equation-modified ASA simulations have been reported. 4,6 ASA solutions of the Westervelt equation 7,8 have also been studied. 9 While commonly used modeling approaches apply the KZK (Khokhlov-Zabolotskaya-Kuznetsov) equation 10,11 to solve for the nonlinear sound field, the Westervelt equation can potentially be more accurate in determining the field, since it does not rely on a parabolic approximation.…”

A review of nondestructive examination technology for polyethylene pipe in nuclear power plant

“…The use of a local K-K relation [61] was suggested for general case, but no method of converting these frequency relations to the time domain was given. Tavakkoli et al [62] derived a relation between arbitrary absorption and dispersion directly in time domain based on the use of second-order operator splitting algorithm, but the relation was unable to describe sound reflection and diffraction.…”

Arterial Plaque Characterization Using IVUS Radio-Frequency Time Echoes

“…The most widely used model for modeling finite amplitude sound beam propagation is the so-called Khokhlov, Zabolotskaya and Kuznetsov (KZK) equation (Kuznestov, 1971). Numerous methods to solve this non-linear model have been proposed (Lee & Hamilton, 1995;Tavakkoli et al, 1998). One of the difficulties for these numerical models was the computational aspect.…”