Simulations and measurements of 3-D ultrasonic fields radiated by phased-array transducers using the westervelt equation

The purpose of this work is to validate, by comparing numerical and experimental results, the ability of the Westervelt equation to predict the behavior of ultrasound beams generated by phased-array transducers. To this end, the full Westervelt equation is solved numerically and the results obtained are compared with experimental measurements. The numerical implementation of the Westervelt equation is performed using the explicit finite-difference time-domain method on a three-dimensional Cartesian grid. The validation of the developed numerical code is first carried out by using experimental data obtained for two different focused circular transducers in the regimes of small-amplitude and finite-amplitude excitations. Then, the comparison of simulated and measured ultrasonic fields is extended to the case of a modified 32-element array transducer. It is shown that the developed code is capable of correctly predicting the behavior of the main lobe and the grating lobes in the cases of zero and nonzero steering angles for both the fundamental and the second-harmonic components.