Time‐domain numerical solution of the KZK equation for modeling sound beams radiated by rectangular sources

A time‐domain numerical solution of the KZK equation for modeling finite‐amplitude sound beams radiated by rectangular sources similar to those used in diagnostic ultrasound is presented. The KZK equation accounts for the effects of diffraction within the parabolic approximation, nonlinearity, and thermoviscous absorption, on the propagation of sound beams. The algorithm is based on that used by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906–917 (1995)] to model circular sources. The diffraction integral has the form of a two‐dimensional diffusion equation. The implicit backward finite difference (IBFD) scheme adapted for two dimensions is used in the near field, where the solution tends to be oscillatory. For the remainder of the field, the alternate direction implicit (ADI) method is used for higher accuracy with larger steps than those used in IBFD. The simulation model may be used to predict the FDA regulatory measurements of medical diagnostic scanners.