Time‐domain modeling of finite‐amplitude sound in relaxing fluids

A time‐domain computer algorithm that solves an augmented Burgers equation is described. The algorithm is a modification of the time‐domain code developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906–917 (1995)] for pulsed finite‐amplitude sound beams in homogeneous, thermoviscous fluids. In the present paper, effects of nonlinearity, absorption and dispersion (both thermoviscous and relaxational), geometrical spreading, and inhomogeneity of the medium are taken into account. The novel feature of the code is that effects of absorption and dispersion due to multiple relaxation phenomena are included with calculations performed exclusively in the time domain. Numerical results are compared with an analytic solution for a plane step shock in a monorelaxing fluid, and with frequency‐domain calculations for a plane harmonic wave in a thermoviscous, monorelaxing fluid. The algorithm is also used to solve an augmented KZK equation that accounts for nonlinearity, thermoviscous absorption, relaxation, and diffraction in directive sound beams. Calculations are presented which demonstrate the effect of relaxation on the propagation of a pulsed, diffracting, finite‐amplitude sound beam.