TIME-DOMAIN MODELING OF FINITE-AMPLITUDE SOUND IN RELAXING FLUIDS

A time-domain computer algorithm that solves an augmented Burgers equa tion is described. The algorithm is a modification of the time-domain code developed by Lee and Hamilton [J. Acoust. Sec. Am. 97, 906-917 (1 995)] for pulsed finite-amplitude sound beams in homogeneous, thermovi scous fluids. In the present paper, effects of nonlinearity, absorptio n and dispersion (both thermoviscous and relaxational), geometrical sp reading, and inhomogeneity of the medium an taken into account. The no vel feature of the code is that effects of absorption and dispersion d ue to multiple relaxation phenomena are included with calculations per formed exclusively in the time domain. Numerical results are compared with an analytic solution for a plane step shock in a monorelaxing flu id, and with frequency-domain calculations for a plane harmonic wave i n a thermoviscous, monorelaxing fluid. The algorithm is also used to s olve an augmented KZK equation that accounts for nonlinearity, thermov iscous absorption, relaxation, and diffraction in directive sound beam s. Calculations are presented which demonstrate the effect of relaxati on on the propagation of a pulsed, diffracting, finite-amplitude sound beam. (C) 1996 Acoustical Society of America.