Robin O. Cleveland
Mark F. Hamilton
David T. Blackstock
Appl. Res. Labs., Univ. of Texas, Austin, TX 78713-8029, and Dept. of Mech. Eng., Univ. of Texas, Austin, TX 78712-1063
Two similar time-domain computer algorithms are described, one that solves an augmented Burgers equation and the other an augmented KZK equation. Both codes include the effects of nonlinearity, absorption, and dispersion (both thermoviscous and relaxational). The Burgers code also accounts for geometrical spreading and inhomogeneity of the medium. The KZK code accounts for diffraction in directive sound beams [Lee and Hamilton, J. Acoust. Soc. Am. 97, 906--917 (1995)]. The novel feature of the codes is that they run exclusively in the time domain, even for the calculation of absorption and dispersion due to multiple relaxation phenomena. For a plane step shock in a monorelaxing fluid, the results from the Burgers code are compared with an analytical prediction of Polyakova et al. [Sov. Phys. Acoust. 8, 78--82 (1962)]. Numerical results are also compared with frequency-domain calculations for a plane harmonic wave in a thermoviscous, monorelaxing fluid. Both comparisons reveal excellent agreement. New results include calculations showing the effect of relaxation on the propagation of a pulsed, diffracting, finite-amplitude sound beam. [Work supported by NASA, the Office of Naval Research, and the IR&D Program at ARL.]