Finite-difference time-domain simulation of acoustic propagation in heterogeneous dispersive medium

Accurate modeling of pulse propagation and scattering is a problem in many disciplines (i.e., electromagnetics and acoustics). It is even more tenuous when the medium is dispersive. Blackstock [D. T. Blackstock, J Acoust Soc Am 77 (1985) 2050] first proposed a theory that resulted in adding an additional term (the derivative of the convolution between the causal time-domain propagation factor and the acoustic pressure) that takes into account the dispersive nature of the medium. Thus deriving a modified wave equation applicable to either linear or nonlinear propagation. For the case of an acoustic wave propagating in a two-dimensional heterogeneous dispersive medium, a finite-difference time-domain representation of the modified linear wave equation can been used to solve for the acoustic pressure. The method is applied to the case of scattering from and propagating through a 2-D infinitely long cylinder with the properties of fat tissue encapsulating a cyst. It is found that ignoring the heterogeneity in the medium can lead to significant error in the propagated/scattered field. (c) 2007 Wiley Periodicals, Inc.