Comparison of homogeneous and heterogeneous modeling of transient scattering from dispersive media directly in the time domain

Accurate modeling of pulse propagation and scattering in dispersive medium is a problem in many disciplines (i.e. electromagnetics and acoustics). The inclusion of an additional term in the wave equation (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 is utilized to make these problems tractable. The resulting modified wave equation (either homogeneous or heterogeneous) is applicable to either linear or non-linear propagation. For the case of an acoustic wave propagating in a two-dimensional heterogeneous dispersive medium, a finite-difference time-domain (FDTD) 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 2D infinitely long cylinder with real world material properties. It is found that ignoring the heterogeneity in the medium can lead to significant error in the propagated/scattered field.