An implementation of a finite difference time domain method for second-order nonlinear acoustic equations

Abstract

The framework of the numerical scheme presented in this talk is that of the finite-difference time-domain (FDTD) method published by Sparrow and Raspet [J. Acoust. Soc. Am. 90, 1991]. The method is fourth-order in space and second-order in time when propagating in homogeneous media. Our implementation resides in a Cartesian coordinate system and is meant to be used in inhomogeneous media. In the neighborhood of inhomogeneities the FDTD method is reduced to second-order in space. Of interest to our applications is the simulation of infinite domains, which is achieved using the perfectly matched layer (PML). The particular PML implementation we consider is one that was designed to absorb linear acoustic waves neglecting thermoviscous effects. In this talk, we will give an overview of our FDTD implementation and show one- and two-dimensional examples to illustrate performance in heterogeneous media that include changes in material properties and scattering objects.