Time-domain calculation of acoustical wave propagation in discontinuous media using acoustical wave propagator with mapped pseudospectral method

The acoustical Wave Propagator (AWP) scheme involves an effective time-domain calculation of sound propagation using the combination of Chebyshev polynomial expansion and the Fourier pseudospectral method. The accuracy of this scheme degrades when the media has discontinuities due to the well-known Gibbs phenomenon. In this paper, several issues concerning AWP are addressed, including an analysis of the effect of Gibbs phenomenon on the accuracy. A mapped pseudospectral method is proposed wherein the grid points are redistributed, with the emphasis across the media discontinuities by a pre-determined smooth mapping curve, then the spatial derivatives are calculated through a modified Fourier pseudospectral method. Using this method, the influence of the Gibbs phenomenon is effectively alleviated while the computational efficiency of AWP is still maintained. The superiority of this improved AWP scheme is illustrated by three one-dimensional (1-D) numerical examples.