Investigation of Dispersion-Relation-Preserving Scheme and Spectral Analysis Methods for Acoustic Waves

Abstract

Important characteristics of acoustic wave propagation are encoded in their dispersion relations. Hence, a computational algorithm, which attempts to preserve these relations, was investigated. Considering the linearized, 2-D Euler equations, simulations were performed to validate this scheme and its boundary conditions. The results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a corner boundary. The time-domain data generated by such computations were often intractable until their spectra was analyzed. For this purpose, the relative merits of three spectral analysis methods were considered. For simple, periodic waves with steep-sloped spectra, the periodogram method produced better estimates than the Blackman-Tukey method, and the Hanning window was more effective when used with the former. For chaotic waves, however, the weighted-overlapped-segment-averaging and Blackman-Tukey methods were better than the periodogram method. Therefore, it was observed that the spectral representation of time-domain data was significantly dependent on the particular method employed.