An analytical and numerical study of the Diaz–Solovchuk–Sheu acoustic model: How does it compare with Blackstock's in approximating the Euler system?

Abstract

Employing primarily numerical methods, and working in 1D, we seek to determine which of two competing finite-amplitude acoustic models, specifically, those of Blackstock and Diaz et al, best approximates the acoustic special case of the Euler system. Working in the context of the classical signaling problem with sinusoidal input, we perform our assessment using not only velocity profile plots, but also a number of metrics. Our findings show, without equivocation, that the simpler Diaz et al model outperforms Blackstock's vis-à-vis all comparisons performed and metrics considered.