A Numerical and Bi-directional Study of the Blackstock and Diaz–Solovchuk–Sheu Models for Approximating the Euler System

Abstract

This paper is a revisitation of a prior analytical and numerical study of two competing finite-amplitude models of one-dimensional acoustic propagation in perfect gases, due to Blackstock and Diaz et al., through comparison with the Euler system specialized to this case. In this study, we consider alternative time-stepping approaches, to validate the findings of the prior numerical study, and refined numerical boundary conditions. We also investigate whether the approximate models can be described as nearly equivalent to the Euler system with modified parameters, and the behavior of reflected waves produced by all three models.