Explicit Predictor-Corrector Method for Nonlinear Acoustic Waves Excited by a Moving Wave Emitting Boundary

TL;DR

This paper introduces an explicit finite difference method for simulating nonlinear acoustic waves from moving boundaries, capturing Doppler effects and shock attenuation with high accuracy.

Contribution

It presents a novel predictor-corrector approach that accurately models nonlinear wave distortion and Doppler shifts from accelerating boundaries in one-dimensional and spherical geometries.

Findings

Successfully predicts Doppler shift in nonlinear wave distortion

Accurately models amplitude modulation due to boundary oscillation

Enhances numerical stability in shock and grid motion scenarios

Abstract

We present an explicit finite difference time domain method to solve the lossless Westervelt equation for a moving wave emitting boundary in one dimension and in spherical symmetry. The approach is based on a coordinate transformation between a moving physical domain and a fixed computational domain. This allows to simulate the combined effects of wave profile distortion due to the constitutive nonlinearity of the medium and the nonlinear Doppler modulation of a pressure wave due to the acceleration of the wave emitting boundary. A predictor-corrector method is employed to enhance the numerical stability of the method in the presence of shocks and grid motion. It is demonstrated that the method can accurately predict the Doppler shift of nonlinear wave distortion and the amplitude modulation caused by an oscillating motion of the wave emitting boundary. The novelty of the presented methodology lies in its capability to reflect the Doppler shift of the rate of nonlinear wave profile distortion and shock attenuation for finite amplitude acoustic waves emitted from an accelerating boundary.