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Exploring Acoustic and Sound Wave Propagation Simulations: A Novel Time Advancement Method for Homogeneous and Heterogeneous Media

Exploring Acoustic and Sound Wave Propagation Simulations: A Novel Time Advancement Method for Homogeneous and Heterogeneous Media

Year:    2025

Author:    Shashi Kumar, Bangaru Ramcharan, Vivek S. Yadav, Ankit Singh, Yogesh G. Bhumkar, Manoj K. Rajpoot

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 315–349

Abstract

In this article, we have developed a new time-marching method to simulate sound and soliton propagation in homogeneous and heterogeneous media. The proposed time integration scheme can numerically preserve physical dispersion over a wide wavenumber range and conserve energy while solving wave propagation problems. Here, the Fourier stability analysis has been used to assess the numerical properties of the developed method. The proposed numerical method’s dispersion and dissipation properties have also been compared with the classical fourth-order Runge-Kutta (RK4) method. Stability property contours for the newly proposed method display that the maximum allowable time step is at least five times higher than the RK4 method. The Fourier stability analysis also explains the dispersion error associated with the used spatio-temporal discretization schemes. It is observed that the dispersion error is significantly small for the proposed time integration schemes compared with the RK4 method. The proposed methods simulate sound propagation problems with fewer computational resources that otherwise demand high computational costs. The efficacy of the proposed time integration methods has been demonstrated by solving benchmark sound wave propagation problems. Moreover, to test the developed method’s efficiency and robustness, we have performed simulations of the sound wave propagation in a layered media, corner-edge model, and damped sine-Gordon equation.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0195

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 1 : pp. 315–349

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:    Time stepping acoustic wave propagation sound wave propagation compact schemes energy conservation sine-Gordon equation.

Author Details

Shashi Kumar

Bangaru Ramcharan

Vivek S. Yadav

Ankit Singh

Yogesh G. Bhumkar

Manoj K. Rajpoot

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