Exploring Acoustic and Sound Wave Propagation Simulations: A Novel Time Advancement Method for Homogeneous and Heterogeneous Media (Advances in Applied Mathematics and Mechanics, 2024)
In this article, we have developed a new time-marching method to simulatesound and soliton propagation in homogeneous and heterogeneous media. The proposed time integration scheme can numerically preserve physical dispersion over awide 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 anddissipation 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 RK4method. The Fourier stability analysis also explains the dispersion error associatedwith the used spatio-temporal discretization schemes. It is observed that the dispersion error is significantly small for the proposed time integration schemes comparedwith the RK4 method. The proposed methods simulate sound propagation problemswith 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 developedmethod’s efficiency and robustness, we have performed simulations of the sound wavepropagation in a layered media, corner-edge model, and damped sine-Gordon equation.