Computational Study of Wave Distortion and Dissipation in Nonlinear Acoustics

Abstract

Nonlinear acoustic wave propagation in high-velocity fluids is a complex phenomenon influenced by the combined effects of nonlinearity, convection, and viscous dissipation. The proposed analysis is essential due to the unique influence of high-speed flow on acoustic waves. We use a Burgers-type nonlinear acoustic model to account for waveform distortion, amplitude variation, and energy attenuation as the wave propagates. A finite difference method is used to solve the governing equations; we ensure numerical stability through careful selection of discretization parameters and the Courant–Friedrichs–Lewy (CFL) condition. An interactive simulation with a MATLAB-based GUI (Graphical user interface) is built that allows the physical parameters to be changed, and propagation variables to be visualized and updated in real time. The results show that linear effects are responsible for wave steepening and distortion, while viscous dissipation arises dispersion. In addition, it is found that not exploiting the parameters properly might lead to numerical issues or unphysical growth of the amplitude. These results demonstrate the necessity of balancing nonlinearity and dissipation to derive realistic and stable results. In summary, this research contributes significantly to the understanding nonlinear acoustic effects and presents a flexible computational framework for future studies in high-velocity fluid settings.