Efficient sound modeling for acoustic monitoring in complex temperature and wind fields

Abstract

Active monitoring of atmospheric processes, combustion characteristics in burning furnaces, and various industrial applications relies on precise reconstruction of temperature and medium flow fields. This paper derives a novel trajectory equation for modeling sound wave trajectories within complex temperature and wind fields. Unlike traditional ray-equations widely used in dynamic media, the newly formulated trajectory equation is based on the propagation distance rather than the sound wave's time of flight. This alteration directly incorporates trajectory curvature, facilitating the development of efficient path tracing algorithms. In scenarios where wind speed is significantly lower than the Laplace sound speed and the wavefront's normal direction aligns closely with the sound wave's propagating direction, a simplified trajectory equation is derived. We develop a shooting method to numerically solve both the general and simplified trajectory equations. The fourth-order Runge-Kutta method (RK4) is employed, known for its high accuracy with a local fifth-order truncation error. A benchmark test, utilizing an analytically known path for the sound wave, confirms the shooting method's high precision. One notable strength of this approach lies in its computational efficiency. Tracing sound trajectories originating from a single source is achieved within seconds or tens of seconds on standard personal computers across various numerical examples. Furthermore, the shooting method effectively models sound trajectories in complex temperature and wind fields, such as those encountered in the near-surface atmosphere and high-temperature furnaces. Due to their efficiency and accuracy, the newly formulated trajectory equations and the accompanying shooting method are not only well suited for acoustic modeling, as demonstrated in this study, but are also poised for seamless integration into acoustic tomography systems in future studies.