Equations for finite-difference, time-domain simulation of sound propagation in moving media with arbitrary Mach numbers

Finite-difference time-domain (FDTD) techniques for sound propagation have become increasingly popular. In moving media, such as the atmosphere, starting equations for FDTD calculations are often limited to low Mach numbers, which may result in significant errors. In this article, two coupled equations for the sound pressure and acoustic particle velocity are derived from the linearized fluid dynamic equations. These coupled equations are valid for arbitrary Mach numbers, in the high-frequency approximation, and can be used in FDTD calculations and other methods for sound propagation in moving media. For low Mach numbers, the equations derived are valid for arbitrary frequencies and are consistent with equations from the literature.