Acoustic solution components beyond the common pressure variable are essential for understanding sound energy transmission and redistribution. In particular, there is a need for accurate predictions of acoustic velocity, while the presently available methods fail short in terms of accuracy and computational efficiency in a number of cases. In this paper, several time domain formulations for computing acoustic velocity in uniform flow are critically reevaluated. First, the acoustic velocity formulation of Mao and coauthors, the so-called formulation V1A and V1A-M is considered and shown to have a few inconsistencies for noise propagation in moving medium due to the missing source terms and incomplete time integration. We then demonstrate how the revealed problems can be alleviated and derive a suitably modified formulation, C1V1A-M and C2V1A-M. Furthermore, a new improved convective vector wave formulation named V2A-M is proposed. The formulation has a compact form, and its acoustic pressure and velocity solutions satisfy the governing linearized Euler equations. All considered acoustic velocity formulations are verified in comparison with the analytical solution for the problem of sound generated by a stationary monopole and a rotating dipole in uniform flow. Compact formulation V2A-M is recommended for best accuracy, universality (applicable both for acoustic near field and far field), and computational efficiency. As a proof-of-concept study for predicting acoustic field generated by aerodynamic flows, the suggested V2A-M formulation is applied for noise generated by a viscous wake flow behind the cylinder. The acoustic field predictions are compared with a direct solution of the governing Navier–Stokes equations.
He et al. (Mon,) studied this question.