The equivalent source method (ESM) is one of the fundamental methods for reconstructing the far-field acoustic pressure and identifying the sources in aeroacoustics. However, it suffers from disturbances of near-field hydrodynamic pressure. We propose a hierarchical ESM (HESM) to suppress the disturbance by filtering out hydrodynamic pressure. The hydrodynamic pressure is filtered out using a frequency-domain convection operator. This operator replaces the prescribed convection velocity in Taylor’s frozen flow hypothesis with an adaptive complex convection velocity. The complex convection velocity is adapted in an iterative way to take into account the multiscale convection and spatial amplification of hydrodynamic pressure. The hydrodynamic pressure associated reconstruction error can thus be suppressed. The proposed HESM is compared with the Ffowcs Williams–Hawkings analogy method and the ESM that directly uses the pressure and the filtered pressure with the widely used uniform convection velocity. The use of complex convection velocity-based hydrodynamic pressure filtering mitigates the overprediction of acoustic pressure and enables precise reconstruction of both acoustic pressure directivity and spectra.
Zhou et al. (Mon,) studied this question.