This study systematically investigates the coupling between acoustic sources and radiated sound in the acoustic perturbation equations (APE1 and APE2), where the acoustic source terms are constructed from incompressible flow simulations, as well as the influence of source truncation and mesh resolution on the accuracy of acoustic predictions. Both formulations are implemented in the open-source platform OpenFOAM and validated using a canonical two-dimensional circular–cylinder flow at Re=150. The flow field is obtained by solving the incompressible Navier–Stokes equations, while the acoustic field is computed through APE1 and APE2. Modal analysis, Helmholtz decomposition, and beamforming are employed to separate the acoustic and hydrodynamic pressure components and to identify the radiation characteristics of spurious sources. To suppress artificial radiation caused by abrupt source truncation, a smooth Hanning-based truncation approach is proposed and quantitatively assessed. In addition, a systematic mesh resolution study is conducted, leading to the establishment of non-dimensional accuracy criteria for both formulations. Results indicate that APE1 provides stable and accurate acoustic predictions even on moderately refined grids when smooth truncation is applied, whereas APE2 effectively suppresses hydrodynamic contamination, exhibits compact source localization near the wall, and therefore requires no truncation but finer spatial resolution. The proposed truncation and resolution strategies are further validated through simulations of tandem square cylinders, demonstrating good generality for multi-bluff-body configurations. These findings provide practical guidelines for balancing computational cost and acoustic accuracy in incompressible hybrid aeroacoustic simulations.
Yuan et al. (Sun,) studied this question.