Abstract: Complex flows such as shear layers and vortices can change the propagation characteristics of aerodynamic noise, resulting in phenomena of refraction, reflection, and scattering, which have an impact on acoustic source measurement and identification. The linearized equation-based algorithm is an important tool for simulating the propagation of acoustic waves in complex flows. This paper briefly outlines the research carried out by our group in recent years to address the challenges associated with acoustic propagation in non-uniform flow. Specifically, we propose an improved gradient term suppression method to mitigate numerical instability when calculating acoustic wave propagating through shear layers using the linearized equations; develop a Boltzmann model-based flux solver under the finite volume method for the linearized equations to simulate acoustic wave propagation in flow fields containing complex geometries; establish a simplified linearized lattice Boltzmann method to reduce the computational memory requirements when using the lattice Boltzmann method; and evaluate the influences of shear layer characteristics on sound source localization, and establish a mathematical model of localization error with jet Mach number and Strouhal number to provide reference for improving the experimental measurement accuracy.