Receptivity of steady shear flows is the main issues for analysis overall acoustic scattering for airfoil trailing edge and near-nozzle lip. This paper focuses on the development of accurate and robust numerical methods to accompany high-order computational aeroacoustics algorithms towards the simulation of trailing edge scattering problem in Category 4 and on the analysis of the generation mechanism of the instability wave by the interaction of trailing edge, shear layer and initial disturbance. The numerical methods is based on Grid-Optimized Dispersion- Relations-Preserving (GODRP) schemes developed with grid-optimization algorithm to make finite difference equations possess the same dispersion relations as the corresponding partial differential equations on general geometries. Acoustic/viscous splitting techniques, based on flow noise solvers using acoustic governing equations such as simplified linearized Euler equations and full linearized Euler equations, are utilized to solve the receptivity by the interactions of trailing edge, shear layer and initial disturbance. The numerical analysis consists of two steps. First, steady mean flow is determined by solution of the compressible Navier-Stokes equation using Roe's scheme for spatial discretization and local time stepping for time discretization. Then, unsteady trailing edge scattering phenomena are simulated with the CAA solvers. Through the comparison of acoustic simulations, it will be shown that mean flow gradient terms play a crucial role in triggering the instability wave
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