A semi-analytical method for two-dimensional sound propagation in subsonic parallel mean flow

This paper presents a semi-analytical method, referred to as the linear-velocity-profile fast field program (LFFP), for predicting two-dimensional sound fields in ambient parallel mean flows. The proposed method incorporates the linear velocity layering method into the fundamental framework of fast field program (FFP) to achieve reduced computational costs and enhanced precision, particularly under high-velocity gradient conditions. The accuracy of LFFP is validated through a two-dimensional jet case by comparison with the linearized Euler equation in frequency-domain. In shear flow cases, results obtained from various combinations of Mach number difference and shear layer thickness suggest that the reason for the higher precision of LFFP, compared to traditional FFP, primarily arises from its consideration of the second velocity gradient term in the Pridmore-Brown operator within each single layer. To systematically and mathematically explain this observation, residual analysis is introduced. Furthermore, based on the residual analysis, the multi-staircase layering model is subsequently developed to improve computational efficiency and adapt to sound field calculations in environments with multiple vertically variable ambient quantities.