The compressible formulation of the time-harmonic linearized Navier-Stokes (LNS) method
for acoustic receptivity prediction is described. The efficiency of the proposed approach
is rooted in the assumption that the problems of interest only require the time-asymptotic
solution of a few select frequencies. We explore the parabolic nature of the basic flow and of the
Stokes layer, and we implement an efficient LU decomposition method to obtain the roughness-
induced steady perturbation and Tollmien-Schlichting wave. Before attempting to predict
receptivity amplitudes, the compressible Stokes layer solution based on the linearized unsteady
boundary layer equations is validated in the subsonic regime against an Orr-Sommerfeld-type
equation. Further testing of the model is conducted by reproducing the experiments of King
&
Breuer in near incompressible conditions. The results are consistent with the analogue
incompressible receptivity model, and reveal excellent agreement with finite-Reynolds number
theory for two-dimensional instabilities. Qualitative agreement with the experimental results
for oblique waves is observed. Differences can be partially explained by the choice of physical
model used to determine the N-factors, which in turn are used to extrapolate amplitudes to
the first-branch of stability. Ultimately, a comprehensive comparison with direct-numerical-
simulation-based subsonic receptivity amplitudes is conducted, demonstrating the correctness
of the mathematical model and numerical implementation described herein.