The eigenvalue approach is a recently developed compressor stability model used to predict stall onset. In this model, the flow field from a Reynolds-averaged Navier–Stokes (RANS) simulation provides the basic flow. This paper presents the effect of the RANS methods (including the computational grid, the turbulence model, and the spatial discretization scheme) on the eigenvalue and investigates the most influencing flow structures to the eigenvalue. The test compressor was the transonic compressor of NASA Rotor 37. Three individual meshes with different grid densities were used to validate the grid independence, and the results indicated that RANS simulation and eigenvalue calculation obtain grid independence at the same grid density. Then, the effect of four turbulence models (including Spalart–Allmaras (SA) turbulence model, two different k–ε models with the extended wall function model (EWFKE), and the Yang–Shih model (YSKE), and k–ω shear stress transport (SST) model), and three spatial discretization schemes (the central scheme, the flux difference splitting (FDS) scheme, and the symmetric total variation diminishing (STVD)) was also studied. Further investigation showed that the SA turbulence model combined with the STVD scheme provided the best stall point prediction, with a relative error of 0.05%. Detailed exploration of the three-dimensional flow field revealed that there were two flow patterns near the blade tip necessary for precisely predicting stall onset: the flow blockage generated by the shockwave-tip leakage vortex (TLV) interaction, and the trailing edge separation and corresponding wake flow. The effect of the blockage was greater than the effect of the trailing edge flow.

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