To develop numerical simulation methods capable of swiftly and accurately predicting the performance of industrial centrifugal compressors basic stages, a study was undertaken using a test rig set up as a centrifugal compressor basic stage. This research discusses model simplification, mesh type and density, boundary conditions, discretization methods, and turbulence models etc, emphasizing the characteristics and applicability of five commonly employed turbulence models(k-ε, RNG k-ε, k-ω, SST, SST-RM). These methods are utilized to predict the aerodynamic performance of the compressor basic stage under various Machine Mach Numbers and are assessed against experimental data. The findings indicate that the numerical simulation can precisely predict performance at most operational points, with significant discrepancies from experimental data happening only during near-stall and near-choke conditions. Among the models studied, the SST-RM turbulence model aligns most closely with experimental results, attributed to its superior accuracy in predicting the onset and area of flow separation compared to other models. The outcomes of this research hold implications for enhancing the accuracy of numerical simulations of industrial centrifugal compressors.