Aerodynamics phenomena in compressors are highly unsteady and turbulent. Selecting a proper turbulence-modeling method is significant to reveal the complex flow mechanism in turbomachines. In the current paper, the shear stress transport (SST) model as an unsteady Reynolds-averaged Navier-Stokes (RANS) method, the scale-adaptive simulation (SAS) model, and the zonal wall-modeled large eddy simulation (zonal-LES) as two hybrid scale-resolving simulation approaches have been compared. These turbulence-modeling methods were employed to simulate a single rotor of a low-speed research compressor featuring a tip clearance of 1.3% of chord length. Comparisons were made between the simulation results and the experimental data at three operating points, and the flow fields at the design point have been specifically discussed in detail. The results show that the advantage of the zonal-LES model becomes obvious as the compressor throttles. The zonal-LES model brings a significant improvement over both the SST model and the SAS model in capturing the experimental data, especially the velocity distribution in the low-span region, as well as the loss near the endwalls. The SAS model as a scale-resolving method presents no benefits in predicting the relevant flow compared with the SST model, as the activation of the SAS source term is limited for this test case. For the loss prediction, the variation in the upper half-span region is mainly due to the different results in modeling turbulent characteristics of the tip leakage flow, whereas the mechanism behind the higher loss at the lower half-span predicted by the zonal-LES model is a consequence of the complex topology of the corner separation and the intensive mixing.