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Numerical analysis methods are used to investigate the flow in a ported-shroud centrifugal compressor under different operating conditions, i.e. several mass flow rates at two different speed lines. A production turbocharger compressor is considered, which is widely used in the heavy automotive sector. Flow solutions obtained under steady-state and transient flow assumptions are compared with available experimental data. The steady-state Reynolds Averaged Navier-Stokes method is used to assess the overall time averaged flow and the global performance parameters. Additionally, the Large Eddy Simulation (LES) approach is employed to capture the transient flow features and the developed flow instabilities at low mass flow rates near the surge line. The aim of this study is to provide new insights on the flow instability phenomena in the compressor flow near surge. Comparison of flow solutions obtained for near-optimal efficiency and near-surge conditions are carried out.