Turbocharging technique will play a fundamental role in the near future not only to improve automotive engine performance, but also to reduce fuel consumption and exhaust emissions both in Spark Ignition and Compression Ignition engines. To this end, one-dimensional (1D) modelling is usually employed to compute the engine-turbocharger matching, to select the boost level in different operating conditions and to estimate low end torque level and transient response. However, 1D modeling of a turbocharged engine requires the availability of the turbine and compressor characteristic maps. This leads to some typical drawbacks: performance maps of the turbocharger device are usually limited to a reduced number of rotational speeds, pressure ratios and mass flow rates. Extrapolation of maps' data is commonly required;performance maps are experimentally derived on stationary test benches, while the turbocharger, coupled to an internal combustion engine, usually operates under unsteady conditions;during low speed, high load engine operation a close-to-stall compressor operation usually occurs. In this case the steady map cannot provide the required information to realize an accurate analysis of the whole turbocharged engine.To overcome the above problems, in the present paper two different numerical procedures are developed: a steady approach is firstly followed to the aim of accurately reproduce the experimentally derived compressor characteristic maps. The steady procedure describes main phenomena and losses arising within the stationary and rotating channels constituting the compressor device. It is utilized to directly compute the related steady map, starting from the specification of a reduced set of geometrical data. An optimization process is also presented to identify a number of tuning constants included in the various loss correlations.Then, a recently proposed and more refined procedure is compared to the previous one. The latter is based on the solution of the 1D unsteady flow within the compressor stationary and rotating channels. The refined methodology is capable of describing the unsteady behaviour of the compressor and to handle typical unstable operating regimes (compressor surging).Both the steady and unsteady procedures are applied to the simulation of three different turbochargers and the numerical results show a good agreement with experimentally derived performance maps.In addition, the comparison between the steady and 1D procedure results highlights the important role played by the unsteady phenomena on the overall turbocharger operation.The proposed methodology can successfully support the design process and transient analysis of turbocharged internal combustion engines.