This work describes the development and the application of a quasi-3D method for the simulation of turbochargers for automotive applications under unsteady flow conditions. The quasi-3D approach is based on the solution of conservation equations for mass, momentum and energy for unsteady flows and applied to 0D and 1D elements arbitrarily oriented in the space. The compressor is divided into different regions, each one treated numerically in a different way. For the impeller region a relative reference system has been used and the presence of a centrifugal force field has been introduced both in the momentum and energy conservation equation. The direction of the ports at the inlet and outlet of the impeller are used to determine the design ...