The behavior of the compression system in turbochargers is studied with a one-dimensional engine simulation code. The system consists of an upstream compressor duct open to ambient, a centrifugal compressor, a downstream compressor duct, a plenum, and a throttle valve exhausting to ambient. The compression system is designed such that surge is the low mass flow rate instability mode, as opposed to stall. The compressor performance is represented through an extrapolated steady-state map. Instead of incorporating a turbine into the model, a drive torque is applied to the turbocharger shaft for simplification. Unsteady compression system mild surge physics is then examined computationally by reducing the throttle valve diameter from a stable operating point. Such an increasing resistance decreases the mass flow rate through the compression system and promotes surge. Mild surge is predicted as the mass flow rate is decreased below the stability limit, with oscillations of mass flow rate and pressure exhibited at the Helmholtz resonance frequency of the compression system. The computational results are shown to be able to reproduce the experimental observations available in the literature.