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Squeeze film dampers (SFDs) are commonly used in turbomachinery in order to introduce external damping, thereby reducing rotor vibrations and acoustic emissions. Since SFDs are of similar geometry as hydrodynamic bearings, the REYNOLDS equation of lubrication can be utilised to predict their dynamic behaviour. However, under certain operating conditions, SFDs can experience significant fluid inertia effects, which are neglected in the usual REYNOLDS analysis. An algorithm for the prediction of these effects on the pressure build up inside a finite-length SFD is therefore presented. For this purpose, the REYNOLDS equation is extended with a first-order perturbation in the fluid velocities to account for the local and convective inertia terms of the NAVIER-STOKES equations. Cavitation is taken into account by means of a mass conserving two-phase model. The resulting equation is then discretized using the finite volume method and solved with an LU factorization. The developed algorithm is capable of calculating the pressure field, and thereby the damping force, inside an SFD for arbitrary operating points in a time-efficient manner. It is therefore suited for integration into transient simulations of turbo machinery without the need for bearing force coefficient maps, which are usually restricted to circular centralized orbits. The capabilities of the method are demonstrated on a transient run-up simulation of a turbocharger rotor with two semi-floating bearings. It can be shown that the consideration of fluid inertia effects introduces a significant shift of the pressure field inside the SFDs, and therefore the resulting damper force vector, at high oil temperatures and high rotational speeds. The effect of fluid inertia on the kinematic behaviour of the whole system on the other hand is rather limited for the examined rotor. [ABSTRACT FROM AUTHOR]