A numerical model for fluid-structure interactions (abbr. FSI) is presented in the context of sloshing effects in movable, partially filled tanks to improve understanding of interactions between the fluid and the dynamics of a tank flexibly attached to a vehicle. The purpose of this model is to counteract the penalizing impact of the added mass effect on classical partitioned FSI coupling scheme: the proposed investigation is based on an added mass corrected version of the classical strongly coupled partitioned scheme presented in (Song et al. 2013). Results show that this corrected version systematically allows convergence to the coupled solution. In the rare cases where convergence is already obtained, the corrected version significantly reduces the number of iterations required. Finally, it is shown that the convergence limit imposed by added mass effect for the non-corrected coupling scheme, is directly dependent on the aspect ratio of the fluid domain and highly related to the precision order of the temporal discretization scheme.