The objective of this research is to understand the physics of the separated unsteady viscous flow over the bilge keels of an FPSO hull subject to roll motions and to predict the corresponding hydrodynamic coefficients. A numerical scheme which is based on the Finite Volume Method (FVM) for the solution of the 2-D Navier-Stokes equations is presented (NS2D). The scheme is validated for a submerged hull roll problem and applied to an FPSO hull subject to roll motions with or without bilge keels. The effects of the bilge keel size and orientation on the hydrodynamic coefficients are investigated. Moreover, a Boundary Element Method (BEM) based potential solver is developed in order to investigate the effects of the non-linear free-surface boundary conditions on the predictions.