The proposed contribution will deal with the general topic of partitioned coupling for fluid-structure interaction with a particular focus on the stability and robustness of temporal schemes for non-linear transient simulations. The main goal is to precisely characterize the so-called added mass effect from a numerical point of view. Its dependence on the modelling conditions, such as the compressible or incompressible nature of the flow, and on the boundary conditions will be investigated to produce reliable highlights guiding the choice of the suitable coupling algorithm in every situation. Practically, the presentation will focus on the coupling between a non-linear explicit solver for the structure and a variety of fluid models, either compressible with another explicit time scheme or incompressible with a semi-implicit scheme involving a global step to compute pressure. The latter case appears as the most challenging regarding the coupling stability and will thus concentrate most of the recent algorithmic developments. In more details, both explicit and implicit dirichlet-neumann coupling schemes will be proposed depending on the intensity of the added mass effect. A particular interest will be paid to different time scale management, mandatory when the structural non-linearities are preferably handled with an explicit time scheme exhibiting a restrictive CFL condition on the usable time step. In the end, the association of an implicit coupling scheme and a properly designed subcycling strategy for the structure will even produce a unified coupling framework for non-linear transients where the dependence from the actual nature of the time scheme used for the structure vanishes in favor of a fully generic algorithm. To achieve the expected level of robustness in the case of implicit coupling, the convergence acceleration techniques applied to the related fixed-point loop will also be discussed. Finally, the findings associated to the numerical developments introduced above will be illustrated and discussed on significant and challenging test cases from the literature. [1] Antonin Leprevost. Couplage partitionné fluide-structure à l’échelle locale avec grille mobile pour des transitoires non-linéaires. Université Paris-Saclay, 2024. Français. [2] Hippolyte Lerogeron, Vincent Faucher, Pierre Boivin, Julien Favier, LBM-based partitioned coupling for fast transient fluid-structure dynamics, Applied Mathematical Modelling (149), 20