Due to its capacity in retrieving the angular resolution of ground-based optical telescopes together with their intrinsic sensitivity, adaptive optics (AO) is well known to be of fundamental importance for a wide range of astronomical applications. In the case of very high-contrast imaging it is even more critical given the limitation due to the atmospheric residuals. The ability of an AO system in "cleaning" the obtained point-spread function before a coronagraphic stage is therefore of central importance - and so the robustness of a given coronagraphic stage with respect to the post-AO atmospheric residuals. Within this framework, the present paper describes the physical ingredients that are necessary to be modelized when designing a detailed numerical simulation study of this kind, together with a typical numerical tool used in this context. An example involving a very high-order AO system is given, a simple implementation of different coronagraphic concepts is exposed, and an illustrative preliminary result involving the high-order AO-correction stage coupled with the different coronagraphic devices implemented is shown.