The title of this chapter was chosen to indicate that its purpose is to complement the analysis through numerical simulations. In a way, we are pursuing our investigations by other means. This is a different objective from software development where the emphasis is on computational science, and from code validation where the emphasis is on numerical methods. In the following, we discuss several situations in the tracer-particle limit before addressing the case of discrete particles. There are reasons to do that. First, we have seen that present formulations of the stochastic model for the velocity of the fluid seen are built as extensions of the ones for fluid particles, and retrieving the fluid limit needs to be assessed in numerical simulations. Second, considering the fluid-limit case allows to discuss key physical phenomena, such as the convective or diffusive regimes in point-source dispersion, in a simplified setting. It also allows to reveal similarities or differences between fluid and discrete particles, e.g. the role of the pressure gradient and the impact of the incompressibility constraint. Only then can we assume that we rely on solid foundations and turn to disperse two-phase flow situations.