The thesis deals with the trajectory of a sphere falling in a tube filled with a Newtonian fluid at rest. This topic is motivated by the understanding of phenomena related to particle transport, including the interactions between the wake downstream of the particle and a wall nearby. The particle transport is widespread in many areas, such as the trajectory of the therapeutic particles in the lungs, the trajectory of the fuel particles and the trajectory of chemical reagents in fluidized beds. The simulations are made possible by the development of the chimera method (management of overlapped grids) implemented in a solver of the Navier-Stokes equation (NSMB software). The developed chimera method is fast, automatic and parallel and it is validated on several static and moving flow cases. This method is firstly applied on the sphere in uniform translation in a tube. The states are similar to the flow past a sphere in infinity area (without wall tube influence). Then the method is performed for the free falling sphere in a tube. Three kinds of trajectory appear in the studied range: a vertical fall along the axis tube, an helical trajectory (no vortex shedding downstream of the sphere) and an helical path with a unsteady radius (flow with vortex shedding).
