We investigate in detail a simple flow with fluid-structure interaction, namely the case of a small rigid body moving parallel to a wall at constant velocity in a quiescent, incompressible and viscous fluid. We concentrate mainly on stationary flows by describing the problem in an adequately chosen reference frame. We prove detailed information on the solution in a specially adapted functional framework and extract an explicit asymptotic expansion to the solution. This is then used to define boundary conditions for the artificial boundaries that appear when truncating the domain in numerical simulations, which are validated against traditional choices of boundary conditions.