On the numerical simulation of the unsteady free fall of a solid in a fluid: I. The Newtonian case

In the last decade, extensive experiments have been carried out in order to gain a better insight in the phenomenology related to the motion of a falling body in a quiescent Newtonian fluid. This renewal of interest in that subject is due not only to the lack of full theoretical explanations of the intricate body motion but also to the high relevance of that issue in applications ranging from meteorology, sedimentology and aerospace engineering to biology. We present a new numerical method for the simulation of the instationary free fall of a unique solid in a fluid. A key ingredient of the proposed approach is the reformulation of the conservation and kinetic equations in the solid frame as well as the explicit treatment of the fluid-body coupling. The issue of non-smooth data in time resulting from our explicit approach is addressed. The time stepping is based on the implicit fractional-step-θ scheme and the spatial discretization relies on the finite element method. Numerical experiments for the steady-falling regime, for the periodic oscillating motion as well as for the tumbling motion are presented following existing experimental set-up. The proposed method is validated by comparison with experimental data.