Modeling free surface flows in presence of an arbitrary moving object

In this study, a numerical algorithm is developed for simulating the interactions between a liquid and a solid object in presence of a free-surface. The presented model is the fast-fictitious-domain method integrated into the volume-of-fluid (VOF) technique used for tracking the free surface motion. First, the governing equations are solved everywhere in the computational domain including the solid object. Next, a rigid body motion is projected onto the region occupied by the solid. The evaluation of the acting forces on the solid object and the application of the no-slip boundary condition on the solid–liquid interface are performed implicitly. In the model developed in this study, the no-slip condition is imposed by attributing a high viscosity to the solid region. The model is validated by a comparison of the simulation results with those of the available experiments in the literature for a sphere during its entry into a liquid free surface and for the free fall of one and two circular particles inside a liquid. For all cases considered, the results are in good agreement with those of the experiments and other numerical studies.