Two-dimensional modelling of free-surface flows in presence of a spherical object using the Modified Volume of Fluid technique

In this paper, a two-dimensional numerical simulation of water entry of a spherical object is achieved using the Modified Volume of Fluid (MVOF) technique. Continuity and Navier–Stokes equations along with an equation for tracking the free-surface motion are considered as the governing equations for 2D incompressible fluid flow. The free-surface deformation is modelled via integration of the fast fictitious domain method into the MVOF technique. The computational domain includes everywhere even the spherical object where the governing equations are solved. A rigid motion of the spherical object is generated by applying the linear and angular conservation laws. To exert the no-slip condition on the solid–liquid interface implicitly, the viscosity of the region arranged within the solid object is increased artificially. The numerical results obtained using the MVOF method are compared with those of the experiments in the literature and the conventional Volume of Fluid method. The results show that the effects of the artificial compression term on the free-surface deformation is very dominant for coarse meshes while this factor becomes minor for fine meshes.