On the finite volume discretization of discontinuous body force field on collocated grid: Application to VOF method

Discontinuities in the body force field typically appear at the interface of two fluid systems. Modeled with the volume-of-fluid (VOF) and discretized with the finite volume method, the discontinuous body force fields are represented as abruptly variable. In the present study, gravity and continuum surface force (CSF) are considered. Such strongly variable body forces can produce unphysical spikes in the velocity field when collocated variable arrangement is used. The spikes can be eliminated following a force field discretization rule which is deduced by imposing a constraint requiring a zero velocity solution when the forces applied to the system are equilibrated with the gradient of the pressure field. It is shown (as a byproduct of the present work) that a zero velocity solution can only be obtained if the force field is conservative on the discrete level, which applies also for the studied case of a stationary bubble. Finally, the case of a rising bubble demonstrates that the proposed rule should be obeyed generally although it is obtained for a quiescent fluid.