Evaluation of advection schemes and surface tension model for algebraic and geometric VOF multiphase flow solvers

This paper addresses the validation and verification of numerical models for complex multiphase flows involving immiscible fluids. Specifically, the focus is on the dynamics of the interface between the fluids, which remains a challenge in many applications. Previous studies have primarily examined simpler flows with limited complexity, while real-world scenarios involve intricate interfaces and turbulent dynamics. To overcome this, a representative test case involving the motion of an oil cube within a water cube proposed by [12] is used. Different computational models using volume-of-fluid (VOF) approaches are validated and compared, with particular attention given to the influence of numerical schemes for convective terms. The impact of these schemes on integral quantities and interface dynamics is analyzed. Particular attention is paid at the surface tension contribution to the energy budgets, which is usually neglected in the available literature. Furthermore, it is shown here that, the model adopted for the surface tension is responsible for an additional contribution to numerical dissipation. To the authors' knowledge, it is the first time that a detailed analysis of such aspects is presented.