We discuss the efficiency of recent advances on the vector penalty-projection methods [1, 2, 3] including the kinematic version [5] which uses fast discrete Helmholtz-Hodge decompositions [4] on edge-based generalized MAC-type unstructured meshes. These methods are especially designed for the computation of incompressible or low-Mach multiphase flows under strong constraints (large density or viscosity ratios, large surface tension) and with Dirichlet [6] or open boundary conditions [7, 8]. We shall explain how these methods are suitable to overcome most drawbacks of the scalar incremental projection methods. The simulation of air bubbles dynamics in a liquid melted steel will be shown which is a highly challenging test case.