SUMMARYIt is often the case that the numerical simulation of two phase ows leads to a number of di culties associated with the solution algorithms utilized. Those di culties manifest themselves as an impossibility to converge the iterative solution process, typical of the ÿnite-volume pressure-correction methods, and are particularly persistent in cases with phase segregation (complete, or almost complete, separation of one phase from the other) and with ÿne meshes. A number of e ective measures to overcome such problems are here proposed and tested, encompassing: (1) modiÿcation of the momentum equations formulation in a way that avoids singularity as volume fractions ( ) tend to zero; (2) bounding of the volume fractions during the iterative algorithm in a way that enforces the physical limits, ¿0 and 61; (3) symmetric treatment of some terms in the equations, and consistent formulation of cell-face uxes in order to prevent numerical-induced oscillations.