Numerical aspects of an algorithm for the Eulerian simulation of two-phase flows

It is often the case that the numerical simulation of two phase flows leads to a number of difficulties associated with the solution algorithms utilized. Those difficulties manifest themselves as an impossibility to converge the iterative solution process, typical of the finite-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 fine meshes. A number of effective measures to overcome such problems are here proposed and tested, encompassing: (1) modification of the momentum equations formulation in a way that avoids singularity as volume fractions ((alpha)) tend to zero; (2) bounding of the volume fractions during the iterative algorithm in a way that enforces the physical limits, (alpha)0 and 1; (3) symmetric treatment of some terms in the equations, and consistent formulation of cell-face fluxes in order to prevent numerical-induced oscillations.