New two-fluid flow formalism:Separation of the flow according to velocities

A new formalism of two-phase flow has been derived. In this formalism the distributions of the phases and their velocities art not treated as uniform in the cross-sectional areas occupied by the fluids, but transverse spatial dependencies are allowed. With suitable dependencies and without using nonphysical fittings, the equation system is well posed; in other words, the characteristic velocities are real.The couplings of the unknown variables create obstacles to numerical solution, but they are easily overcome with a new shape-preserving method, PLIM.The necessary constitutive laws, which appear as the source terms of the equations, have been obtained by considering the time-independent case. The approach is applied to one-dimensional situations in which the total volumetric flux changes rapidly