We focus here on a three-phase flow model in order to represent complex flows involving liquid metal droplets, liquid water, and its vapour. The governing equations and its main properties are given, and focus is given on the pressurevelocity relaxation process on the one hand, and on the structure of solutions of the one-dimensional Riemann problem associated with pure convective effects. A fractional step method that computes successively the convective part and the relaxation effects is used to obtain approximate solutions on unstructured meshes. Details of algorithms are provided, and it is shown that the numerical method preserves positive values of statistical fractions and partial masses. Verification and validation test cases are presented, and some perspectives are eventually drawn.