Euler-Euler simulations of two-phase flows, such as the 6-equations model adopted in many system thermal-hydraulics (STH) codes, become more challenging as the gas-liquid density ratio $\rho_l / \rho_g$ increases. On structured meshes, the association of a staggered "MAC" numerical scheme with a semi-implicit "ICE" solution algorithm has proven particularly robust, and is currently used in the 3D modules of the TRACE, CATHARE and RELAP5-3D codes. However, structured meshes are too restrictive to cover a number of potential applications : apart from the CFD scale, unstructured, polyhedral meshes are also encountered at the component scale when modelling VVER or SFR subassemblies. This later case is the focus of the TrioMC code developed at CEA. In 2019, this code was reimplemented using a new numerical scheme ("PolyMAC") designed to generalise to arbitrary meshes the main properties of the MAC staggered numerical scheme. In 2020-2021, this scheme, originally designed to solve the single-phase thermal-hydraulics equations, was extended to multiphase flows: physical models dedicated to sodium boiling were then implemented in TrioMC, and preliminary validation was carried out against a benchmark sodium boiling test (the KNS-37 L22 test provided by the ESFR-SMART H2020 project). This first validation showed promising results, while highlighting two topics for further model improvements: better prediction of droplet entrainment phenomena and interfacial heat exchanges in the condensation regime. Extending the model to the complete experimental loop via a coupling to the CATHARE code is also planned. Finally, applications of the multiphase numerical scheme and solver developed in this work are planned in the field of multiphase CFD.