Thermal-hydraulic codes require robust and accurate numerical methods capable of handling multiphase flows over a wide range of Mach numbers. In this context, staggered-grid methods provide a particularly attractive framework. This PhD thesis builds upon recent work carried out as part of a previous PhD project, which led to the development of a new method with promising theoretical and numerical properties. The objective is to pursue this work and extend its range of applications. The first part will focus on the theoretical analysis of the explicit version of the scheme applied to the drift-flux model, in order to establish its conservation properties, its behaviour in the low-Mach-number limit, and the convergence of the numerical solutions. The method will then be extended to the Baer-Nunziato two-phase flow model, in which the two phases have distinct velocities and pressures. Finally, high-order reconstruction techniques will be investigated to improve the accuracy of the scheme by reducing numerical dissipation. The expected outcomes are a better mathematical understanding of these schemes and the development of robust and accurate numerical methods suitable for industrial applications. These methods will first be validated in a C++ and Python research code, and then implemented and assessed within the open-source TRUST platform dedicated to high-performance thermal-hydraulic simulations.