The analysis of nuclear reactors for performance and safety assessment benefits from the use of computational tools. In this context, this work aims at the development and application of a thermal-hydraulics methodology and related software that respond to emerging needs in the computational field: 1) greater geometric and physics modelling flexibility; 2) streamlined coupling with other single-physics to enable multi-physics capabilities; 3) parallel scalability on High Performance Computing clusters; 4) adoption of modern programming practices. A coarse-mesh approach is proposed to offer a reasonable balance between computational accuracy, comparable to that of sub-channel codes, and computational burdens. The developed approach can make use of general 3-D geometries with unstructured meshes, which are beneficial to the aforementioned geometric flexibility needs. Additionally, in a multi-physics context, field transfer operations between the different physics are simplified both by the adoption of a coarse-mesh approach and by the use of standardized mesh formats. The employed programming framework consists of the Finite Volume Method-based OpenFOAM library, which offers the desired features of massive parallel scalability and of a modern object-oriented programming paradigm. The coarse-mesh methodology is presented alongside a thorough theoretical derivation of the governing equations for a generic multi-phase system. Based on this, a computer code is developed for the modelling of one-phase and two-phase flows, with a focus on the simulation of Sodium-cooled Fast Reactors (SFRs), which represent the nearest-term deployable fast reactor technology. These were also chosen as the simulation of phase change in sodium represents a challenging case for the numerical stability of two-phase solution algorithms. The main achievements of this development effort consist of: 1) a novel solution algorithm for two-phase pressure-velocity coupling that enhances stability and performances compared to existing algorithms; 2) implementation of the code based on object-oriented programming practices, which allow for a seamless implementation of different working fluids and structure models; 3) code verification via an ad-hoc implementation of the Method of Manufactured Solutions; 4) demonstrated good parallel scaling of the code up to thousands of computer cores. In terms of applications: 1) preliminary validation based on sodium boiling experiments; 2) detailed investigation of existing and novel features for SFR fuel elements. Furthermore, the multi-physics capabilities of the developed methodology are demonstrated by integrating it within the GeN-Foam multi-physics environment. As a test case, the resulting software is applied to the simulation of a Loss Of Flow Without SCRAM test performed at the Fast Flux Test Facility. This benchmark re-analysis takes place within the framework of a coordinated research project by the International Atomic Energy Agency and is set to provide valuable feedback in terms of code-to-code comparison data.