A new multi-physics solver for nuclear reactor analysis, named GeN-Foam (Generalized Nuclear Foam), has been developed by the FAST group at the Paul Scherrer Institut. It is based on OpenFOAM and has been developed for the multi-physics transient analyses of pin-based (e.g., liquid metal Fast Reactors, Light Water Reactors) or homogeneous (e.g., fast spectrum Molten Salt Reactors) nuclear reactors. It includes solutions of coarse or fine mesh thermal-hydraulics, thermal-mechanics and neutron diffusion. In particular, thermal-hydraulics solution can combine on the same mesh both a traditional RANS model and a porous medium model, depending on the desired degree of approximation for each region. In case the active reactor core is modeled as a porous medium, a simple sub-solver computes the sub-scale radial temperature profiles in fuel and cladding. The mesh used for neutronics calculations is deformed according to the displacement field predicted by the thermal-mechanics solver, thus allowing for a direct prediction of expansion-related feedback effects in Fast Reactors. To limit computational requirements, GeN-Foam permits the use of three different unstructured meshes for thermal-hydraulics, thermal-mechanics and neutron diffusion. For the same reason, an adaptive time step is employed. The different equations can be solved altogether or selectively included. In this work, GeN-Foam is applied to the analysis of the European Sodium Fast Reactor (ESFR). In particular, a 3-D model of the ESFR core is set up employing a coarse-mesh porous-medium approach for the thermal-hydraulics. The reactor steady-state and different accidental transients are investigated to offer an overview of GeN-Foam use and capabilities, as well as to preliminarily investigate the impact of a relatively accurate thermal-mechanic treatment on the predicted ESFR behavior. A code-to-code benchmark against the TRACE system code is performed to verify the adequacy of the results provided by the new code. GeN-Foam has proved itself a powerful and flexible tool for the ESFR analysis, allowing also to shed some light on phenomena neglected by more simplified treatments. In addition, the code-to-code benchmark showed that GeN-Foam can provide results consistent with state-of-the-art codes, thus giving confidence about the capability of the code to provide adequate predictions of a reactor behavior.