For nuclear safety calculations as well as for the design of new reactors, it is necessary to accurately simulate two-phase flows. The TrioCFD software, developped at CEA and based on the TRUST digital platform, offers the Front-Tracking module to study a two-phase flow by precisely following the interfaces between the phases. This method is functional and is validated in many application cases. However, it could benefit from recent mathematical developments to improve its robustness and to take into account the singularities in the neighbourhood of the interface. These can appear when two interfaces come together, as it is the case during the coalescence of two bubbles, at the tip of a vortex or at the level of a triple line (water, gas and solid wall). To faithfully resolve the phenomena in these regions, it is currently necessary to significantly refine the mesh around these zones, implying significant computational costs. The aim of this thesis is to propose and implement numerical methods to improve the Front-Tracking of TrioCFD. Firstly, we will seek to improve the current method in terms of robustness. Next, we will look at alternative methods to front tracking. The second part of the thesis work will aim to develop the treatment of interface singularities using a semi-analytic approach, called the singular complement method. This approach would greatly reduce the need for mesh refinement around the singularities of the interface.