Two-phase flow simulation is nowadays an essential tool for reproducing and improving the understanding of fluid dynamics under various physical configurations. Considering 4th generation sodium nuclear reactors, the gas entrainment phenomenon is a major safety issue. For these reactors, the suction of cold liquid sodium towards the core can create vortices at the interface between sodium and neutral gas, which drives gas bubbles that can damage the suction pumps. Reproducing such phenomena requires accurate two-phase flow simulation methods. However, most of these methods have the disadvantage of producing non-physical velocities at the interfaces (spurious currents) generating unexpected physical fields. We propose a new interface tracking method enhancing the use of Front-Tracking module of the TrioCFD code. The method is based on the introduction of intermediate pressure unknowns coupled with an explicit treatment of the velocity continuity condition at the interfaces to guarantee the capture of pressure jumps, which ensures the absence of spurious currents when the numerical curvatures are exact. This last point, therefore, transforms the problem of eliminating spurious currents into a problem of computing numerical curvatures on broken lines and surfaces. We then compare different methods of computing curvatures and show that the error on the computation of discrete curvatures increases with the refinement of the line or broken surface. These findings reinforce the application of smoothing algorithms and advocate for ongoing research into innovative curvature computation methods.