In this paper, we study an interface transport scheme of a two-phase flow of an incompress-ible viscous immiscible fluid. The problem is discretized by the characteristics method in time and finite elements method in space. The interface is captured by the Level-Set function. Appropriate boundary conditions for the problem of mould filling are investigated, a new natural boundary condition under pressure effect for the transport equation is proposed and an algorithm for computing the solution is presented. Finally, numerical experiments show and validate the effectiveness of the proposed scheme.