Numerical methods for the simulation of two-phase flows based on the common one-fluid model suffer from important transfer of momentum between the two-phases when the density ratio becomes important, such as with common air and water. This problem has been addressed from various numerical frameworks. It principally arises from the hypothesis that the momentum equation can be simplified by subtracting the continuity equation to it. While this approach is correct in a continuous point of view, it however brings numerical errors at the discrete level, from both spatial and temporal points of view, errors that can highly deteriorate the fluids dynamic. Moreover, we have found this problem to be more and more present as the grid is refined. To correct this problem, we propose a High-Order Momentum Preserving (HOMP) method that is, additionally, independent on the interface representation (may it be level set, volume of fluid, etc.). Furthermore, HOMP can be easily implemented in an existing finite volume code. We show that this method permits to efficiently suppress dreadful momentum transfers at the interface on demonstrating examples. We also present how it enhances the quality of two-phase flows computation through the simulation of the dynamic of a breaking wave and the impact of a droplet in a liquid pool. Highlights • A consistent spatial and temporal numerical strategy is used for moment preservation. • A generic formulation makes it suitable for various interface methods in 2D and 3D. • The method drastically reduces spurious momentum transfers across the interface. • Stable and accurate incompressible two phase flows complex simulations are performed. • High-order WENO 5, 3 with RK 2 scheme is employed even with thin interface thickness.< Leer menos