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.

基于普通一流体的两相流数值模拟方法当密度比变得重要时，例如在普通的空气和水中，该模型会遭受两相之间动量的重要传递。这个问题已经从各种数值框架中得到解决。它主要源于以下假设：动量方程可以通过减去连续性方程来简化。尽管从连续的角度来看这种方法是正确的，但是从空间和时间的角度来看，它都会在离散级别带来数值误差，这些误差会极大地降低流体动力学。此外，随着网格的完善，我们发现这个问题越来越多。为了纠正此问题，我们提出了一种高阶动量保留（HOMP）方法，该方法另外还独立于界面表示形式（可以是液位设置，流体体积等）。此外，可以在现有的有限体积代码中轻松实现HOMP。我们展示了该方法可以有效地抑制示例示例中界面上的可怕动量传递。我们还介绍了它如何通过模拟破裂波的动态和液滴在液体池中的影响来提高两相流计算的质量。