Abstract A technique based on the finite element method (FEM) is developed to precisely predict the pressure jump due to the surface tension forces in two-phase flow problems. In this method, the FEM shape functions of the active elements (the elements containing both phases) are enhanced by the aid of the moving least-squares (MLS) interpolation functions and used in the FEM calculations. Therefore, this technique is named as moving least-squares aided finite element method (MLS-FEM). The enhanced shape function correlates the value of any unknown parameters (e.g., the velocity, pressure, or stress values) at any arbitrary point inside an active element to its surrounding nodes. When the enhancement is performed only for the pressure (P) shape functions, we briefly name the MLS-FEM as the PMLS method (pressure shape function enhanced by the MLS technique). In this case, it would be possible to predict the pressure discontinuities in a two-phase flow domain. To assess the performance of the PMLS method in the calculation of the velocity components and pressure values in two-phase flow fields, the stationary drop problem is investigated. The results show that by employing the PMLS method, not only the magnitude of the spurious current is significantly reduced but also the pressure jump approaches toward its analytical value, without any pressure fluctuation at the interface. It is also explained that the method can be used to evaluate the extent of the drop deformation in a structured or an unstructured meshing system. Finally, the limitation of the introduced method is discussed, which is the basis for further developments.

中文翻译：

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移动最小二乘辅助有限元法 (MLS-FEM)：一种预测多相流场压力不连续性和减少杂散电流的强大方法

摘要 开发了一种基于有限元法（FEM）的技术来精确预测两相流问题中由表面张力引起的压力跳跃。在该方法中，活动单元（包含两个相的单元）的 FEM 形状函数通过移动最小二乘 (MLS) 插值函数得到增强，并用于 FEM 计算。因此，这种技术被命名为移动最小二乘辅助有限元法（MLS-FEM）。增强的形状函数将活动元素内任意点处的任何未知参数（例如，速度、压力或应力值）的值与其周围节点相关联。当仅对压力（P）形状函数进行增强时，我们将 MLS-FEM 简单地命名为 PMLS 方法（由 MLS 技术增强的压力形状函数）。在这种情况下，可以预测两相流域中的压力不连续性。为了评估 PMLS 方法在计算两相流场中的速度分量和压力值方面的性能，我们研究了平稳下降问题。结果表明，采用PMLS方法，不仅杂散电流的幅度显着降低，而且压力跃变接近其分析值，界面处没有任何压力波动。还解释了该方法可用于评估结构化或非结构化网格系统中下落变形的程度。最后，讨论了引入方法的局限性，