Moving least-squares aided finite element method (MLS-FEM): A powerful means to predict pressure discontinuities of multi-phase flow fields and reduce spurious currents

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.