A finite element technique for multifluid incompressible flow using Eulerian grids

The paper presents a finite element method for 3D incompressible fluid flows with capillary free boundaries. It uses a fixed Eulerian grid of 10 nodes (P2−P1) tetrahedra and tracks the free boundary using a six nodes (P2) triangular surface grid. In order to improve the mass conservation properties of the method, a local enrichment of the finite element basis in the elements intersected by the free boundaries is employed. In addition to the surface tracking, it also advects a smooth indicator function for an easy identification of the fluid properties in the different parts of the domain. The advective part of the Navier–Stokes equations is split and integrated with a characteristic method. The remaining generalized Stokes problem is resolved by means of an inexact outer–inner (Uzawa) iteration with a properly chosen preconditioner. The performance of this technique is evaluated on several problems involving droplets in viscous liquids.