A HYBRID FINITE-ELEMENT-VOLUME-OF-FLUID METHOD FOR SIMULATING FREE-SURFACE FLOWS AND INTERFACES

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength of the fini te element method (FEM) in calculating the field variables for a defor ming boundary and the versatility of the volume-of-fluid (VOF) techniq ue in advection of the fluid interfaces. The advantage of the VOF tech nique is that it allows the simulation of interfaces with large deform ations, including surface merging and breaking. However, its disadvant age is that in solving the flow equations, it cannot resolve interface s smaller than the cell size, since information on the subgrid scale i s lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surfa ce tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of th e boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the tw o methods into a hybrid FEM-VOF method eliminates the major shortcomin gs of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For i llustration, two computational examples are presented, namely the inst ability and break-up of a capillary jet and the coalescence collision of two liquid drops.