A FEM solver coupled to a multilevel VOF method for simulation of axisymmetric jets and to a front-tracking method for simulation of spreading droplets

In this work we review a few studies on the performance of the finite element approach in direct numerical simulations of liquid jet injection and droplet impact on dry surfaces. We consider the single-fluid formulation of the incompressible Navier-Stokes equations, discretize these equations on a fixed grid with the finite element method, and solve the resulting algebraic system with a multigrid technique. The finite element method allows a variational formulation of the capillary force that is implemented both with a volumetric approach and by using the Laplace-Beltrami operator. In order to study the injection of a liquid jet in a gas environment at low Reynolds numbers, we have implemented a multilevel volume of fluid (VOF) method because it can deal with strong topology changes in an automatic way. We have also considered a front-tracking algorithm to study the spreading of a droplet on a dry solid surface, because there is the need of a very precise positioning of the contact point, while there is no breaking or topology change. The results of several numerical experiments are presented and discussed for both cases.