An Arbitrary Lagrangian-Eulerian Based Finite Element for Simulating Capillary Flows

Abstract

The numerical simulation of dynamic wetting phenomena at small length scales, where capillary forces must be taken into account, is considered. We introduce an arbitrary Lagrangian-Eulerian (ALE) formulation for two and three-dimensional sliding droplet simulations. The explicit representation of phase-separating interfaces in the mesh allows for accurate treatment of surface tension. Boundary conditions, including conditions for the controversial contact lines, are naturally incorporated by means of the finite element method (FEM). The dependence of the capillary forces on the geometry introduces a strong nonlinearity on the system of equations. A scheme of time discretization where the geometry is decoupled from the other variables is presented. Optimal temporal convergence for velocity and pressure can be obtained by an extrapolated Crank-Nicolson method in ALE moving grids, as shown by preliminary numerical experiments.