Transient free surface flows via a stabilized ALE finite element method

Free surface problems appear in a wide range of industrial and engineering applications, e.g. when modelling sloshing of fluid in a container or when tracking the free surface evolution in casting and molding processes. A finite element technique is presented to study time-dependent large free surface motions of viscous, incompressible fluids. The approach is based upon an arbitrary Lagrangean-Eulerian (ALE) representation of kinematics and field equations, i.e. continuum mechanical conservation laws. Both convective effects and equal-order interpolation for velocities and pressure are stabilized in a Galerkin least-squares sense. This leads to a fully stabilized finite element method (FEM) for the governing instationary incompressible Navier-Stokes equations. The algorithmic setup is complemented by a combination of the stabilized FEM with direct time integration procedures and fixed point-like iterative schemes. The performance of the overall algorithm is demonstrated with the help of selected two-dimensional numerical examples.