Stabilized Space-Time Finite Element Formulations for Free-Surface Flows

Aspects of a method for 3D finite element computation of unsteady, incompressible freesurface flow are presented. The approach is based on the Deformable-Spatial-Domain/ Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the deformation of the elements in response to the motion of the free surface. The free-surface elevation is governed by a kinematic free-surface condition, which is also solved with a stabilized formulation. A new governing equation and stabilized formulation is derived for cases where the channel walls are not vertical. The parallel implementation based on MPI message-passing standard is fully portable, and have been demonstrated to be scalable on a range of architectures. A 3D computation of a flow past a spillway of a dam is shown as an example application.