Stabilized Space-time FEM and its Applications to Free-surface Flows

We present parallel 3D finite element computations of unsteady, incompressible free-surface flows. The approach is based on the Deformable-Spatial-Domain/ Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the motion of the free surface. The free-surface height is governed by a kinematic free-surface condition, which is also solved with a stabilized formulation. The mesh update can be achieved with general or special-purpose mesh moving schemes. The general mesh update schemes describe the mesh as a fictitious solid material, subject to appropriate constitutive relations. These relations can take the form of linear elasticity, or more complex nonlinear equations. The parallel implementation based on MPI message-passing standard is fully portable, and have been demonstrated to be scalable on a range of