Computational Simulation of Free Surface Flows Using Stabilized Edge-Based Finite Element Method

Flows involving waves and free-surfaces occur in several problems in hydrodynamics, such as sloshing in tanks, waves breaking in ship and motions of offshore platforms. The computation of such wave problems is challenging since the water/air interface (or free-surface) commonly present merging, fragmentation and cusps, leading to the use of interface capturing Arbitrary Lagrangian-Eulerian (ALE) approaches. In such methods the interface between the two fluids is captured by the use of a marking function which is transported in a flow field. In this work we simulate these problems with a 3D incompressible SUPG/PSPG parallel edge-based finite element flow solver associated to the Volume-of-Fluid (VOF) method [1]. The hyperbolic equation for the transport of the marking function is also solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity at the interface. The performance and accuracy of the proposed solution method is tested in the simulation of pulse wave and the interaction of a fixed square cylinder with a progressive wave.