A Stabilized Edge-Based Finite Element Approach to Wave-Structure Interaction Assessment

Abstract

Complex flows involving waves and free-surfaces occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms motions, wave action on harbors and coastal areas. The computation of such highly nonlinear flows is challenging since waves and free-surfaces 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 that 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. 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. All those techniques were successfully implemented in a computational code, which has been suitably used to carry out several studies. The performance and accuracy of the proposed solution method is tested in the simulation waves and in the interaction between waves and a semisubmersible structure. Results count on the establishment of a relaxation zone close to the domain outflow, which partially absorbs incoming waves, avoiding their reflection.

A staggered procedure for fluid–object interaction with free surfaces, large rotations and driven by adaptive time stepping

“…Note that nonlinear iterations for both systems (Navier-Stokes and VOF marker) are halted when the relative residual at every time step decreases 3 orders of magnitudes. We generate a series of waves, that propagates perpendicularly to the ship axis, through the imposition of orbital velocity boundary conditions in one side of the basin and avoid their reflection by using a relaxation zone in the opposite side, as presented in [28,40,41]. Let ðe x ; e y ; e z Þ be the vector basis of the inertial frame, e x being the direction of the wave propagation and e z the vertical.…”