  Venous valves are bicuspidal valves that ensure that blood in veins only
flows back to the heart. To prevent retrograde blood flow, the two intraluminal
leaflets meet in the center of the vein and occlude the vessel. In
fluid-structure interaction (FSI) simulations of venous valves, the large
structural displacements may lead to mesh deteriorations and entanglements,
causing instabilities of the solver and, consequently, the numerical solution
to diverge. In this paper, we propose an Arbitrary Lagrangian-Eulerian (ALE)
scheme for FSI simulations designed to solve these instabilities. A monolithic
formulation for the FSI problem is considered and, due to the complexity of the
operators, the exact Jacobian matrix is evaluated using automatic
differentiation. The method relies on the introduction of a staggered in time
velocity %in the discretization scheme to improve stability, and on fictitious
springs to model the contact force of the valve leaflets. Since the large
structural displacements may compromise the quality of the fluid mesh as well,
a smoother fluid displacement, obtained with the introduction of a scaling
factor that measures the distance of a fluid element from the valve leaflet
tip, guarantees that there are no mesh entanglements in the fluid domain. To
further improve stability, a Streamline Upwind Petrov Galerkin (SUPG) method is
employed. The proposed ALE scheme is applied to a 2D model of a venous valve.
The presented simulations show that the proposed method deals well with the
large structural displacements of the problem, allowing a reconstruction of the
valve behavior in both the opening and closing phase.
