An ALE method for large structural displacements in fluid-structure interaction simulations of venous valves
Veins are blood vessels subjected to very low blood pressures, and they rely on muscle contractions and one-way valves to push blood back to the heart. The main contribution of venous valves is to prevent back flow. In fluid-structure interaction (FSI) simulations of venous valves, the large structural displacements may lead to mesh deterioration and entanglements, causing
instabilities of the solver and, consequently, the numerical solution to diverge. In this talk, I will present an Arbitrary Lagrangian-Eulerian (ALE) scheme for FSI simulations that aims 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 tools. In the literature, ALE methods for large structural displacements either use remeshing techniques or a variational mesh optimization approach to prevent mesh deterioration. In this work, a third way is proposed to guarantee no mesh deterioration, namely, a smoother fluid displacement is obtained with the introduction of a distance function that assures an homogeneous deformation throughout the entire mesh. The presented method is based on three main features: a staggered in time mesh velocity in the discretization scheme to improve computational stability; a scaling factor that measures the distance of a
fluid element from the valve leaflets, to guarantee that there are no mesh entanglements in the fluid domain; and fictitious springs to model the contact force between closing valve leaflets. Numerical results are shown for a 2D model of a venous valve.
This is joint work with Eugenio Aulisa, Texas Tech University.