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- Title
Fluid‐structure interaction simulations of venous valves: A monolithic ALE method for large structural displacements.
- Authors
Calandrini, Sara; Aulisa, Eugenio
- Abstract
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 to improve stability, and on fictitious springs to model the contact force of the valve leaflets. Because 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 two‐dimensional (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. A monolithic ALE scheme for FSI simulations of venous valves designed to resolve instabilities of the solver caused by large structural displacements is presented. The method is based on three main features: a staggered in time mesh velocity 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 leaflets.
- Subjects
VENOUS valves; BLOOD flow; VEINS; COMPUTER simulation; JACOBIAN matrices
- Publication
International Journal for Numerical Methods in Biomedical Engineering, 2019, Vol 35, Issue 2, pN.PAG
- ISSN
2040-7939
- Publication type
Article
- DOI
10.1002/cnm.3156