2018/05/03 by Sara Calandrini, Calandrini, Sara, Eugenio Aulisa +1 · 1 citation
Engineering · #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Vibration Analysis #Hydraulic and Pneumatic Systems #Numerical Analysis (math.NA) #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.1805.01321
openalex publication_date 2018/05/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/01
Venous valves are bicuspidal valves that ensure that blood in veins only\nflows back to the heart. To prevent retrograde blood flow, the two intraluminal\nleaflets meet in the center of the vein and occlude the vessel. In\nfluid-structure interaction (FSI) simulations of venous valves, the large\nstructural displacements may lead to mesh deteriorations and entanglements,\ncausing instabilities of the solver and, consequently, the numerical solution\nto diverge. In this paper, we propose an Arbitrary Lagrangian-Eulerian (ALE)\nscheme for FSI simulations designed to solve these instabilities. A monolithic\nformulation for the FSI problem is considered and, due to the complexity of the\noperators, the exact Jacobian matrix is evaluated using automatic\ndifferentiation. The method relies on the introduction of a staggered in time\nvelocity %in the discretization scheme to improve stability, and on fictitious\nsprings to model the contact force of the valve leaflets. Since the large\nstructural displacements may compromise the quality of the fluid mesh as well,\na smoother fluid displacement, obtained with the introduction of a scaling\nfactor that measures the distance of a fluid element from the valve leaflet\ntip, guarantees that there are no mesh entanglements in the fluid domain. To\nfurther improve stability, a Streamline Upwind Petrov Galerkin (SUPG) method is\nemployed. The proposed ALE scheme is applied to a 2D model of a venous valve.\nThe presented simulations show that the proposed method deals well with the\nlarge structural displacements of the problem, allowing a reconstruction of the\nvalve behavior in both the opening and closing phase.\n