2019/11/22 by Sunčica Čanić, Čanić, Sunčica, Marija Galić +3 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1911.09927
openalex publication_date 2019/11/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We consider a nonlinear, moving boundary, fluid-structure interaction problem\nbetween a time dependent incompressible, viscous fluid flow, and an elastic\nstructure composed of a cylindrical shell supported by a mesh of elastic rods.\nThe fluid flow is modeled by the time-dependent Navier-Stokes equations in a\nthree-dimensional cylindrical domain, while the lateral wall of the cylinder is\nmodeled by the two-dimensional linearly elastic Koiter shell equations coupled\nto a one-dimensional system of conservation laws defined on a graph domain,\ndescribing a mesh of curved rods. The mesh supported shell allows displacements\nin all three spatial directions. Two-way coupling based on kinematic and\ndynamic coupling conditions is assumed between the fluid and composite\nstructure, and between the mesh of curved rods and Koiter shell. Problems of\nthis type arise in many applications, including blood flow through arteries\ntreated with vascular prostheses called stents. We prove the existence of a\nweak solution to this nonlinear, moving-boundary problem by using the time\ndiscretization via Lie operator splitting method combined with an Arbitrary\nLagrangian-Eulerian approach, and a non-trivial extension of the\nAubin-Lions-Simon compactness result to problems on moving domains.\n