Analysis of a 3D nonlinear moving boundary problem describing fluidmeshsell interaction
Abstract. We consider a nonlinear, moving boundary, fluidstructure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The fluid flow is modeled by the timedependent Navier Stokes equations in a threedimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the twodimensional linearly elastic Koiter shell equations coupled to a onedimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Twoway coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many ap plications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary LagrangianEulerian approach, and a nontrivial extension of the AubinLionsSimon compactness result to problems on moving domains.
 Award ID(s):
 1853340
 Publication Date:
 NSFPAR ID:
 10148592
 Journal Name:
 Transactions of the American Mathematical Society
 ISSN:
 23300000
 Sponsoring Org:
 National Science Foundation
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