Zeitschrift für angewandte Mathematik und Physik | 2019

Analysis of a linear 3D fluid–mesh–shell interaction problem



We study a linear fluid–structure interaction problem between an incompressible, viscous 3D fluid flow, a 2D linearly elastic Koiter shell, and an elastic 1D net of curved rods. This problem is motivated by studying fluid–structure interaction between blood flow through coronary arteries treated with metallic mesh-like devices called stents. The flow is assumed to be laminar, modeled by the time-dependent Stokes equations, and the structure displacement is assumed to be small, modeled by a system of linear Koiter shell equations allowing displacement in all three spatial directions. The fluid and the mesh-supported structure are coupled via the kinematic and dynamic coupling conditions describing continuity of velocity and balance of contact forces. The coupling conditions are evaluated along a linearized fluid–structure interface, which coincides with the fixed fluid domain boundary. No smallness on the structure velocity is assumed. We prove the existence of a weak solution to this linear fluid–composite structure interaction problem. This is the first result in the area of fluid–structure interaction that includes a 1D elastic mesh and takes into account structural displacements in all three spatial directions. Numerical simulations based on the finite element discretization of the coupled FSI problem are presented.

Volume 70
Pages 1-38
DOI 10.1007/S00033-019-1087-1
Language English
Journal Zeitschrift für angewandte Mathematik und Physik

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