Communications in Information and Systems

Volume 13 (2013)

Number 3

Special Issue in Honor of Marshall Slemrod: Part 3 of 4

A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof

Pages: 357 – 397



Boris Muha (Department of Mathematics, University of Zagreb, Croatia)

Sunčica Čanić (Department of Mathematics, University of Houston, Texas, U.S.A.)


We study a 3D fluid-structure interaction (FSI) problem between an incompressible, viscous fluid modeled by the Navier-Stokes equations, and the motion of an elastic structure, modeled by the linearly elastic cylindrical Koiter shell equations, allowing structure displacements that are not necessarily radially symmetric. The problem is set on a cylindrical domain in 3D, and is driven by the time-dependent inlet and outlet dynamic pressure data. The coupling between the fluid and the structure is fully nonlinear (2-way coupling), giving rise to a nonlinear, moving-boundary problem in 3D. We prove the existence of a weak solution to this 3D FSI problem by using an operator splitting approach in combination with the Arbitrary Lagrangian Eulerian mapping, which satisfies a geometric conservation law property. We effectively prove that the resulting computational scheme converges to a weak solution of the full, nonlinear 3D FSI problem.


fluid-structure interaction, nonlinear movingboundary problem, existence of a solution

2010 Mathematics Subject Classification

35M33, 35R37

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