We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by 2D incompressible Navier-Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the 1D linearly elastic cylindrical Koiter shell model. The fluid and structure are fully coupled (2-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and balance of contact forces at the fluid-structure interface. We prove existence of weak solutions to the FSI problem as long as the cylinder radius is greater than zero.

The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced by Guidoboni, Canic et al. in 2009 (J of Comp. Phys) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk-Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.

This is a joint work with S. Canic.