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On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations. (English) Zbl 1139.92009
Summary: We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluid-structure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non-standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the coupling of the models. With this we derive an energy estimate for the fully 3D-1D FSI coupling. We consider several possible models for the mechanics of the vessel wall in the 3D problem and show how the 3D-1D coupling depends on them. Several comparative numerical tests illustrating the coupling are presented.

MSC:
92C35Physiological flows
65M12Stability and convergence of numerical methods (IVP of PDE)
76D05Navier-Stokes equations (fluid dynamics)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
74F10Fluid-solid interactions
76Z05Physiological flows
35L20Second order hyperbolic equations, boundary value problems
35L15Second order hyperbolic equations, initial value problems
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References:
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