Abstract |
We discuss the numerical approximation of fluid-structure interaction (FSI)
problems with a particular concern on two hemodynamics applications. For
the first application, blood is modeled as an incompressible fluid and it
interacts with an elastic wall containing a geometric orifice which mimics
a leaky mitral valve. The goal is to simulate hemodynamics conditions
encountered in patients with mitral regurgitation in order to show
strengths and limitations of echocardiographic methods to assess the
severity of the pathology. To solve the coupled problem, we propose a
monolithic approach which consists in preconditioning the linear system
obtained after the space-time discretization and linearization of the FSI
problem with a suitable diagonal scaling combined with an ILU
preconditioner. For the second application, this algorithm is extend to
allow the presence of structures with different mechanical properties with
the aim of testing different configurations for the Left Ventricle Assist
Device aortic anastomosis. In the proposed method, fluid-structure and
structure-structure interactions are treated in the same way.
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