Abstract: In this work, the hemodynamics in the sinuses of
Valsalva after Transcatheter Aortic Valve Implantation is numerically
examined. We focus on the physical results in the two-dimensional
case. We use a finite element methodology based on a Lagrange
multiplier technique that enables to couple the dynamics of blood
flow and the leaflets’ movement. A massively parallel implementation
of a monolithic and fully implicit solver allows more accuracy and
significant computational savings. The elastic properties of the aortic
valve are disregarded, and the numerical computations are performed
under physiologically correct pressure loads. Computational results
depict that blood flow may be subject to stagnation in the lower
domain of the sinuses of Valsalva after Transcatheter Aortic Valve
Implantation.
Abstract: We present in this paper a fully implicit finite element
method tailored for the numerical modeling of inextensible fluidic
membranes in a surrounding Newtonian fluid. We consider a highly
simplified version of the Canham-Helfrich model for phospholipid
membranes, in which the bending force and spontaneous curvature
are disregarded. The coupled problem is formulated in a fully
Eulerian framework and the membrane motion is tracked using
the level set method. The resulting nonlinear problem is solved
by a Newton-Raphson strategy, featuring a quadratic convergence
behavior. A monolithic solver is implemented, and we report several
numerical experiments aimed at model validation and illustrating
the accuracy of the proposed method. We show that stability is
maintained for significantly larger time steps with respect to an
explicit decoupling method.
Abstract: This paper is concerned with the development of a
fully implicit and purely Eulerian fluid-structure interaction method
tailored for the modeling of the large deformations of elastic
membranes in a surrounding Newtonian fluid. We consider a
simplified model for the mechanical properties of the membrane, in
which the surface strain energy depends on the membrane stretching.
The fully Eulerian description is based on the advection of a modified
surface tension tensor, and the deformations of the membrane are
tracked using a level set strategy. The resulting nonlinear problem
is solved by a Newton-Raphson method, featuring a quadratic
convergence behavior. A monolithic solver is implemented, and we
report several numerical experiments aimed at model validation and
illustrating the accuracy of the presented method. We show that
stability is maintained for significantly larger time steps.