6,188 research outputs found
Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement
We present a new model and a novel loosely coupled partitioned numerical
scheme modeling fluid-structure interaction (FSI) in blood flow allowing
non-zero longitudinal displacement. Arterial walls are modeled by a {linearly
viscoelastic, cylindrical Koiter shell model capturing both radial and
longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes
equations for an incompressible, viscous fluid. The two are fully coupled via
kinematic and dynamic coupling conditions. Our numerical scheme is based on a
new modified Lie operator splitting that decouples the fluid and structure
sub-problems in a way that leads to a loosely coupled scheme which is
{unconditionally} stable. This was achieved by a clever use of the kinematic
coupling condition at the fluid and structure sub-problems, leading to an
implicit coupling between the fluid and structure velocities. The proposed
scheme is a modification of the recently introduced "kinematically coupled
scheme" for which the newly proposed modified Lie splitting significantly
increases the accuracy. The performance and accuracy of the scheme were studied
on a couple of instructive examples including a comparison with a monolithic
scheme. It was shown that the accuracy of our scheme was comparable to that of
the monolithic scheme, while our scheme retains all the main advantages of
partitioned schemes, such as modularity, simple implementation, and low
computational costs
Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach
We develop a computational model to study the interaction of a fluid with a
poroelastic material. The coupling of Stokes and Biot equations represents a
prototype problem for these phenomena, which feature multiple facets. On one
hand it shares common traits with fluid-structure interaction. On the other
hand it resembles the Stokes-Darcy coupling. For these reasons, the numerical
simulation of the Stokes-Biot coupled system is a challenging task. The need of
large memory storage and the difficulty to characterize appropriate solvers and
related preconditioners are typical shortcomings of classical discretization
methods applied to this problem. The application of loosely coupled time
advancing schemes mitigates these issues because it allows to solve each
equation of the system independently with respect to the others. In this work
we develop and thoroughly analyze a loosely coupled scheme for Stokes-Biot
equations. The scheme is based on Nitsche's method for enforcing interface
conditions. Once the interface operators corresponding to the interface
conditions have been defined, time lagging allows us to build up a loosely
coupled scheme with good stability properties. The stability of the scheme is
guaranteed provided that appropriate stabilization operators are introduced
into the variational formulation of each subproblem. The error of the resulting
method is also analyzed, showing that splitting the equations pollutes the
optimal approximation properties of the underlying discretization schemes. In
order to restore good approximation properties, while maintaining the
computational efficiency of the loosely coupled approach, we consider the
application of the loosely coupled scheme as a preconditioner for the
monolithic approach. Both theoretical insight and numerical results confirm
that this is a promising way to develop efficient solvers for the problem at
hand
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