1,864 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
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
Computational methods in cardiovascular mechanics
The introduction of computational models in cardiovascular sciences has been
progressively bringing new and unique tools for the investigation of the
physiopathology. Together with the dramatic improvement of imaging and
measuring devices on one side, and of computational architectures on the other
one, mathematical and numerical models have provided a new, clearly
noninvasive, approach for understanding not only basic mechanisms but also
patient-specific conditions, and for supporting the design and the development
of new therapeutic options. The terminology in silico is, nowadays, commonly
accepted for indicating this new source of knowledge added to traditional in
vitro and in vivo investigations. The advantages of in silico methodologies are
basically the low cost in terms of infrastructures and facilities, the reduced
invasiveness and, in general, the intrinsic predictive capabilities based on
the use of mathematical models. The disadvantages are generally identified in
the distance between the real cases and their virtual counterpart required by
the conceptual modeling that can be detrimental for the reliability of
numerical simulations.Comment: 54 pages, Book Chapte
Computational Issues for Optimal Shape Design in Hemodynamics
A Fluid-Structure Interaction model is studied for aortic flow, based on Koiter's shell model for the structure, Navier-Stokes equation for the fluid and transpiration for the coupling. It accounts for wall deformation while yet working on a fixed geometry. The model is established first. Then a numerical approximation is proposed and some tests are given. The model is also used for optimal design of a stent and possible recovery of the arterial wall elastic coefficients by inverse methods
Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows
Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters
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