Computation of Stokes Flow in a Channel with a Collapsible Segment

Lowe, Tim; Pedley, T. J.

doi:10.1006/jfls.1995.1050

Cited by 39 publications

(29 citation statements)

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“…We do not include the stabilization techniques used in the original DSD=ST method, since the main focus of the current study is on devising a numerical scheme to study the fluid-membrane interaction and problems thus considered are generally not convection-dominated flows. Similar studies for the steady state fluid-membrane interaction employing the finite element method 40,41 and finite volume method 42 have been reported recently.…”

Section: Introductionmentioning

confidence: 82%

Finite element computations for unsteady fluid and elastic membrane interaction problems

Liang

Neitzel

Aidun³

1997

Int. J. Numer. Meth. Fluids

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Section: Introductionmentioning

confidence: 82%

Finite element computations for unsteady fluid and elastic membrane interaction problems

Liang

Neitzel

Aidun³

1997

Int. J. Numer. Meth. Fluids

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“…The uid domain was discretized using a mesh of 70 by 5 mixed 9=3 velocity=pressure (Q 2 −P 1 ) elements [16], whereas the structure was discretized employing 25 by 2 displacement-based 9-node elements. This kind of model is used to qualitatively describe the ow of blood inside blood vessels, see for example References [20][21][22]. A similar uid-structure interaction model, in which the system behaviour is not chaotic, was also studied by the authors in References [17,23,24].…”

Section: Collapsible Channel Modelmentioning

confidence: 99%

An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems

Rugonyi

Bathe

2002

Numerical Meth Engineering

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SUMMARYA procedure to calculate the Lyapunov characteristic exponent of the response of structural continuous systems, discretized using ÿnite element methods, is proposed. The Lyapunov characteristic exponent can be used to characterize the asymptotic stability of the system dynamic response, and it is frequently employed to identify a chaotic behaviour. The proposed procedure can also be used in the stability characterization of uid-structure interaction systems in which the focus of the analysis is on the behaviour of the structural part.

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“…Indeed, some of these one-dimensional models are extremely useful in explaining some system mechanisms (Stewart et al 2010;Stewart 2017). A more rational two-dimensional fluid-membrane model was developed by Pedley and coworkers, in which the collapsible tube is represented by a channel with part of the upper wall replaced by a thin and inextensible membrane (Pedley and Luo 1998;Lowe and Pedley 1995;Pedley 1996, 2000). To reflect the fact that physiological vascular walls often experience elastic stretching and bending, Cai and Luo proposed a fluid-beam model and incorporated bending and extensional stiffness into a geometrically nonlinear Lagrangian representation of the wall (Cai and Luo 2003).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional flows in a hyperelastic vessel under external pressure

Zhang

Luo

Cai

2018

Biomech Model Mechanobiol

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We study the collapsible behaviour of a vessel conveying viscous flows subject to external pressure, a scenario that could occur in many physiological applications. The vessel is modelled as a three-dimensional cylindrical tube of nonlinear hyperelastic material. To solve the fully coupled fluid-structure interaction, we have developed a novel approach based on the Arbitrary Lagrangian-Eulerian (ALE) method and the frontal solver. The method of rotating spines is used to enable an automatic mesh adaptation. The numerical code is verified extensively with published results and those obtained using the commercial packages in simpler cases, e.g. ANSYS for the structure with the prescribed flow, and FLUENT for the fluid flow with prescribed structure deformation. We examine three different hyperelastic material models for the tube for the first time in this context and show that at the small strain, all three material models give similar results. However, for the large strain, results differ depending on the material model used. We further study the behaviour of the tube under a mode-3 buckling and reveal its complex flow patterns under various external pressures. To understand these flow patterns, we show how energy dissipation is associated with the boundary layers created at the narrowest collapsed section of the tube, and how the transverse flow forms a virtual sink to feed a strong axial jet. We found that the energy dissipation associated with the recirculation does not coincide with the flow separation zone itself, but overlaps with the streamlines that divide the three recirculation zones. Finally, we examine the bifurcation diagrams for both mode-3 and mode-2 collapses and reveal that multiple solutions exist for a range of the Reynolds number. Our work is a step towards modelling more realistic physiological flows in collapsible arteries and veins.

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Computation of Stokes Flow in a Channel with a Collapsible Segment

Cited by 39 publications

References 0 publications

Finite element computations for unsteady fluid and elastic membrane interaction problems

Finite element computations for unsteady fluid and elastic membrane interaction problems

An evaluation of the Lyapunov characteristic exponent of chaotic continuous systems

Three-dimensional flows in a hyperelastic vessel under external pressure

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