A nonconforming finite element method for fluid–structure interaction problems

Swim, Edward; Seshaiyer, Padmanabhan

doi:10.1016/j.cma.2005.01.017

Cited by 28 publications

(25 citation statements)

References 17 publications

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“…The geometrical inexact schemes have been shown to be stable and accurate in haemodynamics [40,46,15,42,39,2,38,41]. It is moreover well accepted that also an inexact treatment of the fluid non-linearity is enough to recover accurate and stable solutions [15,6,41].…”

Section: Introductionmentioning

confidence: 99%

“…As discussed in the Introduction, in this work we want to extend the semi-implicit schemes [46,15,6,42,10] and, more generally, the geometrical inexact schemes [41] to the case of finite elasticity structure models. In particular, we want to introduce a family of inexact schemes such that, together with the geometrical interface condition and the fluid constitutive non-linearity, also the structure constitutive non-linearity is not treated exactly.…”

Section: Inexact Schemesmentioning

confidence: 99%

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Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Nobile

Pozzoli

Vergara

2014

Journal of Computational Physics

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In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant.

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Section: Introductionmentioning

confidence: 99%

Section: Inexact Schemesmentioning

confidence: 99%

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Nobile

Pozzoli

Vergara

2014

Journal of Computational Physics

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“…Although this method has low computational cost and it is accurate, for large deformations or movement of solid material, uid elements tend to become ill-shaped and the solution accuracy reduces. Some alternatives to the ALE method are the immersed boundary method [20,21], ctitious domain method [22], and the mortar nite element method [23]. In contrast to the ALE technique, other methods use xed uid meshes, and, hence, can simulate large deformation of solid material without mesh folding in the uid domain.…”

Section: Fluid-structure Coupling and Mesh Motionmentioning

confidence: 99%

Fluid–structure interaction analysis of a piezoelectric flexible plate in a cavity filled with a fluid

2016

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Abstract. This study presents a numerical analysis of uid-structure interaction, the structure of which is a exible piezoelectric material. Piezoelectric materials are widely used in aero-elasticity and turbomachinery elds for vibration, utter, and noise control. In this work, a FSI benchmark is revised to contain the piezoelectric materials. The in uence of piezoelectricity on the oscillation of the structure and uid ow is considered. For validation, two benchmark problems are solved and the results of the present code are compared with those of previous work. Current results show that the piezoelectric behavior of a plate signi cantly in uences the oscillation of the plate and the uid ow properties.

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“…Copyright © SIAM Unauthorized reproduction of this article is prohibited Note that together eqs (17) and (18) can be thought of as the standard wave equation. What we are really interested in the movement of the wall, which is the same as the movement of the fluid at the point x = 0.…”

Section: 1mentioning

confidence: 99%

“…Fluid structure interaction models can be used to gain insight into a number of different applications, such as the interaction between airflow and wings of microair vehicles and blood pressure interaction with arterial walls [5,1,18]. This paper focuses on modeling an intracranial saccular aneurysm, which is a focal dilatation of an arterial wall within the brain.…”

Section: Introductionmentioning

confidence: 99%

Modeling, Analysis and Computation of Fluid Structure Interaction Models for Biological Systems

Venuti¹

2010

SIURO

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A mathematical modeling for the interaction of blood flow with the arterial wall surrounded by cerebral spinal fluid is developed. The blood pressure acting on the inner arterial wall is modeled using a Fourier Series, the arterial wall is modeled using a spring-mass system, and the surrounding cerebral spinal fluid is modeled via a simplified Navier-Stokes equation. The resulting coupled system of partial differential equations for this fluid structure interaction with appropriate boundary conditions are solved first analytically using Laplace Transform and then numerically using an implicit finite difference scheme. The solutions are also investigated using computational tools. An application of the model studied to intracranial saccular aneurysms is also presented.

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A nonconforming finite element method for fluid–structure interaction problems

Cited by 28 publications

References 17 publications

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Inexact accurate partitioned algorithms for fluid–structure interaction problems with finite elasticity in haemodynamics

Fluid–structure interaction analysis of a piezoelectric flexible plate in a cavity filled with a fluid

Modeling, Analysis and Computation of Fluid Structure Interaction Models for Biological Systems

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