A three-dimensional computational analysis of fluid–structure interaction in the aortic valve

Hart, de J Jürgen; Peters, Gwm Gerrit; Schreurs, Pjg Piet; Baaijens, Fpt Frank

doi:10.1016/s0021-9290(02)00244-0

Cited by 329 publications

(284 citation statements)

References 14 publications

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“…Within the biomedical field, for example, the interaction of a viscous incompressible fluid, such as blood with a deformable membrane, as found within heart valves, arteries or veins represents an extraordinary challenge. Research within the biomedical field could influence many aspects of diagnosis and treatment as well as the design and implementation of components such as artificial heart valves, stents and many others [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

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SUMMARYThis paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluidstructure interaction. A partitioned time-marching algorithm is employed for the solution to the timedependent coupled discretized problem, thus enabling the use of highly developed, robust and well-tested solvers for each field. Coupling of the fields is achieved through a conservative transfer of information at the fluid-structure interface. An implicit coupling is achieved when the solutions to the fluid and structure subproblems are cycled at each time step until convergence is reached. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time-stepping technique with an explicit multistage Runga-Kutta time stepping in pseudo-time and arbitrary Lagrangian-Eulerian formulation for the moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a NewtonRaphson second-order optimization method. Various test cases are presented for benchmarking and to demonstrate the potential applications of this method.

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Section: Introductionmentioning

confidence: 99%

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Wood

Gil

Hassan

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…For example, models of fluid-structure interaction are of interest in many physiological applications [12,23,26,38]. Examples include the normal stress along arterial walls when assessing the risk of aneurysm rupture [12,11], and the flux through the boundary between a fluid and a porous media when modeling air flow in the lungs [27]. The problems considered here are a necessary step towards an a posteriori error analysis for more complicated multiphysics systems.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems

Asner¹,

Tavener

Kay

2012

SIAM J. Sci. Comput.

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Abstract. We consider time-dependent parabolic problems coupled across a common interface which we formulate using a Lagrange multiplier construction and solve by applying a monolithic solution technique. We derive an adjoint-based a posteriori error representation for a quantity of interest given by a linear functional of the solution. We establish the accuracy of our error representation formula through numerical experimentation and investigate the effect of error in the adjoint solution. Crucially, the error representation affords a distinction between temporal and spatial errors and can be used as a basis for a blockwise time-space refinement strategy. Numerical tests illustrate the efficacy of the refinement strategy by capturing the distinctive behavior of a localized traveling wave solution. The saddle point systems considered here are equivalent to those arising in the mortar finite element technique for parabolic problems. 1. Introduction. We consider an adjoint-based a posteriori error estimator for parabolic problems that are coupled across a given interface and construct an adaptive space-time finite element scheme. A posteriori error estimation is commonly used in parabolic problems for adaptive mesh refinement and the different approaches are described in a detailed review paper [1], as well as in [4,5,14,20,24,35,39,40,41]. In particular, [14,15,16] develop a technique based on solving an adjoint problem to estimate the error in a quantity of interest given by a functional of the solution as opposed to the error in a norm of the solution.Error estimation for coupled problems solved using operator decomposition techniques was considered in [17,18,9,8]. While operator decomposition is traditionally viewed as easy and inexpensive to implement [19,28], its convergence is rarely guaranteed. In this paper we take the alternative, monolithic approach to solving coupled parabolic problems, which do not suffer from this problem. We introduce a Lagrange multiplier (mortar element) space on the interface between the component domains, resulting in a large-scale complex system, which can nevertheless be solved efficiently with special treatment [33,22]. Moreover, the presence of the Lagrange multiplier variable allows us to derive error estimates for a quantity of interest that is supported along the interface. This is particularly useful in applications where the Lagrange

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“…Fluid structure interaction (FSI) problems occur in many different areas including aerodynamics ( [2], [4], [8]), acoustics ( [3], [7], [24]) and medicine ( [9], [12], [15], [14]). The specific FSI phenomenon called aerodynamic flutter is very dangerous and can cause accidents.…”

Section: Introductionmentioning

confidence: 99%

Fluid Structure Interaction Problems: The Necessity of a Well Posed, Stable and Accurate Formulation

Eriksson¹

2010

CICP

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Abstract. We investigate problems of fluid structure interaction type and aim for a formulation that leads to a well posed problem and a stable numerical procedure. Our first objective is to investigate if the generally accepted formulations of the fluid structure interaction problem are the only possible ones. Our second objective is to derive a stable numerical coupling. To accomplish that we will use a weak coupling procedure and employ summation-by-parts operators and penalty terms. We compare the weak coupling with other common procedures. We also study the effect of high order accurate schemes. In multiple dimensions this is a formidable task and we start by investigating the simplest possible model problem available. As a flow model we use the linearized Euler equations in one dimension and as the structure model we consider a spring.

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A three-dimensional computational analysis of fluid–structure interaction in the aortic valve

Cited by 329 publications

References 14 publications

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Adjoint-Based a Posteriori Error Estimation for Coupled Time-Dependent Systems

Fluid Structure Interaction Problems: The Necessity of a Well Posed, Stable and Accurate Formulation

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