Partitioned Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Nobile, Fabio; Vergara, Christian

doi:10.1007/s00032-012-0194-7

Cited by 75 publications

(128 citation statements)

References 43 publications

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“…In the partitioned case the successive solution of the fluid and solid subproblems in an iterative framework is carried out (see, e.g., [9,11,39,46,55,105,134]). In this case, the schemes feature in general poor convergence properties due to the added mass effect, that predicts a breakdown of performances when the values of the densities of fluid and structure are close as it happens in hemodynamics [10,39,69,76,137]. Alternatively, one could consider space-time finite elements, see, e.g., [17,187], or the iso-geometric analysis, see [15].…”

Section: Numerical Discretizationmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

169

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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Section: Numerical Discretizationmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

169

157

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“…If in the particular case = 0, it is known as the algebraic model. Nobile [37] proposed a generalised string model derived from a cylindrical configuration. Let…”

Section: The Structure Problemmentioning

confidence: 99%

“…Several suggestions had been made to overcome the stability issues. Nobile and Vergara [29] proposed Robin interface conditions to be enforced to solve fluid and structure subproblems. Burman and Fernández [28] proposed a stabilized explicit coupling for fluid structure interaction based on Nitsche's scheme.…”

Section: Partitionedmentioning

confidence: 99%

“…In addition, the implicit partitioned algorithms are also affected by the added mass effect in terms of convergence. Special treatment of the interface conditions needs to be considered [8,16,[28][29][30]. To date, it seems that only the monolithic and implicit schemes are applicable in blood flow simulation involving fluid structure interaction.…”

Section: Introductionmentioning

confidence: 99%

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Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

Tang

Amin

2014

Abstract and Applied Analysis

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Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.

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“…Researchers have conducted various studies on certain types of FSI problems (such as fluid-rigid body interaction [41,18,17,28,33], fluid with nonrotational structure [25,44,13,14,37,49], FSI with stationary fluid domain [20,51,52,50]). However, there is a dearth of practical models on the FSI problems involving a structure that rotates and deforms, i.e., an elastic rotor.…”

Section: Introductionmentioning

confidence: 99%

Modeling and simulations for fluid and rotating structure interactions

Yang

Sun

Wang

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure that is immersed and spinning in the fluid. We develop a linear constitutive model to describe the motion of a rotational elastic structure which is suitable for the application of arbitrary LagrangianEulerian (ALE) method in FSI simulation. Additionally, a novel ALE mapping method is designed to generate the moving fluid mesh while the deformable structure spins in a non-axisymmetric fluid channel. The structure velocity is adopted as the principle unknown to form a monolithic saddle-point system together with fluid velocity and pressure. We discretize the nonlinear saddle-point system with mixed finite element method and Newton's linearization, and prove that the derived saddle-point problem is well-posed. The developed methodology is applied to a self-defined elastic structure and a realistic hydroturbine under a prescribed angular velocity. Both illustrate the satisfactory numerical results of an elastic structure that is deforming and rotating while interacting with the fluid. The numerical validation is also conducted to demonstrate the modeling consistency.

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Partitioned Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Cited by 75 publications

References 43 publications

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

Modeling and simulations for fluid and rotating structure interactions

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