Domain decomposition based Newton methods for fluid-structure interaction problems

Fernández, Miguel Ángel; Gerbeau, Jean-Frédéric; Gloria, Antoine; Vidrascu, Marina

doi:10.1051/proc:072206

Cited by 5 publications

(5 citation statements)

References 33 publications

(48 reference statements)

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“…Therefore, an iterative scheme has to be defined to compute the solution of the coupled problem. To that end, one can use any of the formulation in (5), (6) or (7) and corresponding iterative schemes, such as: (i) the one in (6) with Picard like iterative schemes [47,67]; (ii) the one in (7) with Newton [26,50] or quasi-Newton [16,31,64] iterations; (iii) the one in (5) with nonlinear Richardson strategy [18,25].…”

Section: Discrete Force Motion Transfer: Explicit Versus Implicit Schmentioning

confidence: 99%

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Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

et al. 2010

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In this work we consider the fluid-structure interaction in fully nonlinear setting, where different space discretization can be used. The model problem considers finite elements for structure and finite volume for fluid. The computations for such interaction problem are performed by implicit schemes, and the partitioned algorithm separating fluid from structural iterations. The formal proof is given to find the condition for convergence of this iterative procedure in the fully nonlinear setting. Several validation examples are shown to confirm the proposed convergence criteria of partitioned algorithm. The proposed strategy provides a very suitable basics for code-coupling implementation as discussed in Part II.

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Section: Discrete Force Motion Transfer: Explicit Versus Implicit Schmentioning

confidence: 99%

“…Displacements at the fluid-structure interaction interface at the middle and the quarter lengths: u(0.5, 0) and u(0 25,. 0) …”

mentioning

confidence: 99%

Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

et al. 2010

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“…For coupled fluid-structure interaction problems, the monolithic [38,65,20] and partitioned strategy [24,53,59,11,27,58,18,31,26,77] can be used. The monolithic approach is abandoned in favor of the partitioned approach.…”

Section: Introductionmentioning

confidence: 99%

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

Kassiotis

Ibrahimbegović

Matthies

2010

European Journal of Mechanics - B/Fluids

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In this work we discuss a way to compute the impact of free-surface flow on nonlinear structures. The approach chosen rely on a partitioned strategy that allows to solve strongly coupled fluid-structure interaction problem. It is then possible to re-use existing and validated strategy for each sub-problem. The structure is formulated in a Lagrangian way and solved by the finite element method. The free-surface flow approach considers a Volume-Of-Fluid (VOF) strategy formulated in an Arbitrary Lagrangian-Eulerian (ALE) framework, and the finite volume are used to discrete and solve this problem. The software coupling is ensured in an efficient way using the Communication Template Library (CTL). Numerical examples presented herein concern 2D validations case but also 3D problems with a large number of equations to be solved.

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“…Whereas in the algorithms in the nonlinear Steklov–Poincaré operators are linearized, in Fernandez et al . , the Schur complements are computed after linearization. The approach is also based on the Steklov–Poincaré operator on the interface.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of fluid–structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains

Balzani

Deparis

Fausten

et al. 2015

Numer Methods Biomed Eng

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The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd.

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Domain decomposition based Newton methods for fluid-structure interaction problems

Cited by 5 publications

References 33 publications

Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

Nonlinear fluid–structure interaction problem. Part I: implicit partitioned algorithm, nonlinear stability proof and validation examples

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

Numerical modeling of fluid–structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains

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