Algorithms for strong coupling procedures

Matthies, Hermann G.; Niekamp, Rainer; Steindorf, Jan

doi:10.1016/j.cma.2004.11.032

Cited by 193 publications

(161 citation statements)

References 38 publications

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“…A second strategy considered so far consists in applying the Newton or the approximate-Newton method (the latter obtained by approximating the Jacobian) to the monolithic non-linear system (approximate-Newton-based algorithms). In [27], the author proposed a block-diagonal approximation of the Jacobian, leading to a partitioned algorithm where all the interface conditions and non-linearities are treated in the same loop (see also [36,28,33,13,48]). In [41], the authors considered alternative approximations of the Jacobian, leading to algorithms whose general structure consists in an external loop to manage the geometrical interface condition and the constitutive non-linearities and in an internal one to prescribe the physical interface conditions.…”

Section: Introductionmentioning

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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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%

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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“…Algorithms without coupling iterations [23] and Gauss-Seidel iterations [1, 24,25] are mostly unstable in the case of strong interaction between the flow and the structure. However, quasi-Newton iterations [26,27] or Newton-Krylov techniques [28,29] can be used to solve such FSI problems in a partitioned way, even with black-box solvers. The main advantage of monolithic simulations is the stability of the solution process, whereas the most important benefit of the partitioned approach is that existing, mature and optimized codes for the subproblems can be reused.…”

Section: Introductionmentioning

confidence: 99%

Partitioned simulation of the interaction between an elastic structure and free surface flow

Degroote

Souto-Iglesias

Paepegem

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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ARTICLE INFO ABSTRACT Keywords:Fluid-structure interaction Partitioned Free surface Volume-of-fluid Rolling tank Impact IQN-ILS Aitken relaxationCurrently, the interaction between free surface flow and an elastic structure is simulated with monolithic codes which calcúlate the deformation of the structure and the liquid-gas flow simultaneously. In this work, this interaction is calculated in a partitioned way with a sepárate flow solver and a sepárate structural solver using the interface quasi-Newton algorithm with approximation for the inverse of the Jacobian from a leastsquares model (IQN-ILS). The interaction between an elastic beam and a sloshing liquid in a rolling tank is calculated and the results agree well with experimental data. Subsequently, the impact of both a rigid cylinder and a flexible composite cylinder on a water surface is simulated to assess the effect of slamming on the components of certain wave-energy converters. The impact pressure on the bottom of the rigid cylinder is nearly twice as high as on the flexible cylinder, which emphasizes the need for fluid-structure interaction calculations in the design process of these wave-energy converters. For both the rolling tank simulations and the impact simulations, grid refinement is performed and the IQN-ILS algorithm requires the same number of iterations on each grid. The simulations on the coarse grid are also executed using Gauss-Seidel coupling iterations with Aitken relaxation which requires significantly more coupling iterations per time step.

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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%

“…The chosen order of iterations, corresponds to the Block-Gauß-Seidel algorithm for fluid-structure interaction problem [58]. Let us note that not only the value at synchronization points T n or T n+1 , but also the interpolated evolution of variables have to be exchanged in the entire time-interval t ∈ [T n , T n+1 ] when the time steps are not matching between fluid and structure sub-problems.…”

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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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Algorithms for strong coupling procedures

Cited by 193 publications

References 38 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

Partitioned simulation of the interaction between an elastic structure and free surface flow

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

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