On the temporal stability and accuracy of coupled problems with reference to fluid–structure interaction

Joosten, M. M.; Dettmer, Wulf G.; Perić, D.

doi:10.1002/fld.2333

Cited by 20 publications

(25 citation statements)

References 23 publications

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“…Remark 2 A similar problem involving a mass-spring system coupled to a mass-dashpot system was considered in [15,24]. The main difference is the lack of a dissipative term in (8) which will be added in the following subsection.…”

Section: Remarkmentioning

confidence: 95%

“…membrane-wind interaction [43]). Nevertheless, the harmonic oscillator is also useful for the design of staggered procedures as has already been demonstrated in [15] and for determining the stability and accuracy of different time discretizations in the fluid and structure subproblems [24]. We further restrict our investigation to string or membrane structures, but its application to beam or shell structures is straightforward.…”

Section: Introductionmentioning

confidence: 94%

“…Most importantly, the model includes the essential geometrical and physical parameters which contribute to the added-mass effect for thin and lightweight structures: the fluid and structure densities, the structure length and the structure thickness. Under appropriate boundary and initial conditions, the inviscid problem reduces to a simple harmonic oscillator similar to the abstract models in [15,23,24]. We restrict our current study to strongly coupled procedures based on a Dirichlet-Neumann decomposition and a single time discretization for the fluid and structure subproblems.…”

Section: Introductionmentioning

confidence: 98%

“…In this contribution, we propose and analyze a new model problem which attempts to unify previous works in [3] and [15,23,24] while allowing for a rigorous quantitative comparison. In a similar spirit as the model analyzed in [3], we select a simplified model which allows for detailed mathematical and numerical analyses.…”

Section: Introductionmentioning

confidence: 98%

“…The analysis produced simple algebraic expressions predicting the onset of numerical instabilities which were confirmed by numerical experiments. In [23,24], abstract FSI models consisting of linear mass-spring-dashpot systems were used to investigate partitioned algorithms. The linear mass-spring-dashpot system was later used in [15] for the design of a new staggered scheme applied to real FSI problems including convective flows and large interface deformations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A complementary study of analytical and computational fluid-structure interaction

2014

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This paper introduces new initial value problems for the design and analysis of fluid-structure interaction algorithms. The problems are constructed from a finite number of sinusoidal perturbations of thin structures superposed on incompressible fluids. Explicit analytical solutions are provided for rigorous quantitative comparisons including viscous effects. The equation governing a single inviscid mode is split into fluid and structure subproblems and numerical parameters are derived for several partitioned algorithms based on a Dirichlet-Neumann decomposition and a second-order backward difference time discretization. Numerical experiments are performed using a stabilized fractional-step finite element method for the fluid and membrane finite elements for the structure. The convergence behaviour of the finite element solutions to the analytical solutions is demonstrated. Finally, the stability and performance of the numerical parameters derived from a single inviscid mode are presented for more general problems including multiple modes and viscous effects.

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Section: Remarkmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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A complementary study of analytical and computational fluid-structure interaction

2014

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A new staggered scheme for fluid–structure interaction

Dettmer

Perić

2012

Numerical Meth Engineering

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SUMMARY Staggered solution procedures represent the most elementary computational strategy for the simulation of fluid–structure interaction problems. They usually consist of a predictor followed by the separate execution of each subdomain solver. Although it is generally possible to maintain the desired order of accuracy of the time integration, it is difficult to guarantee the stability of the overall computation. In the context of large solid over fluid mass ratios, compressible flows and explicit subsolvers, substantial development has been carried out by Felippa, Park, Farhat, Löhner and others. In this work, a new staggered scheme is presented. It is shown that, for a linear model problem, the scheme is second‐order accurate and unconditionally stable. The dependency of the leading truncation error on the solid over fluid mass ratio is investigated. The strategy is applied to two‐dimensional and three‐dimensional fluid–structure interaction problems. It is shown that the conclusions derived from the investigation of the model problem apply. The new strategy extends the applicability of staggered schemes to problems involving relatively small solid over fluid mass ratios and incompressible fluid flow. It is suggested that the proposed scheme has the same range of applicability as the Dirichlet–Neumann or block Gauß–Seidel type strategies. Copyright © 2012 John Wiley & Sons, Ltd.

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New iterative and staggered solution schemes for incompressible fluid‐structure interaction based on Dirichlet‐Neumann coupling

Dettmer

Lovrić

Kadapa

et al. 2020

Numerical Meth Engineering

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In the presence of strong added mass effects, partitioned solution strategies for incompressible fluid-structure interaction are known to lack robustness and computational efficiency. A number of strategies have been proposed to address this challenge. However, these strategies are often complicated or restricted to certain problem classes and generally require intrusive modifications of existing software. In this work, the well-known Dirichlet-Neumann coupling is revisited and a new combined two-field relaxation strategy is proposed. A family of efficient staggered schemes based crucially on a force predictor is formulated alongside the classical iterative approach. Both methodologies are rigorously analyzed on the basis of a linear model problem derived from a simplified fluid-conveying elastic tube. The investigation suggests that both the robustness and the efficiency of a partitioned Dirichlet-Neumann coupling scheme can be improved by a relatively small nonintrusive modification of a standard implementation. The relevance of the model problem analysis for finite element-based computational fluid-structure interaction is demonstrated in detail for a submerged cylinder subject to an external force.

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On the temporal stability and accuracy of coupled problems with reference to fluid–structure interaction

Cited by 20 publications

References 23 publications

A complementary study of analytical and computational fluid-structure interaction

A complementary study of analytical and computational fluid-structure interaction

A new staggered scheme for fluid–structure interaction

New iterative and staggered solution schemes for incompressible fluid‐structure interaction based on Dirichlet‐Neumann coupling

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