Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations

Zuijlen, A.H. van; Bijl, H.

doi:10.1016/j.compstruc.2004.06.003

Cited by 49 publications

(32 citation statements)

References 17 publications

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“…If both solvers are second-order accurate in time and the flow solver satisfies the geometric conservation law, this ISS scheme is also second-order accurate in time. Higher-order time accuracy was studied by van Zuijlen and Bijl [207]. They integrate the flow equations and the structural equations in time with an implicit Runge-Kutta scheme, except for the coupling terms, which are integrated in time with an explicit Runge-Kutta scheme of the same order.…”

Section: Explicit Couplingmentioning

confidence: 99%

Partitioned Simulation of Fluid-Structure Interaction

Degroote¹

2013

Arch Computat Methods Eng

123

107

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In this review article, the focus is on partitioned simulation techniques for strongly coupled fluid-structure interaction problems, especially on techniques which use at least one of the solvers as a black box. First, a number of analyses are reviewed to explain why Gauss-Seidel coupling iterations converge slowly or not at all for fluid-structure interaction problems with strong coupling. This provides the theoretical basis for the fast convergence of quasi-Newton and multi-level techniques. Second, several partitioned techniques that couple two black-box solvers are compared with respect to implementation and performance. Furthermore, performance comparisons between partitioned and monolithic techniques are examined. Subsequently, two similar techniques to couple a black-box solver with an accessible solver are analyzed. In addition, several other techniques for fluid-structure interaction simulations are studied and various methods to take into account deforming fluid domains are discussed.

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Section: Explicit Couplingmentioning

confidence: 99%

Partitioned Simulation of Fluid-Structure Interaction

Degroote¹

2013

Arch Computat Methods Eng

123

107

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“…see [1,31]. The fluid equations will then be discretized by a finite volume method based on the cell means of the conservative variables and cell volume, i.e.,…”

Section: Application Of Mgark To Coupled Problems Of Fluid-structure mentioning

confidence: 99%

“…Similar to [1,2], we investigate the application of partitioned Runge-Kutta methods to fluid-structure interaction. Hence, this work fits into the category of loosely coupled partitioned schemes as no iterative methods are used for the coupling procedure itself.…”

Section: Introductionmentioning

confidence: 99%

“…For example in [1], an implicit-explicit (IMEX) approach based on partitioned Runge-Kutta schemes allows for explicit coupling of the two physical fields, whereas the same implicit scheme for fluid and structure equations is used. A similar IMEX procedure is used in [2].…”

Section: Introductionmentioning

confidence: 99%

“…Hence, this work fits into the category of loosely coupled partitioned schemes as no iterative methods are used for the coupling procedure itself. Nonetheless, as for the IMEX-Runge-Kutta approach in [1,2], the subsolvers are coupled at the level of interior Runge-Kutta stages in addition to the time levels corresponding to the chosen time step sizes. Furthermore, we combine the IMEX approach with the concept of multirate schemes which allows for different time step sizes of the subsolvers, corresponding to the subcycling strategy in [3,4].…”

Section: Introductionmentioning

confidence: 99%

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On Multirate GARK Schemes with Adaptive Micro Step Sizes for Fluid–Structure Interaction: Order Conditions and Preservation of the Geometric Conservation Law

Bremicker-Trübelhorn

Ortleb

2017

Aerospace

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Abstract:The application of partitioned schemes to fluid-structure interaction (FSI) allows the use of already developed solvers specifically designed for the efficient solution of the corresponding subproblems. In this work, we propose and describe a loosely coupled partitioned scheme based on the recently introduced generalized-structure additively partitioned Runge-Kutta (GARK) framework. The resulting scheme combines implicit-explicit (IMEX) and multirate approaches while coupling of the subproblems is realized both on the level of the discrete time steps and at the level of interior Runge-Kutta stages. Specifically, we allow for varying micro step sizes for the fluid subproblem and therefore extend the multirate GARK framework based on constant micro steps. Furthermore, we derive the order conditions for this extension allowing for coupled time integration schemes of up to third order and discuss specific choices of the Runge-Kutta coefficients complying with the geometric conservation law. Finally, numerical experiments are carried out for uniform flow on a moving grid as well as the classical FSI test case of a moving piston.

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High‐order implicit Runge–Kutta time integrators for fluid‐structure interactions

Cori

Étienne

Garon

et al. 2015

Numerical Methods in Fluids

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SummaryThis paper presents an approach to develop high‐order, temporally accurate, finite element approximations of fluid‐structure interaction (FSI) problems. The proposed numerical method uses an implicit monolithic formulation in which the same implicit Runge–Kutta (IRK) temporal integrator is used for the incompressible flow, the structural equations undergoing large displacements, and the coupling terms at the fluid‐solid interface. In this context of stiff interaction problems, the fully implicit one‐step approach presented is an original alternative to traditional multistep or explicit one‐step finite element approaches. The numerical scheme takes advantage of an arbitrary Lagrangian–Eulerian formulation of the equations designed to satisfy the geometric conservation law and to guarantee that the high‐order temporal accuracy of the IRK time integrators observed on fixed meshes is preserved on arbitrary Lagrangian–Eulerian deforming meshes. A thorough review of the literature reveals that in most previous works, high‐order time accuracy (higher than second order) is seldom achieved for FSI problems. We present thorough time‐step refinement studies for a rigid oscillating‐airfoil on deforming meshes to confirm the time accuracy on the extracted aerodynamics reactions of IRK time integrators up to fifth order. Efficiency of the proposed approach is then tested on a stiff FSI problem of flow‐induced vibrations of a flexible strip. The time‐step refinement studies indicate the following: stability of the proposed approach is always observed even with large time step and spurious oscillations on the structure are avoided without added damping. While higher order IRK schemes require more memory than classical schemes (implicit Euler), they are faster for a given level of temporal accuracy in two dimensions. Copyright © 2015 John Wiley & Sons, Ltd.

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Implicit and explicit higher order time integration schemes for structural dynamics and fluid-structure interaction computations

Cited by 49 publications

References 17 publications

Partitioned Simulation of Fluid-Structure Interaction

Partitioned Simulation of Fluid-Structure Interaction

On Multirate GARK Schemes with Adaptive Micro Step Sizes for Fluid–Structure Interaction: Order Conditions and Preservation of the Geometric Conservation Law

High‐order implicit Runge–Kutta time integrators for fluid‐structure interactions

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